Question

find the amount of energy e dissipated by friction by the time the block stops. express your answer in terms of some or all the variables m, v, and h and any appropriate constants. view available hint(s) e = submit

Explanation:

Step1: Apply Energy Conservation

The initial energy of the block includes kinetic energy ($\frac{1}{2}mv^2$) and gravitational potential energy ($mgh$). When the block stops, its final kinetic energy is 0, and the energy dissipated by friction equals the initial total mechanical energy (by energy conservation, as friction converts mechanical energy to thermal energy).

So, the initial total energy is $E_{initial} = \frac{1}{2}mv^2 + mgh$.

Since the final energy (kinetic + potential) is 0 (block stops, assume it comes to rest at the same or relevant height, but here we consider the total initial mechanical energy dissipated), the energy dissipated by friction $E$ equals the initial total mechanical energy.

Step2: Determine Dissipated Energy

The energy dissipated by friction $E$ is equal to the initial total mechanical energy, so $E = \frac{1}{2}mv^2 + mgh$.

Answer:

$\frac{1}{2}mv^2 + mgh$