As shown in the figure above, a pulley is mounted to the ceiling of an elevator.

Question

As shown in the figure above, a pulley is mounted to the ceiling of an elevator. The elevator is initially traveling with a constant velocity of 1.50 m/s, directed up. The rope (which we assume to have no mass) passing over the pulley has block A tied to one end and block B tied to the other. The mass of block A is 4.00 kg. Block A remains on the floor of the elevator, at rest with respect to the elevator. The mass of block B is 1.70 kg, and block B is also at rest with respect to the elevator, hanging from the rope. Calculate the magnitude of the tension in the rope. N Calculate the magnitude of the force exerted on block A by the floor of the elevator. N The total mass of the pulley and its support is 0.900 kg. Calculate the magnitude of the force exerted by the ceiling of the elevator on the pulley support. N At some later time, the elevator is moving, and it has an acceleration of 1.10 m/s2, directed down. The blocks remain at rest with respect to the elevator. Calculate the magnitude of the tension in the rope now. Calculate the magnitude of the force exerted on block A by the floor of the elevator now. N

Explanation / Answer

as elevator is travelling with constant veloicty, there is no net acceleration.
as acceleration due to gravity is 9.8 m/s^2 downwards, the elevator acceleration 9.8 m/s^2 upwards.

a)let the tension in the rope is T.

from absolute frame of referrence, A is moving at zero acceleration.

hence there is no net force on A

similarly there is no net force on B also.

hence writing force balance equation for B:

T=weight of B=1.7*9.8=16.66 N

b) let force exerted by floor is F.

then writing force balance equation for A,

F+T=weight of the block A

==>F+16.66=4*9.8

==>F=22.54 N

c)total force exerted by the ceiling =weight of the pulley+2*T
=42.14 N

now the blocks are moving at a constant acceleration of 1.1 m/s^2 downward from absolute frame of referrence.

d) then for block B, writing force balance equation:

weight of B-T=mass of B*acceleration

==>1.7*9.8-T=1.7*1.1

==>T=14.79 N

e) let force exerted by the floor is F.

then writing force balance equation for A:

weight of A-F-T=mass of A*acceleration

==>4*9.8-F-14.79=4*1.1

==>F=20.01 N

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