Question

A ball of mass 24.1 g is attached to a cord of length 0.417 m and rotates in a vertical circle. What is the minimum speed the ball must have at the top of the circle so the cord does not become slack? The acceleration of gravity is 9.8 m/s².

Answer in units of m/s.

Answer 1

the minimum speed that the ball must have so that the cord does not become slack is 2.02 m/s.

Step-by-step explanation:

In order to avoid slack, the centripetal force of the ball must equal its weight at the top of the circle. Therefore,

F_c = F_g

m v² / r = m g

v² = g r

v = √[g r]

v = √[(9.8 m/s²)(0.417 m)]

v = 2.02 m/s

Therefore, the minimum speed that the ball must have so that the cord does not become slack is 2.02 m/s.