If a ball swinging in a circle on a string becomes twice as heavy, what force is needed to maintain velocity?

Question

If a ball on a string suddenly becomes twice as heavy, the force on the string necessary to maintain the same velocity will be
a) twice as great
b) four times as great
c) one-half as much
d) one-fourth as much
e) none of the above

Answer 1

Let v = constant = the tangential velocity of the ball on a string of r length.

Let m = mass of the ball and M = 2m after the big expansion.

Assuming the ball is at r, we have f = mv^2/r, which is a force in equilibrium with the centripetal force, the pull of the string.

When the mass doubles F = 2mV^2/r; assuming the string length remains fixed.

Comparing, we have F/f = 2mV^2/r//mv^2/r = 2V^2/v^2 = 2v^2/v^2(assuming the length of string is fixed); so we have F/f = 2/1 because V = v was a given constraint.

F = 2f, the force after expansion must be twice the force before if the tangential velocities are fixed and the length of string is fixed. Ans: a)

Answer 2

Remember the expression for force on an object in circular motion: F=mv^2/r

If the mass increases x2, then the force must also increase x2. So it will be a) twice as great.

Answer 3

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