Question

A ball of mass 50g tied to the end of a 50cm inextensible string is whirled around in a vertical circle. Find the tension in the string when the ball is at the top of the circle. Take g=10ms2.

Answer 1

Answer on Question #55217-Physics-Mechanics-Kinematics-Dynamics

A ball of mass $m = 50\,g = 0.05\,kg$ tied to the end of a $l = 50\,cm = 0.5\,m$ inextensible string is whirled around in a vertical circle. Find the tension in the string when the ball is at the top of the circle. Take $g = 10\,ms^{-2}$.

Solution

If you have a ball on the end of a string and you swing it in a vertical circle the "centripetal force" or the forces causing the acceleration will be a combination of the tension from the string and gravity.

The Tension and Weight are the forces causing the acceleration. The ball is also moving in a circle so at the highest and lowest points

$$Tension + Weight = CentripetalForce.$$

Hence,

$$F_{net} = ma = \frac{mv^2}{r}$$ $$T + W = ma$$

Thus,

$$T = ma - W = \frac{mv^2}{r} - mg = m\left(\frac{v^2}{r} - g\right)$$

The tension depends on speed of ball $v$.

You need to know the speed of ball.

If $v = \sqrt{gr}$, then $T = 0$.

If $> \sqrt{gr}$, then $T > 0$.

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