W of the cart is 0.7 lb Height of the track from a to b is 9 feet the radius of

Question

W of the cart is 0.7 lb

Height of the track from a to b is 9 feet

the radius of the loop is 0.75 ft

The roller coster starts at point A. and is released from rest and slides down the frictionless slope down to the bottom of the loop.

How do I find The force exerted by the surface on the cart as it passes through point B? in lb ( I believe we are looking for Normal force for both B and C?)

Then the roller coster contiunes around past point C.

How do I find The force exerted by the surface on the cart as it passes through point C? in lb

I think this is a conservation of energy problem. I am having issues setting up the equations. I probably have a issue with the free body diagrams and how they relate to each other. I have been working on this for a few hours now. Can anyone help me figure this out. I really appreciate it.

Explanation / Answer

Let us assume that there are no frictional forces. Then by consevation of energy,

P.E.a= K.E.b If the velocity of the body at B is v, then by previous equation, v = sqrt(2*m*g*h/m) = sqrt(2gh) = 24 ft/s = vB

So total nomal reaction at B = mvB2/r + mg = 0.7*(576/0.75 + 32) = 560pdl

Velocity at C is vC = sqrt(2(1/2mvB2 - mghc)/m) = 17.66ft/s

So normal reaction at C = mvc2/r - mg = 268.8 pdl

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