Hey, I have a question regarding 42. How does one know what the frictional force is. Basically how do I know when it should be cos or sin. This aspect confuses me. Thanks
Draw a free body diagram. The geometric relationships of the block on ramp with forces should show you whether it's cos or sin theta. The theta they use in that question is from the ramp bottom angle.
Friction force is Mus or Muk * Normal Force.
On a ramp, normal force is perpendicular to the ramp so we can calculate our normal force from the magnitude of the component of gravitational force in that vector component.
Do geometry with the drawing. SinTheta = O/H and CosTheta = A/H