A car is doing a loop-the-loop. The loop has a radius of .4m. Assume the car is starting with the minimum speed it needs in order to stay in contact with the track at all times (at the top of the track, the car is not applying a force to the track). neglect friction. What is the minimum initial speed the car must have in order to remain in contact with the circular track at all times?
v^2/R = g at top
calculate v^2 at top from that
v^2 = R G
Ke at bottom = m g h + (1/2) m v^2
call speed at bottom u
h = diameter = 2 R
(1/2) m u^2 = m g (2R) + (1/2) m v^2
u^2 = 4 g R + v^2