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Calculate the total mechanical energy of a pendulum (mass 4 kg) as it swings from its highest point to its lowest point. Use the equations for gravitational potential energy and kinetic energy to determine these values based on the data given below. Total energy is the sum of gravitational potential energy and kinetic energy. In this problem, round gravity to: g = 10 m/s^2.

Data:

Mass of pendulum: 4 kg
Gravity: 10 m/s^2
Equations:

Gravitational potential energy: PE = mgh
Kinetic energy: KE = 1/2 mv^2

1 Answer

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The total mechanical energy of the pendulum remains constant during its swing due to the conservation of mechanical energy. Without specific measurements for height and speed, a numerical answer cannot be provided.

To calculate the total mechanical energy of a pendulum with a mass of 4 kg swinging from its highest point to its lowest, we apply the conservation of mechanical energy. At the highest point, the pendulum has maximum potential energy and no kinetic energy. The gravitational potential energy (PE) at the highest point is PE = mgh, where g is the acceleration due to gravity (10 m/s2) and h is the height. The kinetic energy (KE) at the lowest point is given by KE = 1/2 mv2, which will be equal to the potential energy at the highest point due to energy conservation.

In this scenario, we lack the specific height of the pendulum's swing; therefore, we cannot calculate its potential energy explicitly. However, we do know that the total mechanical energy remains the same throughout the motion due to conservation, and we can state that the total mechanical energy at the highest point is equal to the kinetic energy at the lowest point. Since no specific values for velocity or height are provided, we cannot give a numerical final answer.

In conclusion, the total mechanical energy of the pendulum remains constant during its swing, and it is equal to the potential energy at the highest point, which transforms into kinetic energy at the lowest point. Without specific values for height and velocity, we cannot provide a numerical answer.

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