A ball of mass 2.12 kg is tied to a string of length 4.14 m. The ball is initial

Question

A ball of mass 2.12 kg is tied to a string of length 4.14 m. The ball is initially hanging vertically and is given an initial velocity of 9.7 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 32° with the vertical?

What ist he speed of the ball when the string makes an angle 32° with the vertical?

Explanation / Answer

Here ,

mass of ball , m = 2.12 Kg

length , L = 4.14 m

initial velocity , v = 9.7 m/s

initial kinetic energy = 0.5 m * v^2

initial kinetic energy = 0.5 * 2.12 * 9.7^2

initial kinetic energy = 99.74 J

the initial kinetic energy is 99.74 J

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initial potential energy = m * g * 0

initial potential energy = 0 J

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poetential energy of the ball at theta = 32 degree

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

Potential energy = 2.12 * 9.8 * 4.14 * (1 - cos(32))

Potential energy = 13.1 J

the potential energy of the ball is 13.1 J

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kinetic energy = 99.74 - 13.1

kinetic energy = 88.7 J

0.5 * 2.12 * v^2 = 88.7

v = 9.04 m/s

the speed of the ball is 9.04 m/s

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