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1. Homework Statement

1. Homework Statement

A block of known mass

**m**is attached to the free end of a spring, on a flat horizontal surface without friction. The spring is compressed by a known distance

**x**, and then released. The elastic constant of the spring is known

**K**. Calculate:

a. The energy stored in the spring while it's compressed.

b. The Work done by the spring to extend.

c. The speed of the block when the spring passes by its rest position point.

## Homework Equations

Energy stored in spring = 0.5 * K * x

^{2}

Sum of non-conservative forces Work = Mechanical Energy at the end - Mechanical Energy at the start

Kinetic energy = 0.5 * m * v

^{2}

## The Attempt at a Solution

So, what bothers me here are the points a. and b.

The energy stored in the spring should be:

0.5 * K * x

^{2}

The Work done by the spring to extend should be...? I'm assuming they refer to the work done from when the spring is released until it goes back to its rest position. So it should regularly be, again:

0.5*K * x

^{2}

...shouldn't it?

Third point should be simply:

0 = ME_end - ME_start => ME_start = ME_end =>

=> 0.5* k * x

^{2}+ 0.5*m*v

_{0}

^{2}= 0.5* k * x

_{0}

^{2}+ 0.5*m*v

_{f}

^{2}

So v

_{f}= sqrt (k * x

^{2}/ m)