Poblem solving?

Question

a weight of 100N and an unknown load are held on a double frictionless inclined at 45deg and 30deg respectively with the ground. calculate the unknown mass to keep the blocks in equilibrium.

Answer 1

I am going to assume, though you didn't write it, that the blocks are connected to each other with a massless cable over a frictionless pulley, and the cable is parallel with both slopes.

For the 100N block, there are three forces acting upon it:

Gravity acting vertically downwards, force = 100 N

The reaction force of the slope, however it can be ignored as it is acting perpendicularly to the tension in the cable holding the block.

The tension in the cable, this needs to balance the force of gravity pulling the block down the slope, therefore:

T = 100*Cos45

T = 100*0.707

T = 70.7 N

For the second block of unknown mass, the forces are:

Gravity acting vertically downwards, with unknown amount of force.

The reaction force of the slope, which again can be ignored.

The tension in the cable, which we now know is 70.7 N.

Therefore:

70.7 = x*Cos60

70.7 = x*0.5

x = 141 N

The weight of the second block is 141 N.