Prove that when a bodyattached to a cord is revolving in a vertical circle, thet

Question

Prove that when a bodyattached to a cord is revolving in a vertical circle, thetension

in the cord when the bodyis at the lowest point exceeds the tension when it is atits

highest point by six timesthe weight of the body.

Hints: (a) Draw separateFBDs for the body in both positions; (b) apply Newton’ssecond

law in both positions; (c)use the same coordinate system throughout; (d) do notassume

the speed of the ball isthe same throughout the motion; (e) you will need to make useof

the work-energy theorem;(f) convince yourself the tension force does no work(why?);

and (g) the unknown in this problem isTlower–Tupper.

Explanation / Answer

Tt = m vt2 / R- mg     the tension at the top Tb = m vb2 / R+ mg   the tension at the bottom Tb - Tt = m / R(vb2 - vt2) + 2 mg 1/2 m (vb2 -vt2) = 2 m g R    differencein KE at top and bottom due to change in PE (vb2 - vt2) =4 g R Tb - Tt = m / R(vb2 - vt2) + 2 mg = 6 m g after substituting

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