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An elevator is supported by a single cable. There is no counterweight. The elevator receives passengers at the ground floor and takes them to the top floor, where they disembark. New passengers enter and are taken down to the ground floor. During this round trip, when is the force exerted by the cable on the elevator equal to the weight of the elevator plus passengers? Greater? Less?

An elevator is supported by a single cable. There is no counterweight. The elevator receives passengers at the ground floor and takes them to the top floor, where they disembark. New passengers enter and are taken down to the ground floor. During this round trip, when is the force exerted by the cable on the elevator equal to the weight of the elevator plus  passengers? Greater? Less?
 

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
8 years ago
At rest position of the elevator, the total weight of the system (weight of the elevator plus weight of the passenger) and tension acting on the cable exactly balances to each other. That is why the elevator maintains its rest position. Therefore, the force exerted by the cable on the elevator equal to the weight of the elevator plus passenger, when the elevator is at rest position in this round trip.
As the elevator accelerating in upward direction, the tension acting on the cable will be greater than the weight of the system. Therefore the force exerted by the cable on the elevator will be greater than the weight of the elevator plus passenger, when the elevator is accelerating in the upward direction in this round trip.
As the elevator accelerating in downward direction, the tension acting on the cable will be less than the weight of the system. Therefore the force exerted by the cable on the elevator will be less than the weight of the elevator plus passenger, when the elevator is accelerating in the down direction in this round trip.

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