An athlete swings a ball, connected to the end of a chain, in a horizontal circl
ID: 1884025 • 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 8.39 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 6.45 rev/s.
(a) Which rate of rotation gives the greater speed for the ball?
6.45 rev/s8.39 rev/s
(b) What is the centripetal acceleration of the ball at 8.39 rev/s?
m/s2
(c) What is the centripetal acceleration at 6.45 rev/s?
m/s2
Explanation / Answer
Given,
w1 = 8.39 rev/s ; r1 = 0.6 m
w2 = 6.45 rev/s ; r2 = 0.9 m
a)6.45 rev/s
v1 = r1 w1 = 0.6 x 8.39 x 2 x 3.14 = 31.61 m/s
v2 = r2 w2 = 0.9 x 6.45 x 2 x 3.14 = 36.46 m/s
b)a = v^2/r
a1 = 31.61^2/0.6 = 1665.32 m/s^2
Hence, a1 = 1665.32 m/s^2
c)a2 = 36.46^2/0.9 = 1477.04 m/s^2
Hence, a2 = 1477.04 m/s^2