How do I solve static equilibrium problems using components of forces?

[Peter G.]

I learned how to solve static equilibrium problems by taking the horizontal and vertical components of forces.

There is this exercise in my book that says that I can solve using two perpendicular and parallel components to the ramp.

The diagram in the question is shown below, the angle theta being 30 degrees and the weight of the block 50 N

They ask us to write two equations: The components parallel to the ramp and the components perpendicular to the ramp.

The answers are: F = 50 x sin 30 and N = 50 x cos 30 respectively but I have no idea how they got to those answers, can anyone help me please?

Thanks,
Peter G.

 

[gneill]

The idea is to take the weight of the block (which always is directed vertically) and split it into components that are perpendicular to and parallel to the ramp surface. See attached.

 

[Peter G.]

Cool! Got it! Thanks a lot.