(adsbygoogle = window.adsbygoogle || []).push({}); Circular motion problem...ON THANKSGIVING!!!

A sled starts from rest at the top of a hemispherical frictionless hill of radius R.

http://desmond.imageshack.us/Himg37/scaled.php?server=37&filename=sled.png&res=medium [Broken]

a)Find the velocity of the sled at angle theta in terms of theta, R, and g.

b) At what angle does the sled leave the hill?

Using conservation of mechanical energy, for part (a) my velocity was:

U[itex]_{i}[/itex] + K[itex]_{i}[/itex] = U[itex]_{f}[/itex] + K[itex]_{f}[/itex]

mgh[itex]_{i}[/itex]i + 0 = mgh[itex]_{f}[/itex] + ([itex]\frac{1}{2}[/itex])mv[itex]^{2}[/itex]

mgR = mgRcos(theta) + ([itex]\frac{1}{2}[/itex])mv[itex]^{2}[/itex]

...

v[itex]^{2}[/itex] = 2gR(1-cos(theta)), v=[itex]\sqrt{2gR(1-cos(theta))}[/itex]

As for part b, I'm guessing that I use F=ma and try to find the angle where N (normal force) approaches zero. The only way I could think of converting the acceleration to velocity was using the uniform circular motion equation (a=v[itex]^{2}[/itex]/r) but that only applies to objects at a constant speed (and this one started from rest)...so I'm stuck.

Any help would be VERY much appreciated :D

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# Circular motion problem ON THANKSGIVING

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