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UExcel Physics: Study Guide & Test Prep17 chapters | 188 lessons

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Lesson Transcript

Instructor:
*David Wood*

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.

After every Thanksgiving, consuming absurd amounts of turkey, stuffing, mashed potatoes and cranberry sauce, I'm extremely thankful for elastic waistbands. And it's probably a good thing that bungee cords stretch just the right amount. But how exactly do these materials work?

**Elasticity** is a property of a material which allows it to return to its original shape or length after being distorted. Some materials are not at all elastic -- they are brittle and will snap before they bend or stretch. Others, like rubber, for example, will stretch a long way without significant warping or cracking. This is because the materials contain long chain molecules that are wrapped up in a bundle and can straighten out when stretched. Those are the materials we choose for things like waistbands.

But in physics we like numbers. One important number that relates to elasticity is the spring constant. The **spring constant** is a number that represents how much force it takes to stretch a material -- materials with larger spring constants are stiffer.

So these are our properties to describe the stretchiness of materials -- elasticity and the spring constant. But what happens when you're in the process of stretching out a rubber band? Do you need more force at first and less once you've stretched part way? Perhaps it's the other way around? The relationship could be almost anything -- linear, quadratic, variable... so what did scientists discover when they started investigating elastic materials?

Robert Hooke investigated how springs and elastic materials stretch. **Hooke's Law** states that the force needed to compress or extend a spring is directly proportional to the distance you stretch it. Or, in other words, the more you stretch something, the harder it becomes to keep stretching it. It's a linear relationship. Or you could think of it this way: As you stretch something out, there is a restoring force that you have to compete with. That restoring force is trying to spring the object back to how it started.

As an equation, Hooke's Law says that the force applied in newtons (or the restoring force -- it amounts to the same thing) is equal to the negative of the spring constant, *k*, of the material, multiplied by the extension, *x*, of the material, measured in meters. We use the negative sign when we're talking about the restoring force because the restoring force is in the opposite direction to the extension. But if *F* is the force we apply, then the negative sign goes away, and it's just *F* = *kx*.

Okay, let's have a go at applying this equation. Let's say we have a spring that's 2 meters in length, and we stretch it to a length of 7 meters. If the spring constant of the spring is 0.1, what restoring force did the spring apply as we stretched it?

First of all, we should write down what we know. The spring constant, *k*, equals 0.1, the initial length is 2 meters, and the final length is 7 meters...this means that the extension, *x*, must be 7 - 2, which equals 5 meters. Plug these numbers into Hooke's Law, and solve for *F*, and we get negative 0.5 newtons. So the restoring force was 0.5 newtons. Or equivalently, we had to apply a positive 0.5 newtons force to stretch the spring.

And that's it; that's our answer.

**Elasticity** is a property of a material which allows it to return to its original shape or length after being distorted. To put a number to elasticity, we use the spring constant. The **spring constant** is a number that represents how much force it takes to stretch a material -- materials with larger spring constants are stiffer.

Hooke's Law tells us how this spring constant relates to the force we need to apply to stretch the object. **Hooke's Law** states that the force needed to compress or extend a spring is directly proportional to the distance you stretch it. As an equation, Hooke's Law can be represented as *F* = *kx*, where *F* is the force we apply, *k* is the spring constant, and *x* is the extension of the material (typically in meters).

Understanding elasticity is important for all kinds of mechanical applications, including the manufacture of my stretchy waistbands. One thing's for sure -- without physics, bungee jumping would be a much more messy endeavor.

When you are finished, you should be able to:

- State the two terms used to describe stretchiness in physics
- Recite Hooke's Law
- Calculate the force needed to stretch something using Hooke's Law

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UExcel Physics: Study Guide & Test Prep17 chapters | 188 lessons

- Go to Vectors

- Go to Kinematics

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