Conservation of Energy Problem - Very Tricky

[doug1]

Homework Statement

http://imgur.com/ZGvC1

At what angle does the cart fly off of the track?

No other information is provided

Homework Equations

I know that energy is always conserved (total energy before = total energy afterwards).

The Attempt at a Solution

Equation for energy before = energy after:

mgR + Ek = mgh + 1/2mv^2
mgR = mgh + 1/2mv^2 (h is the height above the ground just before the cart leaves the track)

gR = gh + 1/2v^2

v^2 = 2g(R-h) --> This is the velocity just before the cart leaves the track



The dotted line that we see is equal to R.

Thus, Fc (centripetal force) = mv^2/R

If the cart were to leave the track, Fn (normal force) would equal 0

Where do I go from here? Am i on the right track?

 

[haruspex]

So far so good. At the point where the cart leaves the track, what are the forces acting on it? What can you say about its acceleration at that point?

 

[doug1]

After it leaves the track the only force acting on it is gravity. Would I do: mg = mv^2/R

g = v^2/R

R = v^2/g

Plug in v^2 = 2g(R-h)

R = 2g(R-h)/g

R = 2R - 2h

R = 2h

How do I find the angle then?

 

[Doc Al]

After it leaves the track the only force acting on it is gravity.

Good.

Would I do: mg = mv^2/R

Almost. What direction is the centripetal acceleration at the point that it leaves the track? Consider forces along that axis.