Answer to Question #105238 in Classical Mechanics for Anika Roejkjaer

Question

A cable car of mass 1200 kg moves 2km up a slope inclined at 30 degrees to the horizontal at a constant speed. If the resistance to motion is 400N find the work done by the tension in the cable.

Answer 1

First, find the tension:

$$Ox: T-R-mg\text{ sin}30^\circ=0,\\ T=R+mg\text{ sin}30^\circ.\\ W_T=Td=d(R+mg\text{ sin}30^\circ)=\\=2000(400+1200\cdot9.8\text{ sin}30^\circ)=12.56\cdot10^6\text{ J}.$$