Tina squeezes a spring, she knows the spring is storing 321 J of energy and that the spring was distorted by 0.070 m. What is the force Tina is applying to the spring?

Question

Tina squeezes a spring, she knows the spring is storing 321 J of energy and that the spring was distorted by 0.070 m. What is the force Tina is applying to the spring?

Answer 1

Hi Connor,

First, let's establish our given information:

Potential energy = 321 J

Distance (distortion) = 0.070 m

Because we have this information, we can use the formula for the potential energy of a spring:

PE = 1/2 (kx²)

where PE is potential energy, x is the distortion applied to the spring by Tina (measured in meters), and k is the spring constant, which tells you how stiff the spring is, and therefore how much force is needed to distort it.

When we fill in this equation with our given information, we find that we can solve for k, our spring constant. However, this doesn't answer the question of how much force Tina applies to the spring—we need a different formula for that:

F = -kx

This formula, our spring force formula, is given by Hooke's Law. When we input our spring constant for k and our distance for x, we get the force, in Newtons, that Tina applied to the spring to distort it by 0.070 meters.

I hope this is helpful!

-Courtney