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In this chapter we will be concerned with mechanical energy, which comes in two forms: kinetic energy and potential energy. Kinetic energy is also called energy of motion. A moving object has kinetic energy. Potential energy, sometimes called stored energy, comes in several forms.
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An object which changes its height under the influence of gravity alone has a kinetic energy $T$ (or K.E.) due to its motion during the fall, and a potential energy $mgh$, abbreviated $U$ (or P.E.), whose sum is constant: \begin{equation} \underset{\text{K.E.}}{\tfrac{1}{2}mv^2}+ \underset{\text{P.E.}}{\vphantom{\tfrac{1}{2}}mgh}=\text{const ...
The function U(x) is called the potential energy associated with the applied force. The force derived from such a potential function is said to be conservative. Examples of forces that have potential energies are gravity and spring forces.
If you know the potential energies (\(\mathrm{PE}\)) for the forces that enter into the problem, then forces are all conservative, and you can apply conservation of mechanical energy simply in terms of potential and kinetic energy. The equation expressing conservation of energy is: \[\mathrm{KE_i+PE_i=KE_f+PE_f.}\]
Relate the difference of potential energy to work done on a particle for a system without friction or air drag; Explain the meaning of the zero of the potential energy function for a system; Calculate and apply the gravitational potential energy for an object near Earth’s surface and the elastic potential energy of a mass-spring system
The quantity \(\frac{1}{2}mv^2\) in the work-energy theorem is defined to be the translational kinetic energy (KE) of a mass \(m\) moving at a speed \(v\). ( Translational kinetic energy is distinct from rotational kinetic energy, which is considered later.)
Gravitational Potential Energy. The gravitational potential energy of an object with mass at a height h above ground can be calculated by: = h. Note that this is equivalent to the formula to calculate work done by or against gravity.
