The spring is compressed a total of 3.0 cm, and used to set a 500 gram cart into motion. find the speed of the cart at the instant it is released, assuming all the elastic potential energy is converted.

1.15 m/s

Explanation:

Part of the question is missing. Found the missing part on google:

"1. A hanging mass of 1500 grams compresses a spring 2.0 cm.   Find the spring constant in N/m."

Solution:

First of all, we need to find the spring constant. We can use Hooke's law:

where

is the force applied to the spring (the weight of the hanging mass)

x = 2.0 cm = 0.02 m is the compression of the spring

Solving for k, we find the spring constant:

In the second part of the problem, the spring is compressed by

x = 3.0 cm = 0.03 m

So the elastic potential energy of the spring is

This energy is entirely converted into kinetic energy of the cart, which is:

where

m = 500 g = 0.5 kg is the mass of the cart

v is its speed

Solving for v,

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explanation: