posted by Amy on .
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?
Assume that the elevator accelerates at a constant rate a while going up X = 50 m in time t. (Assume it doesn't slow down until it gets to higher floors). The acceleration, a, will be given by
(1/2)at^2 = X
a = 2X/t^2
Cable tension at the breaking point is
95,500 = M(g + a) = 65,660 + M*a
M*a = 29840 N
a = (29840)/6700 = 4.45 m/s^2
Minimum time t = sqrt(2X/a) = 4.74 s