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The century-old ascensores in Valparaiso, Chile, are picturesque cable cars built on stilts to keep the passenger compartments level as they go up and down the steep hillsides. As FIGURE P7.43shows, one car ascends as the other descends. The cars use a two-cable arrangement to compensate for friction; one cable passing around a large pulley connects the cars, the second is pulled by a small motor. Suppose the mass of both cars (with passengers) is 1500kg, the coefficient of rolling friction is 0.020, and the cars move at constant speed. What is the tension in (a) the connecting cable and (b) the cable to the motor?

Short Answer

Expert verified

(a) The tension in the connecting cable is 8190.74N

(b) The tension in the motor cable is481.66N

Step by step solution

01

Given information (part a)

The mass of both the cars m=1500kg

The coefficient of rolling friction k=0.02

The angle between horizontal and cable=35

02

Explanation (part a)

Free body diagram of the lower car:

The net force on the lower car

T2+f=mgsinwherefisthefrictionforcef=rmgcosT2+rmgcos=mgsinT2=mgsin-rmgcosT2=mgsin-rcosT2=1500kg9.8m/s2sin35-0.02cos35T2=8190.74N

The tension in the connecting cable is 8190.74N.

03

Given information (part b)

The mass of both the cars1500kg

The coefficient of rolling friction35

The angle between horizontal and cablelocalid="1649168031616" =0.02

04

Explanation (part b)

The free body diagram of the upper car:

The net force on the upper car

T1+T2=mgsin+rmgcosT1=mgsin+rmgcos-T2T1=mgsin+rcos-T2T1=1500kg9.8m/s2sin35+0.02cos35-8190.74N=481.66N

The tension in the motor cable is481.66N

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