Posted by Genevieve on Friday, October 8, 2010 at 2:14pm.
relate the change in PE from the vertical fall to changes in KE
KE change: 1/2 m v^2
height change: 4.9-radius+ radius(1-CosTheta)
PE change: mg*height change
where theta is the angle measured from the point on the circle to the center and the x axis.
Now, the object flies off when the normal component of weight (mgSinTheta) is equal to centripetal force (mv^2/r)
set the equal.
from setting PE change=KE change, you should be able to solve for v^2. Put that into the equation with the forces, and solve for angle.
I am confused on the height change.
By 4.9 did you mean 4.8? and if so do I set it equal to zero to solve?
is the v in the centripetal force different from the v in KE?
yes, 4.8 I was using my memory of the pic as 4.9
1/2 m v^2=mg(4.8 - radius+ radius(1-cosTheta)
solve for v^2
then put that v^2 in this:
and solve for Theta
You may have some tricky algebra.
It is the same v in KE, and force.
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