The figure below shows two objects with masses m and M which are connected with a taut string running over a pulley. The pulley rotates without friction. The two masses are given as M = 393 g and m = 181 g. A second taut string connects the heavier object vertically from the ceiling. Assuming that both strings and the pulley are mass less, calculate the tension in the string running over the pulley.

Question

The figure below shows two objects with masses m and M which are connected with a taut string running over a pulley. The pulley rotates without friction. The two masses are given as M = 393 g and m = 181 g. A second taut string connects the heavier object vertically from the ceiling. Assuming that both strings and the pulley are mass less, calculate the tension in the string running over the pulley. 
 
Express the result in the unit N and to three significant figures

Gharib · Answer

M=0.393kg
m=0.181kg

Draw the FBD, you will see that

T1+T2-W(of M)=0 Eq 1
T2-W(of m)=0 Eq 2

(T2 is what we need)

now, Eq1-Eq2 => T1+Wm-WM=0
T1= -g(m-M)
T1= x Newtons

now, plug in T1 in Eq 1,
T2=WM-T1

*Reminder W=mass*9.8

Ans: T2=1.77N