Question

A child swings a tennis ball attached to a 0.651-m string in a horizontal circle above his head at a rate of 4.50 rev/s.

What is the centripetal acceleration of the tennis ball?
m/s

Answer 1

The centripetal acceleration of the tennis ball is calculated to be 21,083.76 m/s^2.

Step-by-step explanation:

The centripetal acceleration of an object moving in a circular path can be calculated using the formula:

ac = (v^2) / r

where ac is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path.

In this case, the tennis ball is swinging in a horizontal circle above the child's head, so the radius of the circular path is the length of the string, which is 0.651 m.

Given that the rate of revolution is 4.50 rev/s, we can find the velocity using the formula:

v = (2πr * rev/s)

First, convert the rate of revolution to radians/second:

(4.50 rev/s) * (2π radians/rev) = 28.27 radians/s

Then, calculate the velocity:

v = (2π * 0.651 m * 28.27 radians/s) = 116.77 m/s

Now, we can calculate the centripetal acceleration:

ac = (v^2) / r = (116.77 m/s)^2 / 0.651 m = 21,083.76 m/s^2

Therefore, the centripetal acceleration of the tennis ball is 21,083.76 m/s^2.