Question

A box slides on a frictionless surface with a total energy of 50 J. It hits a spring and compresses the spring of a distance of 25 cm from equilibrium. If the same box with the same initial energy slides on a rough surface, it only compresses the spring a distance of 15 cm, how much energy must have been lost by sliding on the rough surface?

Answer 1

Use the law of conservation of energy( which states that when gravity is the only external influence on an object its mechanical energy remains constant )to to obtain the spring constant.

Therefore

$E_A=E_B$

$E_A=50,E_B=\frac{1}{2}\space kb^{2}$

$50=\frac{1}{2}kb^{2}$

$k=\frac{50\times2}{0.25^{2}}=1600NM^{-1}$

Now using the force constant to calculate the energy that compressed the spring a distance of 0.15 m

$E=\frac{1}{2}\space\times1600\times0.15^{2}=18J$

Energy that must have been lost by sliding through the rough surface is the total energy less the energy that compressed the spring

$50-18=32J$

Answer= 32 J