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Energy
Kinetic energy is equal to one-half of mass times the square of velocity.
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Kinetic energy is equal to one-half of moment of inertia times the square of angular velocity.
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Potential energy due to gravity is equal to the product of mass, acceleration due to gravity, and height (elevation) of the object.
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Potential energy due to spring deformation is equal to one-half the product of the spring constant times the square of the change in length of the spring.
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Definition of terms
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Energy: a theoretically indefinable quantity that describes potential to do work. SI unit for energy is the joule (J). Also common is the calorie (cal).
The joule: defined as the energy needed to push with the force of one newton over the distance of one meter. Equivalent to one newton-meter (N·m) or one watt-second (W·s).
- 1 joule = 1 J = 1 newton • 1 meter = 1 watt • 1 second
Energy comes in many varieties, including Kinetic energy, Potential energy, and Heat energy.
Kinetic energy (K): The energy that an object has due to its motion. Half of velocity squared times mass. Units: joules (J)
Potential energy due to gravity (UG): The energy that an object has stored in it by elevation from a mass, such as raised above the surface of the earth. This energy is released when the object becomes free to move. Mass times height time acceleration due to gravity. Units: joules (J)
Potential energy due to spring compression (UE): Energy stored in spring when it is compressed. Units: joules (J)
Heat energy (Q): Units: joules (J)
Spring compression (Dx): The difference in length between the spring at rest and the spring when stretched or compressed. Units: meters (m)
Spring constant (k): a constant specific to each spring, which describes its “springiness”, or how much work is needed to compress the spring. Units: newtons per meter (N/m)
Change in spring length (Δx): The distance between the at-rest length of the spring minus the compressed or extended length of the spring. Units: meters (m)
Moment of inertia (I): Describes mass and its distribution. (kg•m2)
Angular momentum (ω): Angular velocity times mass (inertia). (rad/s)
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