Potential Energy

The Potential Energy  calculator computes the potential energy of a body with a certain mass (m) at rest at a certain height (y).

INSTRUCTIONS: Choose units and enter the following:

• (m) Mass of the object.
• (y)  Elevation or height of the object.
• (g)  Acceleration due to gravity.

Potential Energy U(y):  The calculator returns the potential energy in Joules (J).  However this can be automatically converted to other energy units via the pull-down menu.

The Math / Science

The formula for Potential Energy is:

• U(y) = m • g • y

where:

• U(y) is potential energy.
• g is the acceleration due to gravity
• m is the mass and
• y is the vertical displacement

The default units for Potential Energy are Joules (J) for potential energy, meters per second (m/s²) for acceleration due to gravity, and meters (m) for vertical displacement.  

The default acceleration due to gravity (g) is that of surface of the Earth at Sea Level (9.80665 m/s² ) .  The user can override the default with other values.

Energy Calculators

• Kinetic Energy:                                    `KE= 1/2 *m * v^2`
• Kinetic Energy (change of velocity):    `KE = 1/2*m*(V_1-V_2)^2`
• Relativistic Kinetic Energy:                    `E_K = (m*c^2)/sqrt(1 - v^2"/"c^2") - m*c^2`
• Potential Energy:                                  `U(y) = m*g*y`
• Potential Energy of Gravity (two bodies):   `U(G) = - (G*m1*m2)/r`
• Nuclear Binding Energy:                       `E = m*c^2`
• Quantum Energy (Planck's Equation):   `E = h*f`
• Energy of a Particle in a Box:                `E_n=(n^2h^2)/(8mL^2)`
• Molecular Kinetic Energy:                      `KE = 3/2 * k_B *T`
• Electrostatic Potential Energy:               `E_(el) = k_e * (Q_1*Q_2)/d`
• Photon Energy from Wavelength:          `E = (h*c)/lambda`
• Heat Energy to Change Material Temperature:  `Q = C * m *DeltaT`

Scientific Application

This equation computes the energy required to move an object to a height.  The energy required is equal to the potential energy the object possesses just by being at that height. This is basically one way to store energy -- move it upward to a point where it has potential to be acted on by gravity.  We use potential energy when we store water above our towns in elevated storage tanks.  We use potential energy when we snowboard down a mountain.

So, if you climb a mountain, or something more well-defined like the famous Manitou Incline (approximately 2000 ft), the energy you must expend to lift your body's weight that distance against the force of gravity (neglecting energy of things like breathing and metabolic processes) is equivalent to the potential energy of your body lifted that distance. The energy spent climbing is equal to the potential energy you have when you have climbed the Incline.

This equation tells you that a 120 lb woman who climbs the Manitou Incline expends minimally about 325,400 Joules of energy.  Her potential energy at the top of the Manitou Incline is equivalent to that much energy.

For comparison:

• a lightning strike is somewhere in the vicinity of a potential energy of 500 Megajoules of energy (500,000,000 MJ).
• lifting a Ford F150 pickup over your head (assuming about 6-1/2 feet) is close to 45,826 Joules of energy.
• a 14 lb bowling ball possesses about 10,535 Joules of potential energy at the top of the Washington Monument (555 feet).
• a 185 lb receiver is lifted two feet of the ground by a linebacker and has the potential energy of around 502 Joules.

1. ^ http://en.wikipedia.org/wiki/Potential_energy
2. ^ http://en.wikipedia.org/wiki/Peanut_butter_and_jelly_sandwich

• More information is available regarding Potential Energy in Light and Matter chapter 12.2 Potential energy: energy of distance or closeness
• YouTube video on Potential Energy