A child is twirling a 0.0255-kg ball on a string in a horizontal circle whose ra

Question

A child is twirling a 0.0255-kg ball on a string in a horizontal circle whose radius is 0.0840 m. The ball travels once around the circle in 0.406 s. (a) Determine the centripetal force acting on the ball. (b) If the speed is doubled, by what factor does the centripetal force increase?

A child is twirling a 0.0255-kg ball on a string in a horizontal circle whose radius is 0.0840 m. The ball travels once around the circle in 0.406 s. (a) Determine the centripetal force acting on the ball. (b) If the speed is doubled, by what factor does the centripetal force increase?

Explanation / Answer

Fc = mv2 / r, where v = 2r / T

==> Fc = m(2r / T)2 / r = 42mr / T2 = 42(0.0255 kg)(0.0840 m) / (0.406 s)2 = 0.513 N

Since Fc is proportional to v2, if v is doubled, then the centripetal force increases by a factor of 4.

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