Question

The 10.2 kg block in figure is held in place by a force applied to a rope passing over two

massless, frictionless pulleys. Find the tensions T 1 to T 5 and the magnitude of force F.

Answer 1

To determine the tensions, 'slice' the system into layers, where each layer of forces equals to zero because the system itself does not move:

$T_1=mg=100\text{ N}.\\ T_2=T_3=T_5,\\ T_2+T_3-T_1=0,\\ T_1=T_2+T_3=2T_2=2T_3=2T_5,\\ T_2=T_3=T_5=T_1/2=50\text{ N},\\ F=T_5=50\text{ N},\\ T_4=T_2+T_3+T_5=150\text{ N}.$