The 2300 kg cable car shown in the figure below descends a 200 m high hill. In a

Question

The 2300 kg cable car shown in the figure below descends a 200 m high hill. In addition to its brakes, the cable car controls its speed by pulling an 1600 kg counterweight up the other side of the hill. The rolling friction of both the cable car and the counterweight are negligible.

http://www.webassign.net/knight/p8-39.gif

(a) How much braking force does the cable car need to descend at constant speed?
_____N

(b) One day the brakes fail just as the cable car leaves the top on its downward journey. What is the runaway car's speed at the bottom of the hill?
_______m/s

Explanation / Answer

tension=T=1600*9.8*sin(20)=5362.875 N force due to gravity on the car=2300*9.8*sin(30)=11270 N so braking force required=5907.125 N b.acceleration=(5907.125/2300)=2.568 m/s^2 distance traveled =200/sin(30)=400 m so speed at bottom=sqrt(2*2.568*400)=45.3254 m/s

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