Question

A 15 kg runaway grocery cart runs into a spring with spring constant 230 N/m and compresses it by 56 cm .What was the speed of the cart just before it hit the spring?

Answer 1

To solve this problem we will apply the concepts related to the conservation of kinetic energy and elastic potential energy. Thus we will have that the kinetic energy is

$KE = \frac{1}{2} mv^2$

And the potential energy is

$PE = \frac{1}{2} kx^2$

Here,

m = mass

v = Velocity

x = Displacement

k = Spring constant

There is equilibrium, then,

KE = PE

$\frac{1}{2} mv^2 = \frac{1}{2} kx^2$

Our values are given as,

$x=0.56m\\k=230N/m\\m=15kg$

Replacing we have that

$\frac{1}{2} (15)v^2 = \frac{1}{2} (230)(0.56)^2$

$v = 2.19m/s$

Therefore the speed of the cart is 2.19m/s