8.8:
Conservation of Energy: Application
Recall the energy conservation law for solving a numerical problem.
A rock of mass 20 kilograms is situated at the edge of a cliff at a height of 5 meters. After sliding down the cliff, its velocity is 9 meters per second. What will be the change in the internal energy of the rock?
Here, the mass of the rock, the height of the rock from the ground, and the velocity of the rock after sliding down are known quantities, and the change in internal energy is an unknown quantity.
Initially, the kinetic energy of the rock is zero, while the potential energy calculated from the weight and height of the rock is 980 joules.
After sliding, the rock has zero potential energy and the kinetic energy calculated from the mass and velocity is 810 joules.
Lastly, substituting the values of change in kinetic and potential energy in the law of conservation of energy equation gives the change in internal energy of the rock as 170 joules.
8.8:
Conservation of Energy: Application
When solving problems using the energy conservation law, the object (system) to be studied should first be identified. Often, in applications of energy conservation, we study more than one body at the same time. Second, identify all forces acting on the object and determine whether each force doing work is conservative. If a non-conservative force (e.g., friction) is doing work, then mechanical energy is not conserved. The system must then be analyzed with non-conservative work. Third, for every force that does work, choose a reference point and determine the potential energy function for that force. The reference points for the various potential energies do not have to be at the same location. Finally, apply the principle of mechanical energy conservation by setting the sum of the kinetic energies and potential energies equal at every point of interest.
Note that systems generally consist of more than one particle or object. However, the conservation of mechanical energy is a fundamental law of physics and applies to any system. In such a case, include the kinetic and potential energies of all the particles and the work done by all the non-conservative forces acting on them.
This text is adapted from Openstax, University Physics Volume 1, Section 8.3: Conservation of Energy.