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Spring Force & Elasticity

Even if you've never played with a spring before, you've definitely used something that has a spring inside: a mattress, a watch, a retractable pen, a scale, or maybe a door that closes on its own. All of these things rely on a spring force to function.

The spring force is pretty simple: if you pull the ends of a spring apart the spring gets longer, and if you push the ends of a spring together the spring gets shorter. And we know from Newton's 3rd law that if you pull or push a spring, the spring pulls or pushes you back with the same force.

In this lesson we'll cover Hooke's law which relates the spring force and the amount that the spring changes length, which depends on the spring constant (which describes the stiffness of the spring). We're only going to work with what we call "ideal springs", which means the spring force varies linearly with the change in length.

We'll also learn about combining springs in series and in parallel to get an "equivalent spring constant".

Finally, we'll learn how this spring-like behavior applies to the elasticity of materials. A rubber band is one example, but it turns out that everything stretches when you apply a force to it - every material actually behaves like a spring.

Springs & Hooke's Law - Part 1 - Introduction (10:30)
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Springs and elasticity

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What is a spring?

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Examples of objects that use springs

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All materials behave like springs

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How does a scale work?

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Spring force, change in length and spring stiffness

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Hooke's law (spring force) equation
Springs & Hooke's Law - Part 2 - Equation and Variables (19:46)
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Spring constant (k)

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Change in length (Δx)

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Spring force (F)

1. Spring Force

2. Elasticity of Materials

Explore this topic

Coming soon! Check out the teaching slides on the Projectile Motion page to see an example.

Study guide with variables, equations and examples of spring force, spring constants and Hooke's Law
Study guide for combining springs in series and parallel, and how to find the equivalent spring constant
Study guide with the variables, equations and examples for elasticity of materials, stress, strain and Young's modulus
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Spring Force and Hooke's Law
Elasticity of Materials
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AP Physics 1 multiple choice questions (MCQ) for spring force and Hooke's law

Answers

Answer and solutions for the AP Physics 1 multiple choice questions (MCQ) for spring force and Hooke's law

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Free-Response Questions

Springs

  • 2024 Q2 - - (Experimental design) Masses oscillating on a spring, simple harmonic motion, energy, momentum
  • 2024 Q4 - - Pendulum on different planets, law of gravitation, simple harmonic motion, work, spring force
  • 2023 Q1 - - Cart oscillating on horizontal spring, simple harmonic motion, energy, work
  • 2023 Q3 - - Block and spring rotating about axle, circular motion, centripetal force, FBDs
  • 2022 Q1 - - Pulley system with 2 blocks and a spring, kinematics, forces, energy, work
  • 2022 Q5 - - Mass oscillating on a vertical spring, simple harmonic motion, energy, work
  • 2019 Q3 - - (Experimental design) Sphere is launched with a spring plunger, projectile motion, energy
  • 2015 Q3 - - Block-spring system sliding on surface, energy, work, friction

Even if you've never played with a spring before, you've definitely used something that has a spring inside: a mattress, a watch, a retractable pen, a scale, or maybe a door that closes on its own. All of these things rely on a spring force to function.

The spring force is pretty simple: if you pull the ends of a spring apart the spring gets longer, and if you push the ends of a spring together the spring gets shorter. And we know from Newton's 3rd law that if you pull or push a spring, the spring pulls or pushes you back with the same force.

In this lesson we'll cover Hooke's law which relates the spring force and the amount that the spring changes length, which depends on the spring constant (which describes the stiffness of the spring). We're only going to work with what we call "ideal springs", which means the spring force varies linearly with the change in length.

We'll also learn about combining springs in series and in parallel to get an "equivalent spring constant".

Finally, we'll learn how this spring-like behavior applies to the elasticity of materials. A rubber band is one example, but it turns out that everything stretches when you apply a force to it - every material actually behaves like a spring.

Preview of the AP Physics 1 multiple choice questions (MCQ) for spring force and Hooke's law
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