How can you express the energy dissipated by friction when the block stops?

The energy dissipated by friction when the block stops can be expressed as the total initial mechanical energy of the block, which consists of its kinetic energy and gravitational potential energy.

When the block is in motion, it possesses kinetic energy given by the formula ( \frac{1}{2} mv^2 ), where ( m ) is the mass of the block and ( v ) is its velocity. If the block is also at a height ( h ) above a reference level, it has gravitational potential energy represented by ( mgh ), where ( g ) is the acceleration due to gravity.

As the block comes to a stop due to the work done by friction, all of this initial mechanical energy is converted into heat energy due to friction. Therefore, the total energy dissipated by friction when the block stops is the sum of its initial kinetic and potential energies:

[ E = \frac{1}{2} mv^2 + mgh. ]

This indicates that the energy involved in bringing the block to rest is equal to the sum of its kinetic and potential energy before it stops. The other choices do not account for both forms of energy or represent them incorrectly, which is why they do not correctly express