A block of mass M hangs in equilibrium. The rope which is fastened to the ceiling has a tension of 64 N and makes an angle Θ = 55° with the ceiling. What is M?

Answer:
5.3 kg
Explanation:
The rope attached to the ceiling has a tension 64 N.
The rope attached to the wall has a tension T.
The rope attached to the block has a tension Mg.
Sum of the forces at the junction in the y direction:
64 sin 55° − Mg = 0
Mg = 64 sin 55°
M = 64 sin 55° / g
M = 64 sin 55° / 9.8
M = 5.3
The mass of the block is 5.3 kg.