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Homework Statement
A block mass M slides down the side of a frictionless circle Radius R. At an angle Theta the mass M flies off the circle, what is the angle?
Homework Equations
PE(top) = KE(point it flies off) + PE(at that point)
Arad = V^2 / R
Sum Of Forces = Mass * Acceleration
The Attempt at a Solution
Okay I actually did this one before and I was trying to do it again but somehow I don't seem to be able to get it. The answer was Inverse Cosine of 1/1.5 or 48 degrees.
The problem was done with energy equations
PE(top) = KE(point) + PE(point)
I set 0 PE to be the middle of the circle so
mgR = .5 mv^2 + mg(Rcos(theta))
mass cancels
gR = .5v^2 + gRcos(theta)
I think I'm going wrong here but I said the only force acting on the block is weight or mg, because at the point is leaves the normal force goes to 0.
so sum forces = mass * acceleration
mg = ma
mass cancels
g = a
then v^2 / R = a , so gR = V^2
then plugging that in
gR = .5v^2 + gRcos(theta)
gR = .5gR + gR cos(theta)
gR cancels
1 = .5 + cos(theta)
and I end up with 60 degrees so I think I missed out a number somewhere but I don't know where.