The figure shows a 2000 kg cable car descending a high hill.A counterweight of mass 1800 kg on the other side of the hill aids the brakes in controlling the cable car's speed.The rolling friction of both the cable car and the counterweight are negligible.How much braking force does the cable car need to descend at constant speed?

Question

Quizplus · Accepted Answer

Since the cable car is descending at a constant speed, the net force on the cable car must be zero. Therefore, the force due to gravity pulling the cable car down the hill must be balanced by the force of the brakes pulling the cable car up the hill. The force due to gravity on the cable car is given by F = mg, where m is the mass of the cable car and g is the acceleration due to gravity (9.8 m/s^2). F = (2000 kg)(9.8 m/s^2) = 19,600 N. The force due to gravity on the counterweight is also 19,600 N. Since the counterweight mass is less than the cable car mass, the brakes must provide a greater force on the cable car to keep it descending at a constant speed. The net force on the cable car is therefore F_net = F_cable car - F_counterweight = 19,600 N - (1800 kg)(9.8 m/s^2) = 3800 N. Therefore, the cable car needs a braking force of 3800 N to descend at a constant speed. The correct answer is A) 3800 N.

The Figure Shows a 2000 Kg Cable Car Descending a High