Question

Ali is pushing a 55 kg desk across the classroom floor with a constant velocity. The coefficient of kinetic friction between the floor and the desk is 0.4. If Ali is pushing the desk by applying a force directed at 45 degrees below the horizontal how much work is Ali doing in pushing the desk a distance of 3.7 meters and how much energy is lost into heat?

Answer 1

Since Ali is pushing the desk at a constant velocity, it means there is no net force on the desk. Ali is doing just enough work to overcome friction.

The force doing work is equal and opposite to the force applied by Ali.

Ali applies a force, $F=u_0mg.$

In this problem, $u_0=0.4$, $m=055kg$,  $g=9.8m/s^2$.

The force doing the work is ,

$F=u_0mg=0.4\times 55kg\times 9.8m/s^2=215.6N$

The work done by this force is

$W=F\times d=215.6N\times 3.7m=797.72J$

The energy lost into heat is equal to the work done by friction. Friction does the same amount of work that Ali does, so the energy lost as heat is 797.72 joules.