Force and Motion Homework: Solving for Mass Comparison on Slopes

[Cantworkit]

Homework Statement

Two blocks rest on slopes and are coonected by a pulley. The left hand slope makes a 60 degree ngla with the horizontal. The right hand slope makes a 20 degree angle. How should the masses compare if the objects do not slide along the frictionless slopes? Book answer is that right hand mass is 2.5 times the left hand mass.

Homework Equations

F = ma

The Attempt at a Solution

For the left-hand mass T + Flg + Nleft = 0

For the right-hand mass T + Frg + N right = 0

Coordinates y is vertical and x is horizontal

Solving for the y components in the left hand mass:

Mlg sin 30 degrees + T sin 60 degrees - Mlg = 0

T = 0.5 Mlg/0.866

Solving for the y components in the right-hand mass:

T sin20 degrees - Mrg + Mrg sin 70 degrees = 0

T = 0.06 Mrg/ 0.342

Equating the two Ts, Mr = 0.5 Ml (0.342)/ (0.866)(0.06) = 3.3

 

[Doc Al]

I'm having a hard time following what you did. Hint: Consider force components parallel to the inclines.