Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 133

Robot retrieval on volcano crater. Figure 8.56 shows a disabled robot of mass \( m = 40 \text{ kg} \) being dragged by a cable up the \( 30^\circ \) inclined wall inside a volcano crater. The applied force \( \vec{F} \) exerted on the robot by the cable has a magnitude of \( 380 \text{ N} \). The kinetic frictional force \( \vec{f}_k \) acting on the robot has a magnitude of \( 140 \text{ N} \). The robot moves through a displacement \( \vec{d} \) of magnitude \( 0.50 \text{ m} \) along the crater wall. (a) How much of the mechanical energy of the robot−Earth system is dissipated by the kinetic frictional force \( \vec{f}_k \) during the displacement? (b) What is the work \( W_g \) done on the robot by its weight during the displacement? (c) What is the work \( W_{app} \) done by the applied force \( \vec{F} \)?