A child is twirling a 0.0116 kg ball on a string in a horizontal circle whose radius is 0.102 m. The ball travels once around the circle in 0.560 s.

Question

(a) Determine the centripetal force acting on the ball.
N

(b) If the speed is doubled, does the centripetal force double?

yes
no

If not, by what factor does the centripetal force increase?

I was able to work the problem but i'm not sure what it means by factor for the third part of the problem. Please help.

Answer 1

Centripetal force is
M V^2/R
In your case V = 2 pi R /(0.56 s) = 1.1144 m/s, so
Force = (0.0116)(1.1144)^2/(0.102)= ? N

If V is charged to 2V, the Force becomes 4 times as large, because the 2 gets squared. The factor they are looking for is 4.