A ball of mass 1.85 kg is tied to a string of length 3.83 m as shown in Figure P

Question

A ball of mass 1.85 kg is tied to a string of length 3.83 m as shown in Figure P6.50. The ball is initially hanging vertically and is given an initial velocity of 7.1 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 28.5degree with the vertical? What is the speed of the ball when the string makes an angle 28.5degree with the vertical?

Explanation / Answer

Here ,

initial kinetic energy = 0.5 * m * v^2

initial kinetic energy = 0.5 * 1.85 * 7.1^2

initial kinetic energy = 46.63 J

the initial kinetic ebergy of the ball is 46.63 J

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initial potential energy = 0 J

the initial potential energy is 0 J

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for theta = 28.5 degree

final potential energy = m*g*L * (1 - cos(theta))

final potential energy = 1.85 * 9.8 * 3.83 * (1 - cos(28.5))

final potential energy = 8.414 J

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let the speed is v

final kinetic energy = initial kinetic energy - potential energy

0.5 * 1.85*v^2 = 46.63 - 8.414

solving for v

v = 6.43 m/s

the speed of the ball is 6.43 m/s

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