A pendulum bob has a mass of 0.50 kg. And is suspended by a massless rod 2.0 met

Question

A pendulum bob has a mass of 0.50 kg. And is suspended by a massless rod 2.0 meters in length. The bob is pulled to an angle of 37 degrees and is released. Calculate its maximum potential energy, the potential energy when the bob makes and angle of 10 degreees to the vertical, its maximum speed, and its speed as it passes through the 10 degree position. A pendulum bob has a mass of 0.50 kg. And is suspended by a massless rod 2.0 meters in length. The bob is pulled to an angle of 37 degrees and is released. Calculate its maximum potential energy, the potential energy when the bob makes and angle of 10 degreees to the vertical, its maximum speed, and its speed as it passes through the 10 degree position.

Explanation / Answer

here,

mass , m = 0.5 kg

l = 2 m

theta1 = 37 degree

the maximum potnetial energy , PEm = m * g * l * ( 1 - cos(37))

PEm = 0.5 * 9.81 * 2 * ( 1 - cos(37)) J

PEm = 1.98 J

when theta2 = 10 degree

the potnetial energy , PE = m * g * l * ( 1 - cos(10))

PE = 0.5 * 9.81 * 2 * ( 1 - cos(10)) J

PE = 0.15 J

let the maximum speed be vm

using conservation of energy

0.5 * m * vm^2 = PEm

0.5 * 0.5 * vm^2 = 1.98

vm = 2.81 m/s

let the speed when theta2 = 10 degree be v

using conservation of energy

PEm - PE = 0.5 * m * v^2

1.98 - 0.15 = 0.5 * 0.5 * v^2

v = 2.7 m/s

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