Question

I'm having a hard time with some free body diagrams. If you have a box on a slope/ramp and the angle of the ramp is X degrees why is it that the angle between the normal force and the gravitational force is also X degrees? Am I missing something obvious here?

Answer 1

Normal means perpendicular to the slope. The slope is at X deg to the horizontal, and the normal is 90 deg to that, so to the horizontal, the normal then is 90+x, but measuring the normal to the perpendicular, you subtract 90, so the normal is to vertical is X deg. gravity is vertical.

Answer 2

Yes, geometry. Sketch it carefully.
Think about what happens to the angle between straight down and the normal from the object to the ramp as the slope increases from zero. At zero you see the normal to the ramp (level road in this case) is straight down like gravity. As the slope goes up, the normal goes up, but gravity remains straight down.

Answer 3

You guys are great! Now I get it!