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Chapter 7: Q. 21 (page 178)

The cable cars in San Francisco are pulled along their tracks by an underground steel cable that moves along at 9.5mph.The cable is driven by large motors at a central power station and extends, via an intricate pulley arrangement, for several miles beneath the city streets. The length of a cable stretches by up to 100ftduring its lifetime. To keep the tension constant, the cable passes around a 1.5mdiameter 鈥渢ensioning pulley鈥� that rolls back and forth on rails, as shown inFIGURE100ft. A 2000kgblock is attached to the tensioning pulley鈥檚 cart, via a rope and pulley, and is suspended in a deep hole. What is the tension in the cable car鈥檚 cable?

Short Answer

Expert verified

The tension in the cable car's cable is9800N.

Step by step solution

01

Given information

Speed of the steel cable=9.5mph

The length of a cable stretch=100ft

The cable passes around the diameter=1.5m

Mass of the cable=2000kg

02

Explanation

As weight is moving uniformly , net force on it will be zero . So total upward force is equal to total downward force.

Force acting downwards

F=mg.....................(1)

Tension of rope be T . So total force acting upwards is 2T . 2T will balance the weight .

Further, the tension localid="1649675027629" 2T=F........................(2)

Since the frictional force=0

Substituting the values in the equation1

F=22009.8F=19600N

Substituting the values in the equation 2

localid="1649613408531" T=19600N2=9800N

The tension in the cable car's cable T=9800N

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