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 8.16 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 6.35 rev/s.(a) Which rate of rotation gives the greater speed for the ball?6.35 8.16 (b) What is the centripetal acceleration of the ball at 8.16 rev/s?m/s2(c) What is the centripetal acceleration at 6.35 rev/s?m/s2

Answer 1

(a) Ball with 6.35 rev/sec gives greater speed

(b) So centripetal acceleration of ball with rotation 8.16 m/sec

`a_c=(v^2)/(r)=(4.896^2)/(0.6)=39.95m/sec^2`

So centripetal acceleration of ball with rotation 6.35 m/sec

`a_c=(v^2)/(r)=(5.75^2)/(0.9)=36.73m/sec^2`

Step-by-step explanation:

(a) In first case angular speed
`\omega =8.16rev/sec`rev/sec and length of the chain = 0.8 m

So velocity
`v=\omega r=8.16* 0.6=4.896 m/sec`

In second case angular speed angular speed
`\omega =6.35rev/sec` and length of the chain that is r = 0.6 m

So velocity
`v=\omega r=6.35* 0.9=5.715m/sec`

So 6.35 rev/sec gives greater speed

(b) Centripetal acceleration is given by
`a_c=(v^2)/(r)`

So centripetal acceleration of ball with rotation 8.16 m/sec

`a_c=(v^2)/(r)=(4.896^2)/(0.6)=39.95m/sec^2`

So centripetal acceleration of ball with rotation 6.35 m/sec

`a_c=(v^2)/(r)=(5.75^2)/(0.9)=36.73m/sec^2`