A small solid marble of mass m and radius r will roll without slipping along the

Question

A small solid marble of mass m and radius r will roll without slipping along the loop-the-loop track shown in Fig. 12-34 if it is released from rest somewhere on the straight section of track. For the following answers use m for the mass, r for the radius of the marble, R for the radius of the loop-the-loop and g for the acceleration due to gravity.
If the marble is released from height 6R above the bottom of the track, what is the magnitude of the horizontal component of the force acting on it at point Q?

Explanation / Answer

So the total change in height is 5R moving to point Q. Using change in energy, we can deduce the velocity at the point.

Vf^2=10g*R

At the point Q, the normal from the ramp on the marble is directed into the center of the arc. Again, Ac=V^2/R
Sum the forces in the x direction,

m*Ac=Fnormal
m*V^2/R=Fnormal
m*10*g=Fnormal

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