Posted by Dermot on Saturday, August 7, 2010 at 2:46pm.
1. Let a be the rate at which the sphere accelerates. After time T from the start of motion, the velocity is
V = a*T and the angular velocity is alpha*T
PE loss equals KE gain.
M g *(1/2)*a T^2*sin 15 = (7/10) M *(a*T)^2
(1/2)a*g*sin15 = (7/10)*a^2
a = (5/7)*g*sin15
The 7/10 comes from adding translational and rotational kinetic energy, using the I value for a solid sphere.
2. Compute V after 3 seconds using the acceleration from part 1. Then compute the total kinetic energy.
3. It rolls to the bottom. Don't you mean how far does it roll in 3 seconds?
yes, sorry after 3 s, thanks.
constant acceleration a
d = (1/2) a t^2
by the way the angular acceleration alpha = a/R
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