Question

A ball is tied to the end of a cable of negligible mass. The ball is spun in a circle with a radius 7.1 m making 3.9 revolutions every 9.4 second. What is the centripetal acceleration of the ball?

Answer 1

48,2 m/s²

Step-by-step explanation:

We're gonna use the Centripetal Acceleration formula: v² / r but before that, we got to know the velocity, that is not shown clearly to us, so....

To know the velocity let's calculate the distance that the ball traveled

The circumference of a circle formula is:

2piR

2 . 3,14 . 7,1 | That is equal to 44,588 m

We know that the ball traveled this distance 3,9 times, so...

44,588 . 3,9 = 173,8932 m

Ok, now we have the distance, just need to know the time, that is 9.4 seconds.

Velocity = Distance / Time

V = 173,8932 / 9,4

V = 18,5 (approximate)

So...

We are back to the first formula:

Ca = v² / r

Ca = 18,5² / 7.1

Ca = 48,2 m/s² (approximate)

I hope it is correct, hahaha.