An athlete swings a ball, connected to the end of a chain, in a horizontal circl
ID: 1407416 • Letter: A
Question
An athlete swings a ball, connected to the end of a chain, in a horizontal circle. The athlete is able to rotate the ball at the rate of 7.89 rev/s when the length of the chain is 0.600 m. When he increases the length to 0.900 m, he is able to rotate the ball only 6.10 rev/s.
(a) Which rate of rotation gives the greater speed for the ball?
6.10 rev/s
7.89 rev/s
(b) What is the centripetal acceleration of the ball at 7.89 rev/s? m/s ^2
(c) What is the centripetal acceleration at 6.10 rev/s? m/s^2
Explanation / Answer
(a)
speed = v = r*w
w1 = 7.89 rev/s = 7.89*2*3.14 rad/s = 49.5 rad/s
r1 = 0.6 m
v1 = r1*w1 = 29.7 m/s
w2 = 6.1 rev/s = 6.1*2*3.14 = 38.2 m/s
r2 = 0.9
v2 = r2*w2 = 38.2*0.9 = 34.4 m/s
v2 > v1
answer is 6.1 rev/s <-answer
++++++++++++
b)
a1 = v1^2/r1 = 29.7^2/0.6 = 1480.1 m/s^2 <<-answer
part(c)
a2 = v2^2/r2 = 34.4^2/0.9 = 1314.8 m/s^2 <<-answer