# How fast does a mass leave a spring?

## Homework Statement

A student uses a force of 24.1 Newtons to push on a 338 gram (.338 kg) mass to compress a spring a horizontal spring a distance of 11.5 centimeters (.115 m). When the student lets go of the mass, the spring uncompresses and shoots the mass away from it.

a) How fast does the mass leave the spring?

b) The spring mass slides along a frictionless surface until it comes to a frictionless incline. How high does it move up the incline.

## Homework Equations

F = -kx for part a)
I'm pretty sure that b) requires me to relate the problem to energy or power, but I'm not sure how.

## The Attempt at a Solution

I assumed that the mass would leave the spring with an acceleration cause by the spring uncompressing. Since 24.1 Newtons was used to compress the spring, the restoring force would also be 24.1 Newtons. Since F=ma, then the mass should accelerate at 71.3 m/s^2.

^This turned out to be wrong. Can someone help me, please.

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I think it would be a wise choice to use energy in this problem. If you find the energy stored in the object at compression, you can use the conversation of energy and potential energy concepts to find the height.

Also, you would have to use these formulas

Energy stored in spring = 1/2 * k * x ^ 2

This formula is more intuitive if you understand the derivation.

x= Distance compressed
k= Spring constant

Energy stored in vertical height = m * g * h

This formula is just a special case of Work= Force * Distance
where the Force = Mass * Gravity

h (m)= Height above a given reference point, in your case it is the ground.
g (m/s/s)= Gravitational acceleration at that given height (Sometimes just assumed to be ~9.8).
m (kg)= Mass of object.

Thank you.