Consider two blocks attached by a massless rope and placed on either side of a frictionless, asymmetric, double ramp.

Question

The rope runs over an ideal pulley at the apex of the double-ramp. The first block (on the side with an incline of θ ​1 ​​ =57.0 ​​ ) has a mass of m ​1 ​​ =13.0 kg. What must the mass, m ​2 ​​ , of the second block be (on the side with an incline of θ ​2 ​​ =34.2​​ ) in order to for system to be in equilibrium as pictured?

Answer 1

1) make a free body diagram of the 13kg block showing the weight vector (13g) pointing vertically down and a tension vector pointing toward the pulley.

2) Write the sum of forces parallel to the ramp to find T-13gsin(57)=0 ... not moving thus ma=0

3) make a second free body diagram of the other block similar to the first

4) Write the sum of forces parallet to the ramp to find T-mgsin(34.2)=0 ... pulley is frictionless thus tension is same everywhere

5) Solve the two simultaneous equations to find m=19.4kg