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How do you calculate the mechanical energy of an object?

Use one of the 4 equations for mechanical energy.

There are 4 main types of mechanical :

  • Potential energy due to gravity
  • Kinetic energy
  • Rotational kinetic energy
  • Potential energy due to a spring.

The equations are as follows:

Potential energy due to gravity: ##U_g##=mgh where m is the mass of the object, g is gravity (9.8##m/s^2##), and h is the vertical height of the center of mass of the object above what you designate as the zero height.

Kinetic energy: K=##1/2 mv^2## Where m is the mass in Kg, and v is the linear velocity of the object in m/s.

Rotational kinetic energy: K=##1/2 I omega^2## I is the of the object ##omega## is the angular velocity in rad/sec You will only need to use this if you have an object rotating in your problem. (Such as a cylinder rolling down a ramp.)

Potential energy due to a spring: ##U_s = 1/2 k x^2## Where k is the spring constant measured in N/m and x is how much the spring is compressed, or stretched, again, in meters.

All the energies have units of Joules.

Now that you know the types of energies, you need to identify what types are present at the point of interest that you want to calculate the mechanical energy. Once you have identified this, it is just a mater of plugging and chugging to get the answer.

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