In Fig. 11-32, a solid brass ball of mass 8.9 g will roll smoothly along a loop-
ID: 2028584 • Letter: I
Question
In Fig. 11-32, a solid brass ball of mass 8.9 g will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R = 2.7 m, and the ball has radius r << R. (a) What is h if the ball is on the verge of leaving the track when it reaches the top of the loop? (b) If the ball is released at height h = 6.00R, what is the magnitude of the horizontal force component acting on the ball at point Q?
Please solve without using energy conservation, as specified by the teacher.
Explanation / Answer
m = 8.9 g, R = 2.7 m, r << R.
(a) What is h if the ball is on the verge of leaving the track when it reaches the top of the loop?
initial energy = mgh
energy at the top = mv2/2 + I2/2 + mg(2R) = mv2/2 + (2mr2/5)*(v/r)2/2 + 2mgR = 0.7mv2 + 2mgR
mgh = 0.7mv2 + 2mgR (1)
"on the verge of leaving the track": mg = mv2/R, v2 = gR
sub it into (1): h = 2.7R = 7.29 m
(b) If the ball is released at height h = 6.00R, what is the magnitude of the horizontal force component acting on the ball at point Q.
initial energy = mgh
energy at Q top = mv2/2 + I2/2 + mgR = mv2/2 + (2mr2/5)*(v/r)2/2 + mgR = 0.7mv2 + mgR
mgh = 0.7mv2 + mgR
mv2/R = 5mg/0.7
at Q: F = mv2/R = 5mg/0.7 = 0.623 N