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## Homework Statement

A ball of mass m hangs vertically from a massless string experiencing a tension T. What force is required to pull the ball out to an angle theta from the vertical?

- 1) mgsin(theta)

- 2) mgcos(theta)

- 3) mgtan(theta)

- 4) 2mg tan (theta)

- 5) mg/cos (theta)

## Homework Equations

no equations

## The Attempt at a Solution

Well, I thought that if we break down the components of gravity acting on an object at an angle theta from the lowest point of it hanging, then we would have a component mg * sin(theta) acting in a direction perpendicular towards the cord [restoring force] and a component mg * cos(theta) acting in a direction antiparallel to the cords tension.

Thus, I would need to apply an equivalent force to mg*sin(theta) in the opposite to counter react the force of gravity's component.

The solutions say that the answer is mg*tan

Well, I thought that if we break down the components of gravity acting on an object at an angle theta from the lowest point of it hanging, then we would have a component mg * sin(theta) acting in a direction perpendicular towards the cord [restoring force] and a component mg * cos(theta) acting in a direction antiparallel to the cords tension.

Thus, I would need to apply [number 3]. Could anyone please explain why their answer is right and why my approach is possibly wrong?