{"id":16611,"date":"2018-01-19T16:26:32","date_gmt":"2018-01-19T16:26:32","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=16611"},"modified":"2022-11-08T08:08:11","modified_gmt":"2022-11-08T08:08:11","slug":"what-is-mechanical-energy","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/what-is-mechanical-energy\/","title":{"rendered":"What is Mechanical Energy"},"content":{"rendered":"
Mechanical energy<\/strong> (and thermal energy) can be separated into two categories, transient and stored. Transient energy is energy in motion, that is, energy being transferred from one place to another. Stored energy is the energy contained within a substance or object. Transient mechanical energy is commonly referred to as work<\/strong>. Stored mechanical energy exists in one of two forms: kinetic<\/strong> or potential<\/strong>:<\/p>\n <\/a><\/p>\n First, the principle of the Conservation of Mechanical Energy<\/strong> was stated:<\/p>\n The total mechanical energy<\/strong> (defined as the sum of its potential and kinetic energies) of a particle being acted on by only conservative forces is constant<\/strong>.<\/span><\/em><\/p>\n <\/a><\/strong><\/p>\n See also: Conservation of Mechanical Energy<\/a>.<\/p>\n An isolated system<\/strong> is one in which no external force<\/strong> causes energy changes. If only conservative forces<\/strong> act on an object and U<\/strong> is the potential energy<\/strong> function for the total conservative force, then:<\/p>\n E<\/strong>mech<\/sub><\/strong> = U + K<\/strong><\/span><\/em><\/p>\n The potential energy, U<\/em><\/strong>, depends on the position of an object subjected to a conservative force.<\/p>\n <\/a><\/p>\n It is defined as the object’s ability to do work and is increased as the object is moved in the opposite direction of the direction of the force.<\/p>\n The potential energy<\/strong> associated with a system consisting of Earth and a nearby particle is\u00a0gravitational potential energy<\/strong>.<\/p>\n <\/a><\/p>\n The kinetic energy, K<\/em><\/strong>, depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them.<\/p>\n \u00a0K = \u00bd mv2<\/sup><\/strong><\/span><\/em><\/p>\n The definition mentioned above (E<\/strong>mech<\/sub><\/strong> = U + K<\/strong>) assumes that the system is free of friction<\/strong> and other non-conservative forces<\/strong><\/a>. The difference between a conservative and a non-conservative force is that when a conservative force moves an object from one point to another, the work done by the conservative force is independent of the path.<\/p>\n In any real situation, frictional forces<\/strong> and other non-conservative forces are present. Still, their effects on the system are so small that the principle of conservation of mechanical energy<\/strong> can be used as a fair approximation in many cases. For example, the frictional force is a non-conservative force because it reduces the mechanical energy in a system.<\/p>\n Note that non-conservative forces do not always reduce mechanical energy. A non-conservative force changes the mechanical energy. Some forces increase the total mechanical energy, like the force provided by a motor or engine, which is also a non-conservative force.<\/p>\n The 1 kg block starts at a height H (let say 1 m) above the ground, with potential energy<\/strong> mgH<\/strong> and kinetic energy<\/strong> equal to 0. It slides to the ground (without friction) and arrives with no potential energy and kinetic energy K = \u00bd mv2<\/sup><\/strong>. Calculate the velocity of the block on the ground and its kinetic energy. => \u00bd mv<\/em><\/strong>2<\/sup><\/em><\/strong> = mgH<\/em><\/strong><\/p>\n => v = \u221a2gH = 4.43 m\/s<\/em><\/strong><\/p>\n => K<\/em><\/strong>2<\/sub><\/em><\/strong> = \u00bd x 1 kg x (4.43 m\/s)<\/em><\/strong>2<\/sup><\/em><\/strong> = 19.62 kg.m<\/em><\/strong>2<\/sup><\/em><\/strong>.s<\/em><\/strong>-2<\/sup><\/em><\/strong> = 19.62 J<\/em><\/strong><\/p>\n <\/a>Assume a pendulum<\/strong> (ball of mass m suspended on a string of length L<\/strong> that we have pulled up so that the ball is a height H < L<\/strong> above its lowest point on the arc of its stretched string motion. The pendulum is subjected to the conservative gravitational force<\/strong> where frictional forces like air drag and friction at the pivot are negligible.<\/p>\n We release it from rest. How fast is it going at the bottom?<\/strong><\/p>\n\n
Conservation of Mechanical Energy<\/h2>\n
Example: Block sliding down a frictionless incline slope<\/h2>\n
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\nE<\/em><\/strong>mech<\/sub><\/em><\/strong> = U + K = const<\/em><\/strong><\/span><\/p>\nExample: Pendulum<\/h2>\n