Question

if 130N centripetal force is needed to keep a 0.45kg ball that is attached to a string that is 0.7m long to complete 5 full rotations every 10 seconds. what is the centripetal acceleration and velocity felt by the ball?

Answer 1

Answer:

centripetal acceleration of the ball is 6.9 m/s/s

tangential speed of the ball is 2.2 m/s

Explanation:

As we know that ball complete 5 rotations in 10 seconds

so frequency of rotation of ball is given as

$f = \frac{5}{10} = 0.5 Hz$

now we know that angular frequency is given as

$\omega = 2\pi f$

$\omega = 2(\pi)(0.5)$

$\omega = \pi rad/s$

Now centripetal acceleration is given as

$a_c = \omega^2 R$

$a_c = \pi^2 (0.7)$

$a_c = 6.9 m/s^2$

now the velocity of the ball at this angular frequency is given as

$v = R\omega$

$v = 0.7 (\pi)$

$v = 2.2 m/s$