The concepts used to solve this question is free body diagram and Newton’s laws of motion.
Initially, draw the free body diagram and then use Newton’s laws of motion to determine the tension in the cable.
”The motion is defined as the change in position of the object from one point to another. The object changes its position because there is a net force acting on the object”
The magnitude of the net force is proportional to the mass of the object and acceleration of the object.
The magnitude of the net force acting on the object is,
Here, is the mass of the object and is the acceleration of the object.
(a)
The free body diagram for the elevator is drawn below.
From, the above diagram, the net force acting on the elevator is,
…… (1)
Here, is the mass of the elevator, is the acceleration due to gravity and is the acceleration of the elevator.
The weight of the elevator is,
Substitute for in the equation (1).
Thus, from the above result, the tension in the cable is greater
(b)
At constant velocity, the acceleration of the elevator is zero.
Therefore,
The tension in the cable when the elevator is moving with constant velocity is,
…… (2)
Substitute for in the equation (2).
(c)
The free body diagram of the elevator is drawn below.
The net force acting on the elevators is,
Hence, from the above result, the tension in the cable is less than the weight of the elevator.
(d.1)
The free body diagram of the elevator is drawn below.
The net force acting on the elevators is,
Substitute for , for and for in the above equation.
(d.2)
The weight of the elevator is,
…… (3)
Substitute for and for in the equation (3).
Hence, from the above two result
Hence, the answer is consistent with part (a).
(e.1)
At constant velocity, the acceleration of the elevator is zero.
Therefore,
The tension in the cable when the elevator is moving with constant velocity is,
…… (4)
Substitute for in the equation (2).
The above equation is modified as,
…… (5)
Substitute for and for in the equation (5).
(e.2)
The weight of the elevator is,
Substitute for and for in the above equation.
Hence, from the above two result
Hence, the answer is consistent with part (b).
(f.1)
The free body diagram of elevator is drawn below.
The net force acting on the elevators is,
…… (6)
Substitute for , for and for in the above equation.
(f.2)
The weight of the elevator is,
…… (7)
Substitute for and for in the equation (7).
Hence, from the above two result
Hence, the answer is consistent with part (c).
Ans: Part aThe tension in the cable is greater than the weight of the elevator.
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