The Physics of Rolling Down a Ramp

[daniel_i_l]

A ball is rolling down a ramp, which of the following is true:
1) gravity is pulling both in the direction of the ramp an perpendicular to that, the perp part is cancled out by the normal force so the ball rolls in the direction of the ramp.
2) gravity pulls down, this causes a normal force which can be split up into two directions - up and to the side, the one going up is cancled out by gravity and that leavs us with a normal force to the side and part of the gravitational force pulling down, the sum of these two forces pulls the ball down the ramp.
The equations suggest 1 but it seems more logical that the sideways force (on the x-axis) is because of the normal force that has a componant in tha direction, as opposed to the gravitational force that does not.

 

[3trQN]

I would be inclined (hah unintentional pun) to side (hoho) with the (2).

Force is a vector quantity, the normal force is a vector which is characterised by the incline of the ramp, a flat ramp would be one in which the entire normal force is vertical.

 

[Hawknc]

Draw a free body diagram with the normal force and what you think, logically, the gravitational force should be. Hint: the gravitational force is always constant for constant mass (F = mg); can the same be said about the normal force?

 

[daniel_i_l]

Ok, this wasn't a homework or school related question!
I was just wondering what was really happening. In both cases the equations give the same answers and they're mathamaticly equal. The question was more of a theoretical one.
Hawhnc: I know that the gravitational force is constant and that the normal force depends on the slope, I was just wondering what was pulling the ball to the side (x-axis) - gravity or the normal force.
Thanks.

 

[Doc Al]

Gravity pulls down. Does a component of gravity pull the ball down the ramp? Of course!

The normal force acts perpendicular to the ramp. Does a component of the normal force pull the ball down the ramp? No! The normal force has no component parallel to the ramp.

There's a third force acting on the ball: Friction. It's friction that makes the ball roll instead of just slide.

 

[Hawknc]

Sorry, I draw a perverse pleasure in being obscure sometimes. :D Gravity is always constant and always acts straight down; the normal force is less than the gravitational force at an angle and thus the remaining net gravitational force is what draws the ball down. I had something about friction in my earlier post as well, but it disappeared in a revision. Doc Al's probably more understandable than my post-midnight rantings.

 

[PPonte]

The normal force acting on a body, as the name suggest, is always normal/perpendicular to the surface where the boby is moving. Since it is normal to the displacement of the body it does no work (Remember $W = Fd\cos(\text{angle between F and d})$. Moreover it is canceled out by the weight. In this situation the normal force is canceled out by the component of the weight on the direction normal to the surface of the ramp. The weight component on the direction of the ramp makes the ball roll along it.

Therefore, (1) is the correct answer.