Physics elastic potential energy question

Question

A spring-loaded toy uses a compressed spring to fire a marble out of a tube. A force of 220 N

compresses the spring by 0.14 m. Calculate the elastic potential energy of the toy.

Answer 1

First the equations we need for this are the equations for force of a spring and potential energy of a spring. Those are as follows:

F = -kx (note this already accounts for compression of a spring with the negative sign. If the spring were being stretched, it would be positive.)

U = (1/2)kx²

Next, write out what we know.

F = 220N

x = 0.14m (this is the amount the spring is displaced from equilibrium)

From here, we can see what we ultimately want is U, but we don't know k. We do know F and x though, so start by solving for k in the first equation.

F = -kx

F/x = -k

-F/x = k

Then, we plug in the values:

-220N/0.14m = 1571.43N/m

Now we have k. Plug k and x into the equation for U.

U = (1/2)kx²

U = (1/2)(1571.43N/m)(0.14m)²

U = 15.4 J

Perform a unit check:

(N/m) * (m²) = N*m = J

This is the unit for energy, so we've done our math correctly.

Final step: profit with your new knowledge!