# A pendulum of length 73 cm and mass 2.4 kg swings with a mechanical energy of 0.019 J. What is the amplitude?

A pendulum of length 73 cm and mass 2.4 kg swings with a mechanical energy of 0.019 J. What is the amplitude? (in cm)

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A pendulum of length 73 cm and mass 2.4 kg swings with a mechanical energy of 0.019 J.

What is the amplitude? (in cm)

The Mechanical energy of 0.019 Joules causes the mass to move from the lowest point the highest point.

The mechanical energy is converted into potential energy as the mass moves from the lowest point the highest point.

Δ Potential energy = mass * 9.8 * Δ height

0.019 = 2.4 * 9.8 * Δ height

Δ height = 0.0008078 m

The length of the pendulum = 73 cm = 0.73 m

Go to the web site below to see a picture of a pendulum

http://

hyperphysics.phy-astr.gsu.edu/hbase/pendl.html

As the pendulum moves in an arc of θ, the mass moves up 0.0008078 m

The mass was 0.73 m below the pivot point.

Now the mass is 0.73 - 0.0008078 = 0.729192177 m

the cos of the angle = 0.729192177 ÷ 0.73

angle = 2.7°

The mass moves 2.6957° as it moves from the lowest point the highest point of its path.

The amplitude is the total distance that the mass moves, which is the distance from the highest point of its path on the left side to the lowest point the highest point of its path and on to the highest point of its path on the right side.

Amplitude = 2 * 2.6957° = 5.3914°

The radius of this arc is 0.73 m. so the circumference of the circle = 2 * π * 0.73 meters

5.3914° ÷ 360° = the fraction of the circle that the mass moved.

(5.3914° ÷ 360°) * (2 * π * 0.73) = the distance the mass moved

(5.3914° ÷ 360°) * (2 * π * 0.73) = 0.06869 m

What is the amplitude? (in cm) = 6.869 cm

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