A ball of mass 1.36 kg is tied to a string of length 4.24 m as shown in Figure P

Question

A ball of mass 1.36 kg is tied to a string of length 4.24 m as shown in Figure P6.50. The ball is initially hanging vertically and is given an initial velocity of 8 m/s in the horizontal direction. The ball then follows a circular arc as determined by the string.

What is the initial kinetic energy of the ball?

What is the initial potential energy of the ball? Assume the height of the ball when it is hanging straight down is zero.

What is the potential energy of the ball when the string makes an angle 31.5° with the vertical?

Explanation / Answer

initial kinetic energy of the ball= 0.5*m*V2= 43.52 Joule

initial potential energy of the ball= zero

potential energy of the ball when the string makes an angle 31.5° with the vertical (if ball is below center) = mgL(1-Cos(31.5) )= 8.3359 Joule

speed of the ball when the string makes an angle 31.5° with the vertical=

0.5*m*V2= 43.52-8.3359

V= 7.193 m/sec

If ball is considered above center then ans will be different

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