A child wants to twirl a small 100 gram ball attached to the end of a 1 meter co
ID: 1862996 • Letter: A
Question
A child wants to twirl a small 100 gram ball attached to the end of a 1 meter cord so that the ball traces a circle in a vertical plane as shown. What minimum initial speed should be given to the ball at point A so that it traces the entire vertical circle without creating any slack in the cord at any instant? Given this speed at point A, compute the tension in the cord when the ball reaches point C. Neglect any small motion of the child
A child wants to twirl a small 100 gram ball attached to the end of a 1 meter cord so that the ball traces a circle in a vertical plane as shown. What minimum initial speed should be given to the ball at point A so that it traces the entire vertical circle without creating any slack in the cord at any instant? Given this speed at point A, compute the tension in the cord when the ball reaches point C. Neglect any small motion of the child's hand. [Hint: Find how tension in the cord is changing with the ball's position. Next, find where the tension would be the least. To avoid slack, that least tension > 0] (Take g = 10 m/s2).Explanation / Answer
For Non Slaking
mv^2/R = mg
Therefore
v = sqrt(Rg)
At the bottom let velocity be u
Therefore
0.5*m*u^2 = mg*(2R) + 0.5*m*(sqrt(Rg))^2
u = sqrt(5gR)
= sqrt(5*10*1)
= 7.07 m/sec
0.5*m*v^2 = 0.5*m*7.07^2 + mgr
0.5*v^2 = 0.5*7.07^2 + 9.8*1
v = 8.34 m/sec
Tension = mv^2/r at C
= 0.100*8.34^2/1
= 6.955 N
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