I was trying to figure out how to get the outward normal vector to the surface of a ramp inclined θ degrees from the horizontal. Say that a block of mass "m" is on the surface and the surface is frictionless. When I draw the free-body diagram, I come up with a downward force of <0,-mg>. To calculate the force in the direction of the incline, I first want to find the normal vector to add to <0,-mg>. Is this the correct way to do this? It looks like |n|=|g|cosθ, but I cannot find the coordinates of this vector. Any ideas?(adsbygoogle = window.adsbygoogle || []).push({});

Edit: Working it out, I came up with the following for the coordinates of the outward normal vector:

x = |g|cosθsinθ

y = |g|cos^{2}θ

Are these correct?

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# Free-Body Diagram

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