# A box slides down a frictionless hill. The spring stops it. When the box stops, how much has the...

## Question:

A box slides down a frictionless hill. The spring stops it. When the box stops, how much has the spring compressed? The hill is 5 m high, the mas of the box is 20 kg, and the spring constant is 350 n/m.

## Conservation of energy:

Conservation of energy principle shows that the energy cannot be created by any means or cannot be destroyed during the process. According to which the energy is interconvertible in nature and can be converted from one form to another, for example, potential energy can be converted into kinetic energy during the conversion.

Given

Height of the hill is {eq}h= 5\ m {/eq}

Mass of the box is {eq}m= 20\ kg {/eq}

Now for the potential energy stored inside the box at the top :

{eq}P.E= mgh\\ P.E =20\times 9.81\times 5\\ P.E= 981\ J {/eq}

This potential energy will be converted into the kinetic energy at the bottom of the slide:

{eq}K.E= 981\ J {/eq}

This kinetic energy is used to compress the spring and will be converted into the spring potential energy :

{eq}981=\frac{1}{2}kx^2\\ 981=\frac{1}{2}(350)\times x^2\\ x^2=2.36\ m {/eq}

Thus, the displacement of the spring is 2.36 m 