Interpreting Circular Motion Diagrams

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AP Physics C: Electricity and Magnetism › Interpreting Circular Motion Diagrams

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1

Rotatingball

A ball of mass is tied to a rope and moves along a horizontal circular path of radius as shown in the diagram (view from above). The maximum tension the rope can stand before breaking is given by $T_{max}$ . Which of the following represents the ball's linear velocity given that the rope does not break?

$v\leq\sqrt{\frac{rT_{max}}{m}}$

$v\geq\sqrt{\frac{rT_{max}}{m}}$

$v\leq\sqrt{rT_{max}}$

$v\geq\sqrt{rT_{max}}$

None of these

Explanation

This is a centripetal force problem. In this case the tension on the rope is the centripetal force that keeps the ball moving on a circle.

$T=F_C=\frac{mv^2}{r}$

If we want for the rope not to break, then the tension should never exceed $T_{max}$ .

$T_{max}\geq\frac{mv^2}{r}$

Now we just solve for velocity:

$v\leq\sqrt{\frac{rT_{max}}{m}}}$

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