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Chapter 1: Q13DQ (page 159)

You are pushing a large crate from the back of a freight elevator to the front as the elevator is moving to the next floor. In which situation is the force you must apply to move the crate the least, and in which is it the greatest: when the elevator is accelerating upward, when it is accelerating downward, or when it is traveling at constant speed? Explain

Short Answer

Expert verified

When the elevator is accelerating downwards, the force must be applied to move the crate the least.

The greatest force is when the acceleration of the elevator is in the upward direction

Step by step solution

01

Significance of the acceleration

The acceleration of an object is described as the rate of the change of the velocity of that object with respect to the time. The acceleration is also inversely proportional to the mass of that object.

02

Determination of the situation

A net force on the crate should be applied in order to accelerate the crate. The frictional force is directly proportional to the normal force the floor exerts. When the acceleration of the elevator is in the upward direction, the crate is also getting accelerated in the upward direction as the upward force is more than the weight of the crate.

When the acceleration of the elevator is in the downward direction, the crate is also getting accelerated in the downward direction as the upward force is less than the weight of the crate.

The normal force of the elevator mainly equals to the weight of the elevator when the elevator is moving at a uniform speed.

Thus, when the elevator is accelerating downwards, the force must be applied to move the crate the least.

03

Determination of the greatest force

The greatest force is the force needed to accelerate the elevator when the normal force is greater than the weight of the elevator.

Thus, the greatest force is when the acceleration of the elevator is in the upward direction.

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