An athlete swings a ball, connected to the end of a chain, in a horizontal circl

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

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