A loaded elevator with very worn cables has a total mass of 2000 kg , and the ca

Question

A loaded elevator with very worn cables has a total mass of 2000 kg , and the cables can withstand a maximum tension of 3.00×104 N .Part A Draw the free-body force diagram for the elevator.(Assume that the elevator is accelerating upward.)Part B Apply Newton's second law to the elevator and find the maximum upward acceleration for the elevator if the cables are not to break?Part C What would be the answer to part B if the elevator were on the moon, where free fall acceleration is g = 1.62 m/s2 .

Explanation / Answer

Total mass, M = 2000 kg
Maximum tension, T = 30 x 103 N.
If we draw the free body diagram, Tension T will be up, Mg will be down and the net force will be up.
Fnet = T - Mg
If the maximum acceleration of the cable is a, then
Ma = T - Mg
T = M (g + a)
g + a = T/M = 15
a = 15 - 9.8 = 5.2 m/s2.

If the elevator were on moon
g = 1.62 m/s2,
a = 15 - 1.62 = 13.38 m/s2

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