How to Solve Loop Problems; Energy and Minimum Speed | Symbolic Physics (AP Free Response C1991M1)
This is a critical energy conservation problem, based on the following AP Free Response from 1991:
C1991M1. A small block of mass 3m moving at speed v0 / 3 enters the bottom of the circular, vertical loop-the-loop shown above, which has a radius r. The surface contact between the block and the loop is frictionless. Determine each of the following in terms of m, v0 , r, and g.
a. The kinetic energy of the block and bullet when they reach point P on the loop
b. The speed vmin of the block at the top of the loop to remain in contact with track at all times
c The new required entry speed v0 ́ at the bottom of the loop such that the conditions in part b apply.
Other problems these results will be helpful for:
At what minimum speed must a roller coaster be traveling so that passen- gers upside down at the top of the circle (Fig. 5–48) do not fall out? Assume a radius of curvature of 8.6 m.
A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.20 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N. (a) Find the speed of the bucket. (b) How fast must the bucket move at the top of the circle so that the rope does not go slack?
A small lead ball, attached to a 1.5-m rope, is being whirled in a circle that lies in the vertical plane. The ball is whirled at a constant rate of three revolutions per second and is released on the upward part of the circular motion when it is 0.75 m above the ground. The ball travels straight upward. In the absence of air resistance, to what maximum height above the ground does the ball rise?