Sample Problem Kinetic Energy And Work

Sample Problem Kinetic Energy And Work

An elevator cab of mass m = 500 kg is descending with speed when its supposing cable begins to slip, allowing it to fall with constant acceleration.

(a) During ‘the fall through a distance d = 12 m, what is the work  done on the cab by the gravitational force.

SOLUTION: The Key Idea here is that we can treat the cab as a particle and thus use the work Wt done on it by (a free body diagram of the cab with the cab’s displacement d included), we see that the angle between the directions of FR and the cab’s displacement.

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(b) During the 12 m fall, what is the work  done on the cab by the upward pull f of the elevator cable?

SOLUTION: A Key Idea here is that we can calculate the work with if we first find an expression for the magnitude T of the cable’s pull.

Next, substituting -for the (downward) acceleration a and then for the angle between the directions of forces f and mg, we find

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An elevator cab. descending with speed Vi' suddenly begins to accelerate downward. (a) It moves through a displacement d with constant acceleration a = giS. (b) A free-body diagram for the cab. displacement included
An elevator cab. descending with
speed Vi’ suddenly begins to accelerate downward. (a) It moves
through a displacement d with constant acceleration 
(b) A free-body diagram for the cab displacement included.

(c) What is the net work W done on the cab during the fall?

SOLUTION: The Key Idea here is that the net work is the sum of the works done by the forces acting on the cab.

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(d) What is the cab’s kinetic energy at the end of the 12 m fall?

SOLUTION: The Key Idea here is that the kinetic energy changes because of the-net work done on the cab, according.

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