An elevator is accelerating upward at a rate of 3.6 m/s2. a block of mass 24 kg hangs by a low-mass rope from the ceiling, and another block of mass 90 kg hangs by a low-mass rope from the upper block. (a) what are the tensions in the upper and lower ropes?

The answer:

When the elevator accelerates upward at a rate of 3.6 m/s², the value of the acceleration becomes

A=g+3.6=13.4 m/s²

and by using the newton's law, F=mass x A, we have

T1 = (24 + 90) x 13.4 = 1527.6 N, where T1 is the Tension in upper rope

and

T2 = (90) x 13.4 = 1206N, where T2 is the Tension in lower rope

When the elevator accelerates downward at a rate of 3.6 m/s², the value of the acceleration becomes

A=9.8 - 3.6 = 6.2 m/s²

T1 = (24 + 90) x 6.2 = 706.8 N, where T1 is the Tension in upper rope

and

T2 = (90) x 6.2 = 558N, where T2 is the Tension in lower rope