A child is twirling a 0.0113-kg ball on a string in a horizontal circle whose radius is 0.147 m. The ball travels once around the circle in 0.388 s. (a) Determine the centripetal force acting on the ball. (b) If the speed is doubled, by what factor does the centripetal force increase

0.435 N

The centripetal force increases by a factor of 4

Explanation:

Let the centripetal force be F

F =mv^2/r

m= mass of the object

v = linear velocity of the object

r = radius of the circular path

but v = 2πr/T = 2 * 3.142 * 0.147 / 0.388

v = 2.38 m/s

F = 0.0113 * (2.38)^2/0.147

F= 0.435 N

if v= 2v

Then;

F = m(2v)^2/r

F = m4v^2/r

F= 4mv^2/r

The centripetal force increases by a factor of 4