ℹ️ Skipped - page is already crawled
| Filter | Status | Condition | Details |
|---|---|---|---|
| HTTP status | PASS | download_http_code = 200 | HTTP 200 |
| Age cutoff | PASS | download_stamp > now() - 6 MONTH | 1 months ago |
| History drop | PASS | isNull(history_drop_reason) | No drop reason |
| Spam/ban | PASS | fh_dont_index != 1 AND ml_spam_score = 0 | ml_spam_score=0 |
| Canonical | PASS | meta_canonical IS NULL OR = '' OR = src_unparsed | Not set |
| Property | Value | ||||||
|---|---|---|---|---|---|---|---|
| URL | https://www.pearson.com/channels/physics/learn/patrick/periodic-motion-new/spring-force-hookes-law | ||||||
| Last Crawled | 2026-03-23 18:10:09 (1 month ago) | ||||||
| First Indexed | 2022-08-03 13:18:36 (3 years ago) | ||||||
| HTTP Status Code | 200 | ||||||
| Content | |||||||
| Meta Title | Spring Force (Hooke's Law) Explained: Definition, Examples, Practice & Video Lessons | ||||||
| Meta Description | Master Spring Force (Hooke's Law) with free video lessons, step-by-step explanations, practice problems, examples, and FAQs. Learn from expert tutors and get exam-ready! | ||||||
| Meta Canonical | null | ||||||
| Boilerpipe Text | 17. Periodic Motion
Spring Force (Hooke's Law): Videos & Practice Problems
Topic summary
When a
force
is applied to a spring, it compresses or stretches, demonstrating Hooke's
Law
, which states that the spring force (F
s
) is equal to the negative of the applied force (F
a
), or F=-kx, where k is the spring constant and x is the deformation. The spring force acts as a restoring force, always opposing the deformation. Understanding these principles is crucial for analyzing mass-spring systems and their motion.
1
concept
Video duration:
5m
Spring Force (Hooke's Law) Video Summary
When interacting with a spring, the forces at play can be understood through the concept of action and reaction pairs. When you apply a force to compress or extend a spring, the spring exerts an equal but opposite force back on you. This relationship is described by Hooke's Law, which states that the spring force (\(F_s\)) is equal to the negative of the applied force (\(F_a\)), mathematically represented as:
\(F_s = -F_a = -k \cdot x\)
In this equation, \(k\) is the spring constant, a measure of the spring's stiffness, and \(x\) represents the deformation of the spring from its equilibrium position. The negative sign indicates that the spring force acts in the opposite direction to the applied force. However, when calculating magnitudes, the negative sign can be omitted, leading to the simplified equation:
\(|F_s| = k \cdot |x|\
To illustrate this, consider an example where an applied force of 120 N compresses a spring with a spring constant \(k\) of 20 N/m. Setting up the equation:
\(120 = 20 \cdot x\
Solving for \(x\) gives:
\(x = \frac{120}{20} = 6 \text{ meters}\
This indicates that the spring compresses by 6 meters from its relaxed position, also known as the equilibrium position, where \(x = 0\).
In another scenario, if you pull on a spring, the same principles apply. Suppose the spring constant \(k\) is now 40 N/m, and the spring is initially 10 meters long but is pulled to 16 meters. The deformation \(x\) is the difference in length:
\(x = 16 - 10 = 6 \text{ meters}\
Using Hooke's Law again:
\(F_s = k \cdot x = 40 \cdot 6 = 240 \text{ N}\
This demonstrates that increasing the spring constant results in a greater restoring force for the same deformation. The units for the spring constant \(k\) are expressed in newtons per meter (N/m), indicating the force required to deform the spring by one meter.
In summary, the spring force acts as a restoring force, always opposing the applied force and striving to return the system to its equilibrium position. Understanding these relationships is crucial for applying Hooke's Law effectively in various physical scenarios.
Study Smarter with Worksheets.
Follow along with each video using our printable worksheets
2
Problem
A 1.0 m-long spring is laid horizontally with one of its ends fixed. When you pull on it with 50 N, it stretches to 1.2 m. (a) What is the spring's force constant (b) How much force is needed to compress it to 0.7 m?
A
250 N/m; 175 N
B
50 N/m; 15 N
C
250 N/m; 75 N
D
50 N/m; 35 N
3
concept
Acceleration of Mass-Spring Systems
Video duration:
3m
Acceleration of Mass-Spring Systems Video Summary
When a mass is attached to a spring, it forms a mass-spring system, where the spring exerts a force in response to an applied force. The spring force, denoted as \( F_s \), acts in the opposite direction of the applied force \( F_A \). This relationship can be expressed mathematically as:
\( F_s = -F_A = -k \cdot x \)
Here, \( k \) represents the spring constant, and \( x \) is the displacement from the equilibrium position. The negative sign indicates that the spring force opposes the direction of the applied force. In a static situation where the mass is held in place, the net force is zero, leading to the equation:
\( m \cdot a = 0 \
Since the mass of the spring is negligible, the acceleration \( a \) is also zero when the applied force is balanced by the spring force. However, when the applied force is removed, the spring force becomes the only force acting on the mass, which can be described by:
\( F_s = m \cdot a \
Substituting the spring force equation gives:
\( -k \cdot x = m \cdot a \
This leads to the formula for acceleration:
\( a = -\frac{k}{m} \cdot x \
The negative sign indicates that the acceleration is directed opposite to the displacement. For example, consider a block with a mass of 0.60 kg attached to a spring with a spring constant \( k = 15 \, \text{N/m} \), stretched 0.2 meters from its equilibrium position. To find the spring force acting on the block, we use:
\( F_s = -k \(\cdot\) x = -15 \(\cdot\) 0.2 = -3 \, \(\text{N}\) \
The negative value indicates that the force acts to the left, opposing the stretch. To calculate the acceleration, we apply the derived formula:
\( a = -\(\frac{15}{0.6}\) \(\cdot\) 0.2 = -5 \, \(\text{m/s}\)^2 \
Again, the negative sign signifies that the acceleration is directed to the left, consistent with the direction of the spring force. This understanding of the mass-spring system illustrates the fundamental principles of forces, motion, and equilibrium in physics.
4
Problem
You push a 3-kg mass against a spring and release it from rest. Its maximum acceleration is 10m/s
2
when pushed back 0.5m. What is the (a)spring constant and (b) restoring force at this point?
A
60 N/m; 30 N
B
120 N/m; 45 N
C
100 N/m; 35 N
D
30 N/m; 15 N
Go over this topic definitions with flashcards
More sets
Spring Force (Hooke's Law) definitions
17. Periodic Motion
15 Terms
1
student found this helpful
Spring Force (Hooke's Law) quiz
17. Periodic Motion
15 Terms
Take your learning anywhere!
Prep for your exams on the go with video lessons and practice problems in our mobile app.
Here’s what students ask on this topic:
Your Physics tutor | ||||||
| Markdown | [Skip to main content](https://www.pearson.com/channels/physics/learn/patrick/periodic-motion-new/spring-force-hookes-law#main-content-starts)
Physics
Get exam ready
Upload syllabus
Create Account
Sign in
[My Course](https://www.pearson.com/channels/physics)[Learn](https://www.pearson.com/channels/physics/learn/patrick/math-review/math-review)[Exam Prep](https://www.pearson.com/channels/physics/exam-prep)[AI Tutor](https://www.pearson.com/channels/physics/ai-tutor)[Study Guides](https://www.pearson.com/channels/physics/study-guides)[Textbook Solutions](https://www.pearson.com/channels/physics/textbook-solutions)[Flashcards](https://www.pearson.com/channels/physics/flashcards)[Explore](https://www.pearson.com/channels/physics/explore/math-review/math-review)
- [My Course](https://www.pearson.com/channels/physics)
- [Learn](https://www.pearson.com/channels/physics/learn/patrick/math-review/math-review)
- [Exam Prep](https://www.pearson.com/channels/physics/exam-prep)
- [AI Tutor](https://www.pearson.com/channels/physics/ai-tutor)
- [Study Guides](https://www.pearson.com/channels/physics/study-guides)
- [Textbook Solutions](https://www.pearson.com/channels/physics/textbook-solutions)
- [Flashcards](https://www.pearson.com/channels/physics/flashcards)
- [Explore](https://www.pearson.com/channels/physics/explore/math-review/math-review)
?
Select textbook and Institution
Improve your experience by picking them
By Exams
By Chapters
Table of contents
[Skip topic navigation](https://www.pearson.com/channels/physics/learn/patrick/periodic-motion-new/spring-force-hookes-law#guided-main-content-starts)
### Prepare for your exams
Upload your syllabus and get recommendations on what to study and when. No syllabus? Sharing your exam schedule works too.
Upload syllabus
or
Add exam schedule
[Skip topic navigation](https://www.pearson.com/channels/physics/learn/patrick/periodic-motion-new/spring-force-hookes-law#guided-main-content-starts)
- 0\. Math Review31m
Chapter worksheet
- [Math Review 31m](https://www.pearson.com/channels/physics/learn/patrick/math-review/math-review)
- 1\. Intro to Physics Units1h 29m
Chapter worksheet
- [Introduction to Units 26m](https://www.pearson.com/channels/physics/learn/patrick/units-vectors/units-metric-prefixes-scientific-notation)
- [Unit Conversions 18m](https://www.pearson.com/channels/physics/learn/patrick/units-vectors/units-conversions)
- [Solving Density Problems 13m](https://www.pearson.com/channels/physics/learn/patrick/units-vectors/solving-mass-volume-density-problems)
- [Dimensional Analysis 10m](https://www.pearson.com/channels/physics/learn/patrick/units-vectors/dimensional-analysis)
- [Counting Significant Figures 5m](https://www.pearson.com/channels/physics/learn/patrick/units-vectors/metric-prefixes)
- [Operations with Significant Figures 14m](https://www.pearson.com/channels/physics/learn/patrick/units-vectors/significant-figures-error)
- 2\. 1D Motion / Kinematics3h 56m
Chapter worksheet
- [Vectors, Scalars, & Displacement 13m](https://www.pearson.com/channels/physics/learn/patrick/1d-motion-kinematics-new/displacement)
- [Average Velocity 32m](https://www.pearson.com/channels/physics/learn/patrick/1d-motion-kinematics-new/intro-to-kinematics)
- [Intro to Acceleration 7m](https://www.pearson.com/channels/physics/learn/patrick/1d-motion-kinematics-new/constant-acceleration)
- [Position-Time Graphs & Velocity 26m](https://www.pearson.com/channels/physics/learn/patrick/1d-motion-kinematics-new/position-velocity-graphs)
- [Conceptual Problems with Position-Time Graphs 22m](https://www.pearson.com/channels/physics/learn/patrick/1d-motion-kinematics-new/conceptual-problems-position-time-graphs)
- [Velocity-Time Graphs & Acceleration 5m](https://www.pearson.com/channels/physics/learn/patrick/1d-motion-kinematics-new/velocity-time-graphs-acceleration)
- [Calculating Displacement from Velocity-Time Graphs 15m](https://www.pearson.com/channels/physics/learn/patrick/1d-motion-kinematics-new/calculating-displacement-from-velocity-time-graphs)
- [Conceptual Problems with Velocity-Time Graphs 10m](https://www.pearson.com/channels/physics/learn/patrick/1d-motion-kinematics-new/conceptual-problems-in-velocity-time-graphs)
- [Calculating Change in Velocity from Acceleration-Time Graphs 10m](https://www.pearson.com/channels/physics/learn/patrick/1d-motion-kinematics-new/calculating-change-in-velocity-from-acceleration-time-graphs)
- [Graphing Position, Velocity, and Acceleration Graphs 11m](https://www.pearson.com/channels/physics/learn/patrick/1d-motion-kinematics-new/graphing-position-velocity-and-acceleration-graphs)
- [Kinematics Equations 37m](https://www.pearson.com/channels/physics/learn/patrick/1d-motion-kinematics-new/kinematics-equations)
- [Vertical Motion and Free Fall 19m](https://www.pearson.com/channels/physics/learn/patrick/1d-motion-kinematics-new/vertical-motion-and-free-fall)
- [Catch/Overtake Problems 23m](https://www.pearson.com/channels/physics/learn/patrick/1d-motion-kinematics-new/catch-overtake-problems)
- 3\. Vectors2h 43m
Chapter worksheet
- [Review of Vectors vs. Scalars 1m](https://www.pearson.com/channels/physics/learn/patrick/vectors/review-of-vectors-vs-scalars)
- [Introduction to Vectors 7m](https://www.pearson.com/channels/physics/learn/patrick/vectors/vectors-scalars-and-displacement)
- [Adding Vectors Graphically 22m](https://www.pearson.com/channels/physics/learn/patrick/vectors/adding-vectors-graphically)
- [Vector Composition & Decomposition 11m](https://www.pearson.com/channels/physics/learn/patrick/vectors/vector-composition-decomposition)
- [Adding Vectors by Components 13m](https://www.pearson.com/channels/physics/learn/patrick/vectors/adding-vectors-by-components)
- [Trig Review 24m](https://www.pearson.com/channels/physics/learn/patrick/vectors/trig-review)
- [Unit Vectors 15m](https://www.pearson.com/channels/physics/learn/patrick/vectors/unit-vectors)
- [Introduction to Dot Product (Scalar Product) 12m](https://www.pearson.com/channels/physics/learn/patrick/vectors/scalar-product-dot-product)
- [Calculating Dot Product Using Components 12m](https://www.pearson.com/channels/physics/learn/patrick/vectors/intro-to-dot-product-scalar-product)
- [Intro to Cross Product (Vector Product) 23m](https://www.pearson.com/channels/physics/learn/patrick/vectors/vector-product-cross-product)
- [Calculating Cross Product Using Components 17m](https://www.pearson.com/channels/physics/learn/patrick/vectors/calculating-cross-product-using-components)
- 4\. 2D Kinematics1h 42m
Chapter worksheet
- [Intro to Motion in 2D: Position & Displacement 20m](https://www.pearson.com/channels/physics/learn/patrick/2d-motion/displacement-position-in-2d)
- [Velocity in 2D 27m](https://www.pearson.com/channels/physics/learn/patrick/2d-motion/velocity-in-2d)
- [Acceleration in 2D 12m](https://www.pearson.com/channels/physics/learn/patrick/2d-motion/acceleration-in-2d)
- [Kinematics in 2D 18m](https://www.pearson.com/channels/physics/learn/patrick/2d-motion/kinematics-in-2d)
- [Intro to Relative Velocity 23m](https://www.pearson.com/channels/physics/learn/patrick/2d-motion/relative-motion-in-1d)
- 5\. Projectile Motion3h 6m
Chapter worksheet
- [Intro to Projectile Motion: Horizontal Launch 35m](https://www.pearson.com/channels/physics/learn/patrick/projectile-motion/intro-to-projectile-motion)
- [Negative (Downward) Launch 24m](https://www.pearson.com/channels/physics/learn/patrick/projectile-motion/projectile-motion-negative-downward-launch)
- [Symmetrical Launch 25m](https://www.pearson.com/channels/physics/learn/patrick/projectile-motion/projectile-motion-symmetric-launch)
- [Projectiles Launched From Moving Vehicles 15m](https://www.pearson.com/channels/physics/learn/patrick/projectile-motion/projectile-motion-launch-from-moving-object)
- [Special Equations in Symmetrical Launches 16m](https://www.pearson.com/channels/physics/learn/patrick/projectile-motion/special-equations-in-symmetric-launch)
- [Positive (Upward) Launch 50m](https://www.pearson.com/channels/physics/learn/patrick/projectile-motion/positive-upward-launch)
- [Using Equation Substitution 17m](https://www.pearson.com/channels/physics/learn/patrick/projectile-motion/projectile-motion-finding-initial-velocity)
- 6\. Intro to Forces (Dynamics)3h 22m
Chapter worksheet
- [Newton's First & Second Laws 16m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-1/newton-s-3-laws)
- [Types Of Forces & Free Body Diagrams 20m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-1/types-of-forces-free-body-diagrams)
- [Forces & Kinematics 12m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-1/forces-in-kinematics)
- [Vertical Forces & Acceleration 23m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-1/vertical-forces)
- [Vertical Equilibrium & The Normal Force 18m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-1/vertical-equilibrium-normal-force)
- [Forces in 2D 36m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-1/forces-in-2d)
- [Equilibrium in 2D 24m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-1/2d-equilibrium)
- [Newton's Third Law & Action-Reaction Pairs 11m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-1/types-of-forces)
- [Forces in Connected Systems of Objects 38m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-1/systems-of-objects)
- 7\. Friction, Inclines, Systems2h 44m
Chapter worksheet
- [Inclined Planes 20m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-2/inclined-planes)
- [Kinetic Friction 17m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-2/kinetic-friction)
- [Static Friction 21m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-2/static-friction)
- [Inclined Planes with Friction 37m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-2/inclines-with-friction)
- [Systems of Objects with Friction 10m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-2/advanced-systems-of-objects-with-inclines-and-friction)
- [Systems of Objects on Inclined Planes with Friction 19m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-2/systems-of-objects-on-inclined-planes-with-friction)
- [Stacked Blocks 16m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-2/friction)
- [Intro to Springs (Hooke's Law) 20m](https://www.pearson.com/channels/physics/learn/patrick/forces-dynamics-part-2/spring-force-hooke-s-law)
- 8\. Centripetal Forces & Gravitation7h 26m
Chapter worksheet
- [Uniform Circular Motion 7m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/circular-motion-2)
- [Period and Frequency in Uniform Circular Motion 20m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/period-and-frequency-in-uniform-circular-motion)
- [Centripetal Forces 15m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/centripetal-forces)
- [Vertical Centripetal Forces 10m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/intro-to-centripetal-forces)
- [Flat Curves 9m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/centripetal-forces-curves)
- [Banked Curves 10m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/flat-banked-curve)
- [Newton's Law of Gravity 30m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/newtons-law-of-gravity)
- [Gravitational Forces in 2D 25m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/gravitational-forces-in-2d)
- [Acceleration Due to Gravity 13m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/acceleration-due-to-gravity)
- [Satellite Motion: Intro 5m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/satellite-motion-intro)
- [Satellite Motion: Speed & Period 35m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/satellite-motion-speed-period)
- [Geosynchronous Orbits 15m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/geosynchronous-orbits)
- [Overview of Kepler's Laws 5m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/overview-keplers-laws)
- [Kepler's First Law 11m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/keplers-first-law)
- [Kepler's Third Law 16m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/kepler-s-third-law)
- [Kepler's Third Law for Elliptical Orbits 15m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/keplers-third-law-for-elliptical-orbits)
- [Gravitational Potential Energy 21m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/gravitational-potential-energy)
- [Gravitational Potential Energy for Systems of Masses 17m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/gravitational-potential-energy-for-systems-of-masses)
- [Escape Velocity 21m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/escape-velocity)
- [Energy of Circular Orbits 23m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/energy-of-circular-orbits)
- [Energy of Elliptical Orbits 36m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/energy-of-elliptical-orbits)
- [Black Holes 16m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/black-holes)
- [Gravitational Force Inside the Earth 13m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/gravitational-force-inside-the-earth)
- [Mass Distribution with Calculus 45m](https://www.pearson.com/channels/physics/learn/patrick/centripetal-forces-gravitation/mass-distribution-with-calculus)
- 9\. Work & Energy1h 59m
Chapter worksheet
- [Intro to Energy & Kinetic Energy 5m](https://www.pearson.com/channels/physics/learn/patrick/work-energy/intro-to-energy)
- [Intro to Calculating Work 27m](https://www.pearson.com/channels/physics/learn/patrick/work-energy/intro-to-calculating-work)
- [Net Work & Work-Energy Theorem 25m](https://www.pearson.com/channels/physics/learn/patrick/work-energy/net-work-kinetic-energy)
- [Work On Inclined Planes 16m](https://www.pearson.com/channels/physics/learn/patrick/work-energy/work-by-gravity-inclined-planes)
- [Work By Springs 16m](https://www.pearson.com/channels/physics/learn/patrick/work-energy/work-by-variable-forces-springs)
- [Work As Area Under F-x Graphs 7m](https://www.pearson.com/channels/physics/learn/patrick/work-energy/more-work-energy-problems)
- [Power 19m](https://www.pearson.com/channels/physics/learn/patrick/work-energy/power)
- 10\. Conservation of Energy2h 54m
Chapter worksheet
- [Intro to Energy Types 3m](https://www.pearson.com/channels/physics/learn/patrick/conservation-of-energy/intro-to-energy-types)
- [Gravitational Potential Energy 10m](https://www.pearson.com/channels/physics/learn/patrick/conservation-of-energy/gravitational-potential-energy-1)
- [Intro to Conservation of Energy 32m](https://www.pearson.com/channels/physics/learn/patrick/conservation-of-energy/intro-to-conservation-of-energy)
- [Energy with Non-Conservative Forces 20m](https://www.pearson.com/channels/physics/learn/patrick/conservation-of-energy/energy-with-non-conservative-forces)
- [Springs & Elastic Potential Energy 19m](https://www.pearson.com/channels/physics/learn/patrick/conservation-of-energy/springs-elastic-potential-energy)
- [Solving Projectile Motion Using Energy 13m](https://www.pearson.com/channels/physics/learn/patrick/conservation-of-energy/solving-projectile-motion-using-energy)
- [Motion Along Curved Paths 4m](https://www.pearson.com/channels/physics/learn/patrick/conservation-of-energy/motion-along-curved-paths)
- [Rollercoaster Problems 13m](https://www.pearson.com/channels/physics/learn/patrick/conservation-of-energy/rollercoaster-problems)
- [Pendulum Problems 13m](https://www.pearson.com/channels/physics/learn/patrick/conservation-of-energy/pendulum-problems)
- [Energy in Connected Objects (Systems) 24m](https://www.pearson.com/channels/physics/learn/patrick/conservation-of-energy/energy-in-connected-objects-systems)
- [Force & Potential Energy 18m](https://www.pearson.com/channels/physics/learn/patrick/conservation-of-energy/force-potential-energy)
- 11\. Momentum & Impulse3h 40m
Chapter worksheet
- [Intro to Momentum 11m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/intro-to-momentum-and-impulse)
- [Intro to Impulse 14m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/intro-to-impulse)
- [Impulse with Variable Forces 12m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/impulse-with-variable-forces)
- [Intro to Conservation of Momentum 17m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/intro-to-conservation-of-momentum)
- [Push-Away Problems 19m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/push-away-problems)
- [Types of Collisions 4m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/types-of-collisions)
- [Completely Inelastic Collisions 28m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/completely-inelastic-collisions)
- [Adding Mass to a Moving System 8m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/adding-mass-to-a-moving-system)
- [Collisions & Motion (Momentum & Energy) 26m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/collisions-with-energy)
- [Ballistic Pendulum 14m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/ballistic-pendulum)
- [Collisions with Springs 13m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/collisions-with-springs)
- [Elastic Collisions 24m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/elastic-collisions)
- [How to Identify the Type of Collision 9m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/how-to-identify-the-type-of-collision)
- [Intro to Center of Mass 15m](https://www.pearson.com/channels/physics/learn/patrick/momentum-impulse/center-of-mass)
- 12\. Rotational Kinematics2h 59m
Chapter worksheet
- [Rotational Position & Displacement 25m](https://www.pearson.com/channels/physics/learn/patrick/rotational-kinematics/displacement-velocity-acceleration)
- [More Connect Wheels (Bicycles) 29m](https://www.pearson.com/channels/physics/learn/patrick/rotational-kinematics/more-connect-wheels-bicycles)
- [Rotational Velocity & Acceleration 20m](https://www.pearson.com/channels/physics/learn/patrick/rotational-kinematics/equations-of-rotational-motion)
- [Equations of Rotational Motion 20m](https://www.pearson.com/channels/physics/learn/patrick/rotational-kinematics/rotational-energy)
- [Converting Between Linear & Rotational 26m](https://www.pearson.com/channels/physics/learn/patrick/rotational-kinematics/rotational-work-power)
- [Types of Acceleration in Rotation 26m](https://www.pearson.com/channels/physics/learn/patrick/rotational-kinematics/types-of-acceleration-in-rotation)
- [Rolling Motion (Free Wheels) 16m](https://www.pearson.com/channels/physics/learn/patrick/rotational-kinematics/rolling-motion-free-wheels)
- [Intro to Connected Wheels 12m](https://www.pearson.com/channels/physics/learn/patrick/rotational-kinematics/connected-wheels-bicycles)
- 13\. Rotational Inertia & Energy7h 4m
Chapter worksheet
- [More Conservation of Energy Problems 54m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/more-conservation-of-energy-problems)
- [Conservation of Energy in Rolling Motion 45m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/conservation-of-energy-in-rolling-motion)
- [Parallel Axis Theorem 13m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/parallel-axis-theorem)
- [Intro to Moment of Inertia 28m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/intro-to-torque)
- [Moment of Inertia via Integration 18m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/moment-of-inertia-via-integration)
- [Moment of Inertia of Systems 23m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/rotational-dynamics)
- [Moment of Inertia & Mass Distribution 10m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/moment-of-inertia-mass-distribution)
- [Intro to Rotational Kinetic Energy 16m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/intro-to-rotational-kinetic-energy)
- [Energy of Rolling Motion 18m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/energy-of-rolling-motion)
- [Types of Motion & Energy 24m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/types-of-motion-energy)
- [Conservation of Energy with Rotation 35m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/conservation-of-energy-with-rotation)
- [Torque with Kinematic Equations 56m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/torque-with-kinematic-equations)
- [Rotational Dynamics with Two Motions 50m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/rotational-dynamics-with-two-motions)
- [Rotational Dynamics of Rolling Motion 27m](https://www.pearson.com/channels/physics/learn/patrick/rotational-inertia-energy/rotational-dynamics-of-rolling-motion)
- 14\. Torque & Rotational Dynamics2h 5m
Chapter worksheet
- [Torque & Acceleration (Rotational Dynamics) 15m](https://www.pearson.com/channels/physics/learn/patrick/torque-rotational-dynamics/torque-acceleration-rotational-dynamics)
- [How to Solve: Energy vs Torque 10m](https://www.pearson.com/channels/physics/learn/patrick/torque-rotational-dynamics/how-to-solve-energy-vs-torque)
- [Torque Due to Weight 23m](https://www.pearson.com/channels/physics/learn/patrick/torque-rotational-dynamics/torque-due-to-weight)
- [Intro to Torque 26m](https://www.pearson.com/channels/physics/learn/patrick/torque-rotational-dynamics/rotational-equilibrium)
- [Net Torque & Sign of Torque 13m](https://www.pearson.com/channels/physics/learn/patrick/torque-rotational-dynamics/angular-momentum)
- [Torque on Discs & Pulleys 35m](https://www.pearson.com/channels/physics/learn/patrick/torque-rotational-dynamics/rotational-collisions)
- 15\. Rotational Equilibrium3h 39m
Chapter worksheet
- [Equilibrium with Multiple Objects 30m](https://www.pearson.com/channels/physics/learn/patrick/rotational-equilibrium/problems-with-multiple-objects)
- [Equilibrium with Multiple Supports 15m](https://www.pearson.com/channels/physics/learn/patrick/rotational-equilibrium/equilibrium-with-multiple-supports)
- [Center of Mass & Simple Balance 29m](https://www.pearson.com/channels/physics/learn/patrick/rotational-equilibrium/center-of-mass-simple-balance)
- [Equilibrium in 2D - Ladder Problems 40m](https://www.pearson.com/channels/physics/learn/patrick/rotational-equilibrium/equilibrium-in-2d-ladder-problems)
- [Beam / Shelf Against a Wall 53m](https://www.pearson.com/channels/physics/learn/patrick/rotational-equilibrium/beam-shelf-against-a-wall)
- [More 2D Equilibrium Problems 14m](https://www.pearson.com/channels/physics/learn/patrick/rotational-equilibrium/more-2d-equilibrium-problems)
- [Review: Center of Mass 14m](https://www.pearson.com/channels/physics/learn/patrick/rotational-equilibrium/review-center-of-mass)
- [Torque & Equilibrium 22m](https://www.pearson.com/channels/physics/learn/patrick/rotational-equilibrium/torque-equilibrium)
- 16\. Angular Momentum3h 6m
Chapter worksheet
- [Opening/Closing Arms on Rotating Stool 18m](https://www.pearson.com/channels/physics/learn/patrick/angular-momentum/more-conservation-problems)
- [Conservation of Angular Momentum 46m](https://www.pearson.com/channels/physics/learn/patrick/angular-momentum/conservation-of-angular-momentum)
- [Angular Momentum & Newton's Second Law 10m](https://www.pearson.com/channels/physics/learn/patrick/angular-momentum/more-angular-momentum)
- [Intro to Angular Collisions 15m](https://www.pearson.com/channels/physics/learn/patrick/angular-momentum/angular-collisions)
- [Jumping Into/Out of Moving Disc 23m](https://www.pearson.com/channels/physics/learn/patrick/angular-momentum/topic-1)
- [Spinning on String of Variable Length 20m](https://www.pearson.com/channels/physics/learn/patrick/angular-momentum/spinning-on-string-of-variable-length)
- [Angular Collisions with Linear Motion 8m](https://www.pearson.com/channels/physics/learn/patrick/angular-momentum/angular-collisions-with-linear-motion)
- [Intro to Angular Momentum 15m](https://www.pearson.com/channels/physics/learn/patrick/angular-momentum/intro-to-angular-momentum)
- [Angular Momentum of a Point Mass 21m](https://www.pearson.com/channels/physics/learn/patrick/angular-momentum/angular-momentum-of-a-point-mass)
- [Angular Momentum of Objects in Linear Motion 7m](https://www.pearson.com/channels/physics/learn/patrick/angular-momentum/angular-momentum-of-objects-in-linear-motion)
- 17\. Periodic Motion2h 9m
Chapter worksheet
- [Spring Force (Hooke's Law) 14m](https://www.pearson.com/channels/physics/learn/patrick/periodic-motion-new/spring-force-hookes-law)
- [Intro to Simple Harmonic Motion (Horizontal Springs) 30m](https://www.pearson.com/channels/physics/learn/patrick/periodic-motion-new/intro-to-simple-harmonic-motion-horizontal-springs)
- [Energy in Simple Harmonic Motion 22m](https://www.pearson.com/channels/physics/learn/patrick/periodic-motion-new/energy-in-simple-harmonic-motion)
- [Simple Harmonic Motion of Vertical Springs 20m](https://www.pearson.com/channels/physics/learn/patrick/periodic-motion-new/simple-harmonic-motion-of-vertical-springs)
- [Simple Harmonic Motion of Pendulums 25m](https://www.pearson.com/channels/physics/learn/patrick/periodic-motion-new/simple-harmonic-motion-of-pendulums)
- [Energy in Pendulums 15m](https://www.pearson.com/channels/physics/learn/patrick/periodic-motion-new/energy-in-pendulums)
- 18\. Waves & Sound3h 40m
Chapter worksheet
- [Intro to Waves 11m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/intro-to-waves)
- [Velocity of Transverse Waves 21m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/velocity-of-transverse-waves)
- [Velocity of Longitudinal Waves 11m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/velocity-of-longitudinal-waves)
- [Wave Functions 31m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/wave-functions)
- [Phase Constant 14m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/phase-constant)
- [Average Power of Waves on Strings 10m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/average-power-of-waves-on-strings)
- [Wave Intensity 19m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/wave-intensity)
- [Sound Intensity 13m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/sound-intensity)
- [Wave Interference 8m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/wave-interference)
- [Superposition of Wave Functions 3m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/superposition-of-wave-functions)
- [Standing Waves 30m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/standing-waves)
- [Standing Wave Functions 14m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/standing-wave-functions)
- [Standing Sound Waves 12m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/standing-sound-waves)
- [Beats 8m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/beats)
- [The Doppler Effect 7m](https://www.pearson.com/channels/physics/learn/patrick/18-waves-and-sound/the-doppler-effect)
- 19\. Fluid Mechanics4h 27m
Chapter worksheet
- [Density 29m](https://www.pearson.com/channels/physics/learn/patrick/fluid-mechanics/fluids-density)
- [Intro to Pressure 1h 10m](https://www.pearson.com/channels/physics/learn/patrick/fluid-mechanics/intro-to-pressure)
- [Pascal's Law & Hydraulic Lift 28m](https://www.pearson.com/channels/physics/learn/patrick/fluid-mechanics/pascal-law-hydraulic-lift)
- [Pressure Gauge: Barometer 13m](https://www.pearson.com/channels/physics/learn/patrick/fluid-mechanics/gauge-barometer)
- [Pressure Gauge: Manometer 14m](https://www.pearson.com/channels/physics/learn/patrick/fluid-mechanics/gauge-manometer)
- [Pressure Gauge: U-shaped Tube 21m](https://www.pearson.com/channels/physics/learn/patrick/fluid-mechanics/gauge-u-shaped-tube)
- [Buoyancy & Buoyant Force 1h 4m](https://www.pearson.com/channels/physics/learn/patrick/fluid-mechanics/buoyancy-buoyant-force)
- [Ideal vs Real Fluids 3m](https://www.pearson.com/channels/physics/learn/patrick/fluid-mechanics/ideal-real-fluids)
- [Fluid Flow & Continuity Equation 21m](https://www.pearson.com/channels/physics/learn/patrick/fluid-mechanics/fluid-flow-continuity)
- 20\. Heat and Temperature3h 7m
Chapter worksheet
- [Temperature 16m](https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/temperature)
- [Linear Thermal Expansion 14m](https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/zeroth-law-of-thermodynamics)
- [Volume Thermal Expansion 14m](https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/thermal-expansion)
- [Moles and Avogadro's Number 14m](https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/moles-avogadros-number)
- [Specific Heat & Temperature Changes 12m](https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/specific-heat)
- [Latent Heat & Phase Changes 16m](https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/changes-in-phase-latent-heat)
- [Intro to Calorimetry 21m](https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/calorimetry)
- [Calorimetry with Temperature and Phase Changes 15m](https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/changes-in-temperature-heat-capacity)
- [Advanced Calorimetry: Equilibrium Temperature with Phase Changes 9m](https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/temperature-change-across-phases)
- [Phase Diagrams, Triple Points and Critical Points 6m](https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/phase-diagrams-triple-points-and-critical-points)
- [Heat Transfer 44m](https://www.pearson.com/channels/physics/learn/patrick/heat-temperature-and-kinetic-theory-of-gasses/heat-transfer)
- 21\. Kinetic Theory of Ideal Gases1h 50m
Chapter worksheet
- [The Ideal Gas Law 32m](https://www.pearson.com/channels/physics/learn/patrick/kinetic-theory-of-ideal-gases/ideal-gas-law)
- [Kinetic-Molecular Theory of Gases 1m](https://www.pearson.com/channels/physics/learn/patrick/kinetic-theory-of-ideal-gases/kinetic-theory-of-gases)
- [Average Kinetic Energy of Gases 10m](https://www.pearson.com/channels/physics/learn/patrick/kinetic-theory-of-ideal-gases/kinetic-energy-gases)
- [Internal Energy of Gases 14m](https://www.pearson.com/channels/physics/learn/patrick/kinetic-theory-of-ideal-gases/internal-energy-gases)
- [Root-Mean-Square Velocity of Gases 15m](https://www.pearson.com/channels/physics/learn/patrick/kinetic-theory-of-ideal-gases/root-mean-square-velocity-of-gases)
- [Mean Free Path of Gases 20m](https://www.pearson.com/channels/physics/learn/patrick/kinetic-theory-of-ideal-gases/mean-free-path)
- [Speed Distribution of Ideal Gases 15m](https://www.pearson.com/channels/physics/learn/patrick/kinetic-theory-of-ideal-gases/speed-distribution-of-ideal-gases)
- 22\. The First Law of Thermodynamics1h 26m
Chapter worksheet
- [Heat Equations for Special Processes & Molar Specific Heats 15m](https://www.pearson.com/channels/physics/learn/patrick/the-first-and-second-laws-of-thermodynamics/heat-capacities)
- [First Law of Thermodynamics 22m](https://www.pearson.com/channels/physics/learn/patrick/the-first-and-second-laws-of-thermodynamics/first-law-of-thermodynamics)
- [Work Done Through Multiple Processes 16m](https://www.pearson.com/channels/physics/learn/patrick/the-first-and-second-laws-of-thermodynamics/intro-to-thermal-processes)
- [Cyclic Thermodynamic Processes 20m](https://www.pearson.com/channels/physics/learn/patrick/the-first-and-second-laws-of-thermodynamics/cyclic-thermal-processes)
- [PV Diagrams & Work 12m](https://www.pearson.com/channels/physics/learn/patrick/the-first-and-second-laws-of-thermodynamics/work-pv-diagrams)
- 23\. The Second Law of Thermodynamics3h 11m
Chapter worksheet
- [Heat Engines and the Second Law of Thermodynamics 31m](https://www.pearson.com/channels/physics/learn/patrick/the-second-law-of-thermodynamics/intro-to-heat-engines)
- [Heat Engines & PV Diagrams 18m](https://www.pearson.com/channels/physics/learn/patrick/the-second-law-of-thermodynamics/heat-engines-pv-diagrams)
- [The Otto Cycle 28m](https://www.pearson.com/channels/physics/learn/patrick/the-second-law-of-thermodynamics/four-stroke-piston-engine)
- [The Carnot Cycle 21m](https://www.pearson.com/channels/physics/learn/patrick/the-second-law-of-thermodynamics/carnot-cycle)
- [Refrigerators 22m](https://www.pearson.com/channels/physics/learn/patrick/the-second-law-of-thermodynamics/intro-to-refrigerators)
- [Entropy and the Second Law of Thermodynamics 31m](https://www.pearson.com/channels/physics/learn/patrick/the-second-law-of-thermodynamics/entropy)
- [Entropy Equations for Special Processes 24m](https://www.pearson.com/channels/physics/learn/patrick/the-second-law-of-thermodynamics/entropy-special-processes)
- [Statistical Interpretation of Entropy 11m](https://www.pearson.com/channels/physics/learn/patrick/the-second-law-of-thermodynamics/statistical-interpretation-of-entropy)
- 24\. Electric Force & Field; Gauss' Law3h 42m
Chapter worksheet
- [Electric Charge 15m](https://www.pearson.com/channels/physics/learn/patrick/electric-force-field-gauss-law/electric-charge)
- [Charging Objects 6m](https://www.pearson.com/channels/physics/learn/patrick/electric-force-field-gauss-law/charging-objects)
- [Charging By Induction 3m](https://www.pearson.com/channels/physics/learn/patrick/electric-force-field-gauss-law/charging-by-induction)
- [Conservation of Charge 5m](https://www.pearson.com/channels/physics/learn/patrick/electric-force-field-gauss-law/conservation-of-charge)
- [Coulomb's Law (Electric Force) 47m](https://www.pearson.com/channels/physics/learn/patrick/electric-force-field-gauss-law/coulomb-law-electric-force)
- [Electric Field 40m](https://www.pearson.com/channels/physics/learn/patrick/electric-force-field-gauss-law/electric-field)
- [Electric Fields in Capacitors 16m](https://www.pearson.com/channels/physics/learn/patrick/electric-force-field-gauss-law/electric-fields-in-capacitors)
- [Electric Field Lines 16m](https://www.pearson.com/channels/physics/learn/patrick/electric-force-field-gauss-law/electric-field-lines)
- [Dipole Moment 8m](https://www.pearson.com/channels/physics/learn/patrick/electric-force-field-gauss-law/dipole-moment)
- [Electric Fields in Conductors 7m](https://www.pearson.com/channels/physics/learn/patrick/electric-force-field-gauss-law/electric-fields-in-conductors)
- [Electric Flux 21m](https://www.pearson.com/channels/physics/learn/patrick/electric-force-field-gauss-law/electric-flux)
- [Gauss' Law 32m](https://www.pearson.com/channels/physics/learn/patrick/electric-force-field-gauss-law/gauss-law)
- 25\. Electric Potential1h 51m
Chapter worksheet
- [Electric Potential Energy 7m](https://www.pearson.com/channels/physics/learn/patrick/electric-potential/electric-potential-energy)
- [Electric Potential 27m](https://www.pearson.com/channels/physics/learn/patrick/electric-potential/electric-potential)
- [Work From Electric Force 31m](https://www.pearson.com/channels/physics/learn/patrick/electric-potential/work-due-to-electric-force)
- [Relationships Between Force, Field, Energy, Potential 25m](https://www.pearson.com/channels/physics/learn/patrick/electric-potential/relationships-between-force-field-energy-potential)
- [The ElectronVolt 5m](https://www.pearson.com/channels/physics/learn/patrick/electric-potential/the-electronvolt)
- [Equipotential Surfaces 13m](https://www.pearson.com/channels/physics/learn/patrick/electric-potential/equipotential-surfaces)
- 26\. Capacitors & Dielectrics2h 2m
Chapter worksheet
- [Capacitors & Capacitance 8m](https://www.pearson.com/channels/physics/learn/patrick/capacitors-and-dielectrics/capacitors-capacitance)
- [Parallel Plate Capacitors 19m](https://www.pearson.com/channels/physics/learn/patrick/capacitors-and-dielectrics/parallel-plate-capacitors)
- [Energy Stored by Capacitor 15m](https://www.pearson.com/channels/physics/learn/patrick/capacitors-and-dielectrics/energy-stored-by-capacitor)
- [Capacitance Using Calculus 7m](https://www.pearson.com/channels/physics/learn/patrick/capacitors-and-dielectrics/capacitance-calculus)
- [Combining Capacitors in Series & Parallel 15m](https://www.pearson.com/channels/physics/learn/patrick/capacitors-and-dielectrics/combining-capacitors-in-series-parallel)
- [Solving Capacitor Circuits 29m](https://www.pearson.com/channels/physics/learn/patrick/capacitors-and-dielectrics/solving-capacitor-circuits)
- [Intro To Dielectrics 18m](https://www.pearson.com/channels/physics/learn/patrick/capacitors-and-dielectrics/intr-to-dielectrics)
- [How Dielectrics Work 2m](https://www.pearson.com/channels/physics/learn/patrick/capacitors-and-dielectrics/how-dielectrics-work)
- [Dielectric Breakdown 4m](https://www.pearson.com/channels/physics/learn/patrick/capacitors-and-dielectrics/dielectric-breakdown)
- 27\. Resistors & DC Circuits3h 8m
Chapter worksheet
- [Intro to Current 6m](https://www.pearson.com/channels/physics/learn/patrick/resistors-and-dc-circuits/intro-to-current)
- [Resistors and Ohm's Law 14m](https://www.pearson.com/channels/physics/learn/patrick/resistors-and-dc-circuits/resistors-ohms-law)
- [Power in Circuits 11m](https://www.pearson.com/channels/physics/learn/patrick/resistors-and-dc-circuits/power-in-circuits)
- [Microscopic View of Current 8m](https://www.pearson.com/channels/physics/learn/patrick/resistors-and-dc-circuits/macroscopic-view-of-current)
- [Combining Resistors in Series & Parallel 37m](https://www.pearson.com/channels/physics/learn/patrick/resistors-and-dc-circuits/combining-resistors-in-series-parallel)
- [Kirchhoff's Junction Rule 4m](https://www.pearson.com/channels/physics/learn/patrick/resistors-and-dc-circuits/kirchhoffs-junction-rule)
- [Solving Resistor Circuits 31m](https://www.pearson.com/channels/physics/learn/patrick/resistors-and-dc-circuits/solving-resistor-circuits)
- [Kirchhoff's Loop Rule 1h 14m](https://www.pearson.com/channels/physics/learn/patrick/resistors-and-dc-circuits/kirchhoffs-loop-rule)
- 28\. Magnetic Fields and Forces2h 23m
Chapter worksheet
- [Magnets and Magnetic Fields 21m](https://www.pearson.com/channels/physics/learn/patrick/magnetic-field-and-magnetic-forces/magnets-magnetic-fields)
- [Summary of Magnetism Problems 9m](https://www.pearson.com/channels/physics/learn/patrick/magnetic-field-and-magnetic-forces/summary-of-magnetism-problems)
- [Force on Moving Charges & Right Hand Rule 26m](https://www.pearson.com/channels/physics/learn/patrick/magnetic-field-and-magnetic-forces/force-on-moving-charges-right-hand-rule)
- [Circular Motion of Charges in Magnetic Fields 11m](https://www.pearson.com/channels/physics/learn/patrick/magnetic-field-and-magnetic-forces/circular-motion-of-charges-in-magnetic-fields)
- [Mass Spectrometer 33m](https://www.pearson.com/channels/physics/learn/patrick/magnetic-field-and-magnetic-forces/mass-spectrometer)
- [Magnetic Force on Current-Carrying Wire 22m](https://www.pearson.com/channels/physics/learn/patrick/magnetic-field-and-magnetic-forces/magnetic-force-on-current-carrying-wire)
- [Force and Torque on Current Loops 17m](https://www.pearson.com/channels/physics/learn/patrick/magnetic-field-and-magnetic-forces/force-and-torque-on-current-loops)
- 29\. Sources of Magnetic Field2h 30m
Chapter worksheet
- [Magnetic Field Produced by Moving Charges 10m](https://www.pearson.com/channels/physics/learn/patrick/sources-of-magnetic-field/magnetic-field-produced-by-moving-charges)
- [Magnetic Field Produced by Straight Currents 27m](https://www.pearson.com/channels/physics/learn/patrick/sources-of-magnetic-field/magnetic-field-produced-by-straight-currents)
- [Magnetic Force Between Parallel Currents 12m](https://www.pearson.com/channels/physics/learn/patrick/sources-of-magnetic-field/magnetic-force-between-parallel-currents)
- [Magnetic Force Between Two Moving Charges 9m](https://www.pearson.com/channels/physics/learn/patrick/sources-of-magnetic-field/magnetic-force-between-two-moving-charges)
- [Magnetic Field Produced by Loops andSolenoids 42m](https://www.pearson.com/channels/physics/learn/patrick/sources-of-magnetic-field/magnetic-field-produced-by-loops-and-solenoids)
- [Toroidal Solenoids aka Toroids 12m](https://www.pearson.com/channels/physics/learn/patrick/sources-of-magnetic-field/toroidal-solenoids-aka-toroids)
- [Biot-Savart Law (Calculus) 18m](https://www.pearson.com/channels/physics/learn/patrick/sources-of-magnetic-field/biot-savart-law-with-calculus)
- [Ampere's Law (Calculus) 17m](https://www.pearson.com/channels/physics/learn/patrick/sources-of-magnetic-field/ampere-law-with-calculus)
- 30\. Induction and Inductance3h 38m
Chapter worksheet
- [Intro to Induction 5m](https://www.pearson.com/channels/physics/learn/patrick/electromagnetic-induction/induction-experiments)
- [Magnetic Flux 12m](https://www.pearson.com/channels/physics/learn/patrick/electromagnetic-induction/magnetic-flux)
- [Faraday's Law 28m](https://www.pearson.com/channels/physics/learn/patrick/electromagnetic-induction/faraday-s-law)
- [Lenz's Law 22m](https://www.pearson.com/channels/physics/learn/patrick/electromagnetic-induction/lenz-s-law)
- [Motional EMF 18m](https://www.pearson.com/channels/physics/learn/patrick/electromagnetic-induction/motional-emf)
- [Transformers 8m](https://www.pearson.com/channels/physics/learn/patrick/electromagnetic-induction/transformers)
- [Mutual Inductance 24m](https://www.pearson.com/channels/physics/learn/patrick/electromagnetic-induction/mutual-inductance)
- [Self Inductance 18m](https://www.pearson.com/channels/physics/learn/patrick/electromagnetic-induction/self-inductance)
- [Inductors 7m](https://www.pearson.com/channels/physics/learn/patrick/electromagnetic-induction/inductors)
- [LR Circuits 22m](https://www.pearson.com/channels/physics/learn/patrick/electromagnetic-induction/lr-circuits)
- [LC Circuits 35m](https://www.pearson.com/channels/physics/learn/patrick/electromagnetic-induction/lc-circuits)
- [LRC Circuits 14m](https://www.pearson.com/channels/physics/learn/patrick/electromagnetic-induction/lrc-circuits)
- 31\. Alternating Current2h 37m
Chapter worksheet
- [Alternating Voltages and Currents 18m](https://www.pearson.com/channels/physics/learn/patrick/alternating-current/alternating-voltages-and-currents)
- [RMS Current and Voltage 9m](https://www.pearson.com/channels/physics/learn/patrick/alternating-current/rms-current-and-voltag)
- [Phasors 20m](https://www.pearson.com/channels/physics/learn/patrick/alternating-current/phasors)
- [Resistors in AC Circuits 9m](https://www.pearson.com/channels/physics/learn/patrick/alternating-current/resistors-in-ac-circuits)
- [Phasors for Resistors 7m](https://www.pearson.com/channels/physics/learn/patrick/alternating-current/phasors-for-resistors)
- [Capacitors in AC Circuits 16m](https://www.pearson.com/channels/physics/learn/patrick/alternating-current/capacitors-in-ac-circuits)
- [Phasors for Capacitors 8m](https://www.pearson.com/channels/physics/learn/patrick/alternating-current/phasors-for-capacitors)
- [Inductors in AC Circuits 13m](https://www.pearson.com/channels/physics/learn/patrick/alternating-current/inductors-in-ac-circuits)
- [Phasors for Inductors 7m](https://www.pearson.com/channels/physics/learn/patrick/alternating-current/phasors-for-inductors)
- [Impedance in AC Circuits 18m](https://www.pearson.com/channels/physics/learn/patrick/alternating-current/impedance-in-ac-circuits)
- [Series LRC Circuits 11m](https://www.pearson.com/channels/physics/learn/patrick/alternating-current/series-lrc-circuits)
- [Resonance in Series LRC Circuits 10m](https://www.pearson.com/channels/physics/learn/patrick/alternating-current/resonance-in-lrc-circuits)
- [Power in AC Circuits 5m](https://www.pearson.com/channels/physics/learn/patrick/alternating-current/power-in-ac-circuits)
- 32\. Electromagnetic Waves2h 14m
Chapter worksheet
- [Intro to Electromagnetic (EM) Waves 23m](https://www.pearson.com/channels/physics/learn/patrick/32-electromagnetic-waves/intro-to-electromagnetic-em-waves)
- [The Electromagnetic Spectrum 7m](https://www.pearson.com/channels/physics/learn/patrick/32-electromagnetic-waves/the-electromagnetic-spectrum)
- [Intensity of EM Waves 22m](https://www.pearson.com/channels/physics/learn/patrick/32-electromagnetic-waves/intensity-of-em-waves)
- [Wavefunctions of EM Waves 19m](https://www.pearson.com/channels/physics/learn/patrick/32-electromagnetic-waves/wavefunctions-of-em-waves)
- [Radiation Pressure 24m](https://www.pearson.com/channels/physics/learn/patrick/32-electromagnetic-waves/radiation-pressure)
- [Polarization & Polarization Filters 30m](https://www.pearson.com/channels/physics/learn/patrick/32-electromagnetic-waves/polarization-and-polarization-filters)
- [The Doppler Effect of Light 6m](https://www.pearson.com/channels/physics/learn/patrick/32-electromagnetic-waves/the-doppler-effect-of-light)
- 33\. Geometric Optics2h 57m
Chapter worksheet
- [Ray Nature Of Light 10m](https://www.pearson.com/channels/physics/learn/patrick/33-geometric-optics/ray-nature-of-light)
- [Reflection of Light 9m](https://www.pearson.com/channels/physics/learn/patrick/33-geometric-optics/reflection-of-light)
- [Index of Refraction 16m](https://www.pearson.com/channels/physics/learn/patrick/33-geometric-optics/index-of-refraction)
- [Refraction of Light & Snell's Law 22m](https://www.pearson.com/channels/physics/learn/patrick/33-geometric-optics/refraction-of-light-and-snells-law)
- [Total Internal Reflection 5m](https://www.pearson.com/channels/physics/learn/patrick/33-geometric-optics/total-internal-reflection)
- [Ray Diagrams For Mirrors 35m](https://www.pearson.com/channels/physics/learn/patrick/33-geometric-optics/ray-diagrams-for-mirrors)
- [Mirror Equation 19m](https://www.pearson.com/channels/physics/learn/patrick/33-geometric-optics/mirror-equation)
- [Refraction At Spherical Surfaces 9m](https://www.pearson.com/channels/physics/learn/patrick/33-geometric-optics/refraction-at-spherical-surfaces)
- [Ray Diagrams For Lenses 22m](https://www.pearson.com/channels/physics/learn/patrick/33-geometric-optics/ray-diagrams-for-lenses)
- [Thin Lens And Lens Maker Equations 24m](https://www.pearson.com/channels/physics/learn/patrick/33-geometric-optics/thin-lens-and-lens-maker-equations)
- 34\. Wave Optics1h 15m
Chapter worksheet
- [Diffraction 8m](https://www.pearson.com/channels/physics/learn/patrick/wave-optics/diffraction)
- [Diffraction with Huygen's Principle 14m](https://www.pearson.com/channels/physics/learn/patrick/wave-optics/diffraction-with-huygen-s-principle)
- [Young's Double Slit Experiment 24m](https://www.pearson.com/channels/physics/learn/patrick/wave-optics/young-s-double-slit-experiment)
- [Single Slit Diffraction 27m](https://www.pearson.com/channels/physics/learn/patrick/wave-optics/single-slit-diffraction)
- 35\. Special Relativity2h 10m
Chapter worksheet
- [Inertial Reference Frames 14m](https://www.pearson.com/channels/physics/learn/patrick/special-relativity/inertial-reference-frames)
- [Special Vs. Galilean Relativity 17m](https://www.pearson.com/channels/physics/learn/patrick/special-relativity/special-vs-galilean-relativity)
- [Consequences of Relativity 52m](https://www.pearson.com/channels/physics/learn/patrick/special-relativity/consequences-of-relativity)
- [Lorentz Transformations 45m](https://www.pearson.com/channels/physics/learn/patrick/special-relativity/lorentz-transformations)
17\. Periodic Motion
Spring Force (Hooke's Law)
17\. Periodic Motion
# Spring Force (Hooke's Law): Videos & Practice Problems
[Video Lessons](https://www.pearson.com/channels/physics/learn/patrick/periodic-motion-new/spring-force-hookes-law)[Practice](https://www.pearson.com/channels/physics/exam-prep/periodic-motion-new/spring-force-hookes-law)[Worksheet](https://www.pearson.com/channels/physics/learn/patrick/periodic-motion-new/spring-force-hookes-law/worksheet)
Topic summary
When a force is applied to a spring, it compresses or stretches, demonstrating Hooke's Law, which states that the spring force (Fs) is equal to the negative of the applied force (Fa), or F=-kx, where k is the spring constant and x is the deformation. The spring force acts as a restoring force, always opposing the deformation. Understanding these principles is crucial for analyzing mass-spring systems and their motion.
Show more
1
concept
## Spring Force (Hooke's Law)
Video duration:
5m
Play a video:
AI tutor
AI tutor for
13 Comments
13 Comments for
Was this helpful?
445
Bookmarked
### Spring Force (Hooke's Law) Video Summary
When interacting with a spring, the forces at play can be understood through the concept of action and reaction pairs. When you apply a force to compress or extend a spring, the spring exerts an equal but opposite force back on you. This relationship is described by Hooke's Law, which states that the spring force (\\(F\_s\\)) is equal to the negative of the applied force (\\(F\_a\\)), mathematically represented as:
\\(F\_s = -F\_a = -k \\cdot x\\)
In this equation, \\(k\\) is the spring constant, a measure of the spring's stiffness, and \\(x\\) represents the deformation of the spring from its equilibrium position. The negative sign indicates that the spring force acts in the opposite direction to the applied force. However, when calculating magnitudes, the negative sign can be omitted, leading to the simplified equation:
\\(\|F\_s\| = k \\cdot \|x\|\\
To illustrate this, consider an example where an applied force of 120 N compresses a spring with a spring constant \\(k\\) of 20 N/m. Setting up the equation:
\\(120 = 20 \\cdot x\\
Solving for \\(x\\) gives:
\\(x = \\frac{120}{20} = 6 \\text{ meters}\\
This indicates that the spring compresses by 6 meters from its relaxed position, also known as the equilibrium position, where \\(x = 0\\).
In another scenario, if you pull on a spring, the same principles apply. Suppose the spring constant \\(k\\) is now 40 N/m, and the spring is initially 10 meters long but is pulled to 16 meters. The deformation \\(x\\) is the difference in length:
\\(x = 16 - 10 = 6 \\text{ meters}\\
Using Hooke's Law again:
\\(F\_s = k \\cdot x = 40 \\cdot 6 = 240 \\text{ N}\\
This demonstrates that increasing the spring constant results in a greater restoring force for the same deformation. The units for the spring constant \\(k\\) are expressed in newtons per meter (N/m), indicating the force required to deform the spring by one meter.
In summary, the spring force acts as a restoring force, always opposing the applied force and striving to return the system to its equilibrium position. Understanding these relationships is crucial for applying Hooke's Law effectively in various physical scenarios.
Show more
Study Smarter with Worksheets.
Follow along with each video using our printable worksheets
See worksheets
2
Problem
## A 1.0 m-long spring is laid horizontally with one of its ends fixed. When you pull on it with 50 N, it stretches to 1.2 m. (a) What is the spring's force constant (b) How much force is needed to compress it to 0.7 m?
A
250 N/m; 175 N
B
50 N/m; 15 N
C
250 N/m; 75 N
D
50 N/m; 35 N
AI tutor
AI tutor for
0 Comments
0 Comments for
Show Answer
Show Answer for
More options for
3
concept
## Acceleration of Mass-Spring Systems
Video duration:
3m
Play a video:
AI tutor
AI tutor for
1 Comment
1 Comment for
Was this helpful?
138
Bookmarked
### Acceleration of Mass-Spring Systems Video Summary
When a mass is attached to a spring, it forms a mass-spring system, where the spring exerts a force in response to an applied force. The spring force, denoted as \\( F\_s \\), acts in the opposite direction of the applied force \\( F\_A \\). This relationship can be expressed mathematically as:
\\( F\_s = -F\_A = -k \\cdot x \\)
Here, \\( k \\) represents the spring constant, and \\( x \\) is the displacement from the equilibrium position. The negative sign indicates that the spring force opposes the direction of the applied force. In a static situation where the mass is held in place, the net force is zero, leading to the equation:
\\( m \\cdot a = 0 \\
Since the mass of the spring is negligible, the acceleration \\( a \\) is also zero when the applied force is balanced by the spring force. However, when the applied force is removed, the spring force becomes the only force acting on the mass, which can be described by:
\\( F\_s = m \\cdot a \\
Substituting the spring force equation gives:
\\( -k \\cdot x = m \\cdot a \\
This leads to the formula for acceleration:
\\( a = -\\frac{k}{m} \\cdot x \\
The negative sign indicates that the acceleration is directed opposite to the displacement. For example, consider a block with a mass of 0.60 kg attached to a spring with a spring constant \\( k = 15 \\, \\text{N/m} \\), stretched 0.2 meters from its equilibrium position. To find the spring force acting on the block, we use:
\\( F\_s = -k \\(\\cdot\\) x = -15 \\(\\cdot\\) 0.2 = -3 \\, \\(\\text{N}\\) \\
The negative value indicates that the force acts to the left, opposing the stretch. To calculate the acceleration, we apply the derived formula:
\\( a = -\\(\\frac{15}{0.6}\\) \\(\\cdot\\) 0.2 = -5 \\, \\(\\text{m/s}\\)^2 \\
Again, the negative sign signifies that the acceleration is directed to the left, consistent with the direction of the spring force. This understanding of the mass-spring system illustrates the fundamental principles of forces, motion, and equilibrium in physics.
Show more
4
Problem
## You push a 3-kg mass against a spring and release it from rest. Its maximum acceleration is 10m/s2 when pushed back 0.5m. What is the (a)spring constant and (b) restoring force at this point?
A
60 N/m; 30 N
B
120 N/m; 45 N
C
100 N/m; 35 N
D
30 N/m; 15 N
AI tutor
AI tutor for
3 Comments
3 Comments for
Show Answer
Show Answer for
More options for
## Do you want more practice?
[More sets](https://www.pearson.com/channels/physics/exam-prep?chapterId=1450d765)
[Spring Force (Hooke's Law) 17. Periodic Motion 7 problems Topic  Patrick](https://www.pearson.com/channels/physics/exam-prep/set/default/spring-force-hookes-law)
[17\. Periodic Motion - Part 1 of 2 4 topics 10 problems Chapter  Patrick](https://www.pearson.com/channels/physics/exam-prep/set/default/17-periodic-motion-part-1-of-2)
[17\. Periodic Motion - Part 2 of 2 3 topics 9 problems Chapter  David-Paige](https://www.pearson.com/channels/physics/exam-prep/set/default/17-periodic-motion-part-2-of-2)
Show more
## Go over this topic definitions with flashcards
[More sets](https://www.pearson.com/channels/physics/flashcards)
- [Spring Force (Hooke's Law) definitions 17. Periodic Motion 15 Terms **1** student found this helpful](https://www.pearson.com/channels/physics/flashcards/topics/spring-force-hookes-law/spring-force-hookes-law-definitions)
- [Spring Force (Hooke's Law) quiz 17. Periodic Motion 15 Terms](https://www.pearson.com/channels/physics/flashcards/topics/spring-force-hookes-law/spring-force-hookes-law-quiz)
Take your learning anywhere\!
Prep for your exams on the go with video lessons and practice problems in our mobile app.
Continue in the app
## Here’s what students ask on this topic:
### What is Hooke's Law and how is it mathematically represented?
Hooke's Law states that the force exerted by a spring is directly proportional to the displacement or deformation of the spring from its equilibrium position. Mathematically, it is represented as:
F \= \- k x
where F is the spring force, k is the spring constant, and x is the deformation. The negative sign indicates that the force exerted by the spring is in the opposite direction of the applied force.
### How do you calculate the spring constant (k) in Hooke's Law?
The spring constant k can be calculated using Hooke's Law formula:
F \= \- k x
Rearranging the formula to solve for k gives:
k \= F x
Here, F is the force applied to the spring, and x is the deformation of the spring. The units of k are Newtons per meter (N/m).
### What is the significance of the negative sign in Hooke's Law?
The negative sign in Hooke's Law, F \= \- k x, indicates that the spring force is a restoring force. This means that the force exerted by the spring is always in the opposite direction of the applied force. If you compress the spring, it pushes back; if you stretch the spring, it pulls back. The negative sign ensures that the spring force always acts to return the spring to its equilibrium position.
### How do you determine the deformation of a spring when a force is applied?
To determine the deformation x of a spring when a force F is applied, you can use Hooke's Law:
F \= \- k x
Rearranging the formula to solve for x gives:
x \= F \- k
Here, F is the applied force, and k is the spring constant. The deformation x is measured in meters (m).
### What is a mass-spring system and how does it relate to Hooke's Law?
A mass-spring system consists of a mass attached to a spring. When the mass is displaced from its equilibrium position, the spring exerts a restoring force described by Hooke's Law:
F \= \- k x
In this system, the mass experiences an acceleration due to the spring force, which can be described by Newton's second law:
F \= m a
Combining these equations gives:
\- k x \= m a
This relationship helps analyze the motion of the mass-spring system, including oscillations and vibrations.
[Previous Topic: Angular Momentum of Objects in Linear Motion](https://www.pearson.com/channels/physics/learn/patrick/angular-momentum/angular-momentum-of-objects-in-linear-motion)[Next Topic: Intro to Simple Harmonic Motion (Horizontal Springs)](https://www.pearson.com/channels/physics/learn/patrick/periodic-motion-new/intro-to-simple-harmonic-motion-horizontal-springs)
### Your Physics tutor
[ Patrick Ford Physics and Maths lead instructor](https://www.pearson.com/channels/tutors/patrick-ford)
[Download the Mobile app](https://www.pearson.com/en-us/pearsonplus/mobile-app.html)
[Terms of use](https://www.pearson.com/en-us/legal-information/terms-of-use.html)
Cookies
[Accessibility](https://www.pearson.com/en-us/legal-information/accessibility.html)
[Privacy](https://www.pearson.com/en-us/pearsonplus/legal/user-privacy-policy.html)
[Do not sell my personal information](https://www.pearson.com/en-us/pearsonplus/legal/cookie-policy.html)
[Patent notice](https://www.pearson.com/en-us/pearsonplus/legal/patent-notice.html)
[Sitemap](https://www.pearson.com/channels/sitemap)
[AI Tutor](https://www.pearson.com/channels/ai-tutor)
[Online Calculators](https://www.pearson.com/channels/calculators)
[Blog](https://www.pearson.com/channels/blog)
© 1996–2026 Pearson All rights reserved.
Need help with this topic?
Practice quizzes, ask questions and more
## Privacy and cookies
We and our third-party partners use cookies and similar technologies to run the website. Some cookies are strictly necessary. We also use optional cookies to provide a more personalized experience, improve the way our websites work and support our marketing operations. Optional cookies will only be set with your consent. You can manage your cookie preferences through the "Cookie Settings" button. For more information see our [Privacy Notice](https://www.pearson.com/en-gb/privacy-center/privacy-notices.html)
Cookie Settings
Reject All
Accept All
## Pearson Privacy Preference Center
When you visit any website, it may store or retrieve information on your browser, mostly in the form of cookies. This information might be about you, your preferences or your device and is mostly used to make the site work as you expect it to. The information does not usually directly identify you, but it can give you a more personalized web experience. Because we respect your right to privacy, you can choose not to allow some types of cookies. Click on the different category headings to find out more and change our default settings. However, blocking some types of cookies may impact your experience of the site and the services we are able to offer.
[More information](https://www.pearson.com/en-us/legal-information/cookie-policy.html)
Allow All
### Manage Consent Preferences
#### Strictly Necessary Cookies
Always Active
These cookies are necessary for the website to function and cannot be switched off in our systems. They are usually only set in response to actions made by you which amount to a request for services, such as setting your privacy preferences, logging in or filling in forms. You can set your browser to block or alert you about these cookies, but some parts of the site will not then work. These cookies do not store any personally identifiable information.
View Vendor Details
#### Functional Cookies
Functional Cookies
These cookies enable the website to provide enhanced functionality and personalisation. They may be set by us or by third party providers whose services we have added to our pages. If you do not allow these cookies then some or all of these services may not function properly.
View Vendor Details
#### Performance Cookies
Performance Cookies
These cookies allow us to count visits and traffic sources so we can measure and improve the performance of our site. They help us to know which pages are the most and least popular and see how visitors move around the site. All information these cookies collect is aggregated and therefore anonymous. If you do not allow these cookies we will not know when you have visited our site, and will not be able to monitor its performance.
View Vendor Details
#### Targeting Cookies
Targeting Cookies
These cookies may be set through our site by our advertising partners. They may be used by those companies to build a profile of your interests and show you relevant adverts on other sites. They do not store directly personal information, but are based on uniquely identifying your browser and internet device. If you do not allow these cookies, you will experience less targeted advertising.
View Vendor Details
### Vendors List
Clear
- checkbox label
label
Apply
Cancel
Consent Leg.Interest
checkbox label
label
checkbox label
label
checkbox label
label
Reject All
Confirm My Choices
[](https://www.onetrust.com/products/cookie-consent/) | ||||||
| Readable Markdown | 17\. Periodic Motion
Spring Force (Hooke's Law): Videos & Practice Problems
Topic summary
When a force is applied to a spring, it compresses or stretches, demonstrating Hooke's Law, which states that the spring force (Fs) is equal to the negative of the applied force (Fa), or F=-kx, where k is the spring constant and x is the deformation. The spring force acts as a restoring force, always opposing the deformation. Understanding these principles is crucial for analyzing mass-spring systems and their motion.
1
concept
Video duration:
5m
Spring Force (Hooke's Law) Video Summary
When interacting with a spring, the forces at play can be understood through the concept of action and reaction pairs. When you apply a force to compress or extend a spring, the spring exerts an equal but opposite force back on you. This relationship is described by Hooke's Law, which states that the spring force (\\(F\_s\\)) is equal to the negative of the applied force (\\(F\_a\\)), mathematically represented as: \\(F\_s = -F\_a = -k \\cdot x\\) In this equation, \\(k\\) is the spring constant, a measure of the spring's stiffness, and \\(x\\) represents the deformation of the spring from its equilibrium position. The negative sign indicates that the spring force acts in the opposite direction to the applied force. However, when calculating magnitudes, the negative sign can be omitted, leading to the simplified equation: \\(\|F\_s\| = k \\cdot \|x\|\\ To illustrate this, consider an example where an applied force of 120 N compresses a spring with a spring constant \\(k\\) of 20 N/m. Setting up the equation: \\(120 = 20 \\cdot x\\ Solving for \\(x\\) gives: \\(x = \\frac{120}{20} = 6 \\text{ meters}\\ This indicates that the spring compresses by 6 meters from its relaxed position, also known as the equilibrium position, where \\(x = 0\\). In another scenario, if you pull on a spring, the same principles apply. Suppose the spring constant \\(k\\) is now 40 N/m, and the spring is initially 10 meters long but is pulled to 16 meters. The deformation \\(x\\) is the difference in length: \\(x = 16 - 10 = 6 \\text{ meters}\\ Using Hooke's Law again: \\(F\_s = k \\cdot x = 40 \\cdot 6 = 240 \\text{ N}\\ This demonstrates that increasing the spring constant results in a greater restoring force for the same deformation. The units for the spring constant \\(k\\) are expressed in newtons per meter (N/m), indicating the force required to deform the spring by one meter. In summary, the spring force acts as a restoring force, always opposing the applied force and striving to return the system to its equilibrium position. Understanding these relationships is crucial for applying Hooke's Law effectively in various physical scenarios.
Study Smarter with Worksheets.
Follow along with each video using our printable worksheets
2
Problem
A 1.0 m-long spring is laid horizontally with one of its ends fixed. When you pull on it with 50 N, it stretches to 1.2 m. (a) What is the spring's force constant (b) How much force is needed to compress it to 0.7 m?
A
250 N/m; 175 N
B
50 N/m; 15 N
C
250 N/m; 75 N
D
50 N/m; 35 N
3
concept
Acceleration of Mass-Spring Systems
Video duration:
3m
Acceleration of Mass-Spring Systems Video Summary
When a mass is attached to a spring, it forms a mass-spring system, where the spring exerts a force in response to an applied force. The spring force, denoted as \\( F\_s \\), acts in the opposite direction of the applied force \\( F\_A \\). This relationship can be expressed mathematically as: \\( F\_s = -F\_A = -k \\cdot x \\) Here, \\( k \\) represents the spring constant, and \\( x \\) is the displacement from the equilibrium position. The negative sign indicates that the spring force opposes the direction of the applied force. In a static situation where the mass is held in place, the net force is zero, leading to the equation: \\( m \\cdot a = 0 \\ Since the mass of the spring is negligible, the acceleration \\( a \\) is also zero when the applied force is balanced by the spring force. However, when the applied force is removed, the spring force becomes the only force acting on the mass, which can be described by: \\( F\_s = m \\cdot a \\ Substituting the spring force equation gives: \\( -k \\cdot x = m \\cdot a \\ This leads to the formula for acceleration: \\( a = -\\frac{k}{m} \\cdot x \\ The negative sign indicates that the acceleration is directed opposite to the displacement. For example, consider a block with a mass of 0.60 kg attached to a spring with a spring constant \\( k = 15 \\, \\text{N/m} \\), stretched 0.2 meters from its equilibrium position. To find the spring force acting on the block, we use: \\( F\_s = -k \\(\\cdot\\) x = -15 \\(\\cdot\\) 0.2 = -3 \\, \\(\\text{N}\\) \\ The negative value indicates that the force acts to the left, opposing the stretch. To calculate the acceleration, we apply the derived formula: \\( a = -\\(\\frac{15}{0.6}\\) \\(\\cdot\\) 0.2 = -5 \\, \\(\\text{m/s}\\)^2 \\ Again, the negative sign signifies that the acceleration is directed to the left, consistent with the direction of the spring force. This understanding of the mass-spring system illustrates the fundamental principles of forces, motion, and equilibrium in physics.
4
Problem
You push a 3-kg mass against a spring and release it from rest. Its maximum acceleration is 10m/s2 when pushed back 0.5m. What is the (a)spring constant and (b) restoring force at this point?
A
60 N/m; 30 N
B
120 N/m; 45 N
C
100 N/m; 35 N
D
30 N/m; 15 N
## Go over this topic definitions with flashcards
[More sets](https://www.pearson.com/channels/physics/flashcards)
- [Spring Force (Hooke's Law) definitions 17. Periodic Motion 15 Terms **1** student found this helpful](https://www.pearson.com/channels/physics/flashcards/topics/spring-force-hookes-law/spring-force-hookes-law-definitions)
- [Spring Force (Hooke's Law) quiz 17. Periodic Motion 15 Terms](https://www.pearson.com/channels/physics/flashcards/topics/spring-force-hookes-law/spring-force-hookes-law-quiz)
Take your learning anywhere\!
Prep for your exams on the go with video lessons and practice problems in our mobile app.
## Here’s what students ask on this topic:
### Your Physics tutor | ||||||
| ML Classification | |||||||
| ML Categories |
Raw JSON{
"/Science": 927,
"/Science/Physics": 800
} | ||||||
| ML Page Types |
Raw JSON{
"/Article": 777,
"/Article/Tutorial_or_Guide": 753
} | ||||||
| ML Intent Types |
Raw JSON{
"Informational": 999
} | ||||||
| Content Metadata | |||||||
| Language | en | ||||||
| Author | null | ||||||
| Publish Time | not set | ||||||
| Original Publish Time | 2022-08-03 13:18:36 (3 years ago) | ||||||
| Republished | No | ||||||
| Word Count (Total) | 4,152 | ||||||
| Word Count (Content) | 1,023 | ||||||
| Links | |||||||
| External Links | 1 | ||||||
| Internal Links | 356 | ||||||
| Technical SEO | |||||||
| Meta Nofollow | No | ||||||
| Meta Noarchive | No | ||||||
| JS Rendered | Yes | ||||||
| Redirect Target | null | ||||||
| Performance | |||||||
| Download Time (ms) | 786 | ||||||
| TTFB (ms) | 776 | ||||||
| Download Size (bytes) | 56,945 | ||||||
| Shard | 60 (laksa) | ||||||
| Root Hash | 7904195208629309660 | ||||||
| Unparsed URL | com,pearson!www,/channels/physics/learn/patrick/periodic-motion-new/spring-force-hookes-law s443 | ||||||