# Practice Applying Spring Constant Formulas

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• 0:04 Spring Constant Formula
• 1:08 Calculating the Spring…
• 2:13 Two-Step Problems
• 3:54 Comparing the Effect…
• 4:58 Calculating Displacement
• 6:11 Lesson Summary

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Lesson Transcript
Instructor: Amanda Robb
In this lesson, you'll have the chance to practice using the spring constant formula. The lesson includes four problems of medium difficulty involving a variety of real-life applications.

## Spring Constant Formula

Have you ever played with a slinky? A slinky is a type of spring. When you hang the slinky, it will spring back and forth until it settles at equilibrium. The motion of the slinky is based on an idea called the spring constant.

All springs have a characteristic called a spring constant, which describes the strength of a spring. If a spring is very stiff, it has a high spring constant, while a spring with a low spring constant, like a worn-out slinky, is very loose.

Robert Hooke was a scientist that came up with the spring constant formula that describes how much force a given spring exerts if it's stretched over a particular distance:

F = -kx

Here, F is the applied force measured in Newtons (N), k is the spring constant measured in Newtons per meter (N/m) and x is the displacement the spring travels measured in meters (m). The negative sign means that the spring moves in the opposite direction of the force. If you pull a spring down, it moves in the opposite direction when you release it.

## Calculating the Spring Constant

When solving any physics problem, identify the question, the information you're given and the equations you need to use. Let's apply this approach to a spring constant problem.

You hang a spring from a ring stand and apply 20N of downward force. If the spring compresses with a displacement of 0.1m, what is the spring constant of this spring?

Let's apply the strategy we just discussed to this problem:

• What are you looking for? The spring constant.
• What information are you given? A force of -20N, since you are pulling the spring down, and a displacement of 0.1m.
• What equation should you use? F = -kx.

You know the spring constant equation, but you need to rearrange it to solve for the spring constant:

• F = -kx
• k = -F / x

Now, plug in the values and solve:

• k = -(-20N) * 0.1m
• k = 2N/m

## Two-Step Problems

Sometimes you don't have all the information you need to complete a problem in one step. To solve multistep problems, you can apply the same strategy we just used. Let's look at an example.

A girl with a mass of 56kg sits on a metal horse held up by a spring on a playground. If the spring constant is 1,000N/m, how far will the spring sink when she sits on it?

Here you want to know the displacement of the spring, or how far it will move from its resting position when force is applied. You know that the girl has a mass of 56kg and that the spring constant is 1,000N/m. To use the spring constant equation, you need to know the mass. Is there any information you could use to solve for mass?

You may have learned that force is equal to mass multiplied by acceleration, or F = mg. Since the girl's mass is pushing down on the spring, you can use the acceleration due to gravity (g).

The value of g is constant for everything on Earth and is equal to -9.8m/s2.

You can use the F = mg formula to solve for force:

• F = 56kg * -9.8m/s2
• F = -549N

You now have all the variables you need to solve for displacement in the spring constant equation:

• F = -kx
• x = -F / k
• x = -(-549N) / 1,000N/m
• x = 0.549m

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