What Angles Affect the Vector Components of a Weight on an Inclined Plane?

[dandy9]

Homework Statement

The weight of a book sliding down a frictionless inclined plane can be broken into two vector components: one acting parallel to the plane, and the other acting perpendicular to the plane.
(a) At what angle is the components equal?
(b) At what angle is the component parallel to the plane equal to zero?
(c) At what angle is the component parallel to the plane equal to the weight?

Homework Equations

Fnet = ma

The Attempt at a Solution

I'm not really sure how to approach this.
My guess for (a) is 45 just because it sounds reasonable that the components would be equal at the middle of 0 to 90 degrees.

 

[cupid.callin]

try to imagine a book on a inclined plane inclined at say angle a...
If weight is mg, component of weight perpendicular to incline is ..?
what is the component of weight parallal to incline?

draw figure and then you'll easily solve it

 

[dandy9]

Thank you!

I got them all - thanks for getting me started! This is how I did it:
(a) cos and sin are equal at 45degrees
(b) the sin of 0 gives a component of 0.
(c) if the component and weight are equal then you take the inverse sin of 1 and get 90.

 

[cupid.callin]

Very good.