<\/a><\/p>\nwhere L<\/em><\/strong> is the length of the pendulum and g<\/em><\/strong> is the local acceleration of gravity. For small swings, the period of swing is approximately the same for different size swings. That is, the period is independent of amplitude<\/strong>.<\/div><\/div><\/div>\nThe Law of Conservation of Energy – Non-conservative Forces<\/h3>\n
We now take into account non-conservative forces<\/strong> such as friction since they are important in real situations. For example, consider the pendulum again, but this time let us include air resistance<\/strong>. The pendulum will slow down because of friction. In this and other natural processes, the mechanical energy<\/strong> (sum of the kinetic and potential energies) does not remain constant<\/strong> but decreases. Because frictional forces<\/strong> reduce the mechanical energy (but not the total energy), they are called non-conservative forces<\/strong> (or dissipative forces<\/strong>). But in the nineteenth century, it was demonstrated the total energy is conserved in any process<\/strong>. In the case of the pendulum, its initial kinetic energy is all transformed into thermal energy.<\/p>\nFor each type of force, conservative or non-conservative, it has always been found possible to define a type of energy that corresponds to the work done by such a force. And it has been found experimentally that the total energy E<\/strong> always remains constant. The general law of conservation of energy<\/strong> can be stated as follows:<\/p>\nThe total energy E of a system (the sum of its mechanical energy and its internal energies, including thermal energy) can change only by amounts of energy transferred to or from the system.<\/span><\/em><\/strong><\/p>\nConservation of Momentum and Energy in Collisions<\/h3>\n
The use of the conservation laws for momentum and energy<\/strong> is also very important in particle collisions<\/strong>. This is a very powerful rule because it can allow us to determine the results of a collision without knowing the details of the collision. The law of conservation of momentum<\/strong> states that the total momentum is conserved<\/strong> in the collision of two objects such as billiard balls. The assumption of conservation of momentum and the conservation of kinetic energy makes possible the calculation of the final velocities<\/strong> in two-body collisions. At this point, we have to distinguish between two types of collisions:<\/p>\n\n- Elastic collisions<\/strong><\/li>\n
- Inelastic collisions<\/strong><\/li>\n<\/ul>\n
Elastic Collisions<\/h3>\n
A perfectly elastic collision<\/strong> is defined as one in which there is no net conversion of kinetic energy<\/strong> into other forms (such as heat or noise). For the brief moment during which the two objects are in contact, some (or all) of the energy is stored momentarily in the form of elastic potential energy<\/strong>. But if we compare the total kinetic energy just before the collision with the total kinetic energy just after the collision, they are found to be the same. We say that the total kinetic energy is conserved<\/strong>.<\/p>\n