a ball with:
rolling down a track of length 1.26m.
Find a) the minimum height the track must be for the ball to go around the loop. Loop has a diameter/height of .3m
The Attempt at a Solution
I did conservation of mechanical energy with just the loop by doing KE total(bottom) = PE(top) to find the initial velocity of the ball before going up loop, giving me a tangential velocity of 1.879 m/s. I used this number to put into the kinematics equation vf=sqrrt(vi^2 + 2ad), to give me an acceleration of 1.401 m/s^2. I then used dynamics F=ma to get a force of the ball going down the slope of .09418 N, used the weight force to get a Fwt = .6594 N, and set up a triangle to find theta (call it @ here). did sin@=.09418/.6594, and solved to get a @ of 8.21 deg. I then put that angle back into the first ramp, and used trig to get a height of .18 m, or 18 cm.
If you can follow that, I have 2 questions:
1) Did i do this problem right, or am i all wrong?
2) When I try to solve for friction, I use the conservation of ME formula, to get PE - Ff = KE...however when I plug my numbers back in, I get a bigger number on the KE side then the PE side...which leads me to think I did this problem wrong in the first place? I've been working on this for about 1.5 hours now and can't seem to figure it out..past what I have done already. :( ...and yes I did add rotational KE to my totatl KE when I did the problem...