A construction worker of mass M is sitting on a platform of mass m that is suspe

Question

A construction worker of mass M is sitting on a platform of mass   m that is suspended by a single cable and system of pulleys as shown (Figure 1) . He needs to pull on the cable with a force of magnitude F, so as to be able to go up and down (as need be) through several floors of a building to do some restoration work. The cables and pulleys are ideal (massless and frictionless), and let us say that the pulleys are not rotating and the cable can slip freely on the pulleys.

Let us say the worker is working on the 7th floor and decides to losen his grip to come down to the 2nd floor. In doing so, he realizes that he is accelerating too rapidly and tightens his grip to slow down his downward acceleration so as to maintain a constant downward acceleration of g/5 for a short while. With what magnitude of force F must he pull on the cable to achieve this condition?

Explanation / Answer

We Know,
F = M*a
Acceleartion a = g/5

(M+m)*a = T - (M+m)*g
(M+m)*g/5 = T - (M+m)*g
T = (6/5)*(M+m)*g

T = 2 * tension in the cable
Tension in the cable = T/2
Force F = T/2
F = ((6/5)*(M+m)*g) /2
Force, F = (6/10)*(M+m)*g

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