An elevator's cable can handle a tension of 95,500N.Assuming the car has a mass of 2950 kg and it is carrying a full load of passengers whose combined mass is 3750 kg,what is the minimum time required for the elevator to rise 50.0 m from rest?
A)2.65 s
B)3.35 s
C)4.74 s
D)5.96 s

Question

Quizplus · Accepted Answer

The total mass that the cable needs to support is:
2950 kg (mass of the car) + 3750 kg (mass of the passengers) = 6,700 kg

The force of gravity acting on this mass is:
Fg = (6,700 kg)(9.81 m/s^2) = 65,687 N

The tension in the cable when the elevator is rising at a constant speed is equal to the force of gravity plus the force required to accelerate the elevator:
T = Fg + ma

We can rearrange this equation to solve for the minimum acceleration needed to lift the elevator:
a = (T - Fg)/m

a = (95,500 N - 65,687 N)/(2950 kg + 3750 kg) = 5.92 m/s^2

Now we can use the kinematic equation:
y = 1/2at^2

where y = 50.0 m and a = 5.92 m/s^2 to solve for the minimum time required:
t = sqrt(2y/a) = sqrt(2(50.0 m)/(5.92 m/s^2)) = 4.74 s

Therefore, the minimum time required for the elevator to rise 50.0 m from rest is 4.74 s, which is answer C.

An Elevator's Cable Can Handle a Tension of 95,500N