A ball of mass 1.44 kg is tied to a string of length 3.9 m. The ball is initiall

Question

A ball of mass 1.44 kg is tied to a string of length 3.9 m. The ball is initially hanging vertically and is given an initial velocity of 6.8 m/s in the horizontal direction. The ball then follows a circular arc as determined by the string.

1. What is the initial kinetic energy of the ball?

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

3. What is the potential energy of the ball when the string makes an angle 27° with the vertical?

4. What ist he speed of the ball when the string makes an angle 27° with the vertical?

Explanation / Answer

1. KE = mv^2/2 = 1.44 x 6.8^2 /2 = 33.29 J

2. PE = mgh = 0

3. h = L - Lcos27 = 3.9 ( 1 - cos27) = 0.425 m

PE = mgh = 1.44 x 9.81 x 0.425 = 6 J

4. using energy conservation ,

initial PE + KE = final PE + KE

0 + 33.29 = 6 + 1.44v^2 /2

v = 6.16 m/s

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