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PinkEraser

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## Homework Statement

A ball of mass M is attached to a string of length R and negligible mass. The ball moves clockwise in a vertical circle. When the ball is at point P, the string is horizontal. point Q is at the bottom of the circle and point Z is at the top of the circle. Air resistance is negligible. Express all algebraic answers in terms of the given quantities and fundamental constants.

a.What are the forces exerted on the ball at point P and Q,respectively

b. Derive an expression for Vmin, the minumum speed the ball can have at point Z without leaving the circular path.

c. The maximum tension the string can have without breaking is Tmax. Derive an expression for Vmax, the maximum speed the ball can have at point Q without breaking the string

d.Suppose the string breaks at the instant the ball is at point P. Describe the motion of the ball immediately after the string breaks

## Homework Equations

Fc = mac

ac = V^2/r

## The Attempt at a Solution

a. At point P, Tension is to the right, Gravity is pusing the mass down, and the centripetal force is going to the center of the circle so it is also going to the right

At point Q which is at the bottom of the circle, Tension is now going up as well as the centripetal force. Gravity is pushing down

b. At point Z, all forces are going down.

So Fc = mac

T + mg = m(Vmin)^2 / R

Vmin^2 = R(T+mg) / m

Vmin = radical R(T + mg) /m

c. Same thing, just with maximum tension at pt Q

Fc = mac

Tmax - mg = m(Vmax)^2 / R

Vmax = radical R(Tmax - mg) / m

d. It goes up with the same speed as it was going in a circle. Gravity is the only force pushing down on it

Is this correct? I'm not sure where the centripetal force is at in point P, Q, and Z