Definition of work: The work done by a constant force acting on an object is equal to the product of the magnitudes of the displacement and the component of the force parallel to that displacement. In (a), there is a force but no displacement: no work is done. In (b), the force is parallel to the displacement, and in (c) the force is at an angle to the displacement. If the force is at an angle to the displacement, as in (c), a more general form for the work must be used: Unit of work: newton • meter (N • m) 1 N • m is called 1 joule. If the force (or a component) is in the direction of motion, the work done is positive. If the force (or a component) is opposite to the direction of motion, the work done is negative. If there is more than one force acting on an object, it is useful to define the net work: The total, or net, work is defined as the work done by all the forces acting on the object, or the scalar sum of all those quantities of work. The force exerted by a spring varies linearly with the displacement: A plot of force versus displacement allows us to calculate the work done: The net force acting on an object causes the object to accelerate, changing its velocity: We can use this relation to calculate the work done: Kinetic energy is therefore defined: The net work on an object changes its kinetic energy. This relationship is called the work–energy theorem. Potential energy may be thought of as stored work, such as in a compressed spring or an object at some height above the ground. Work done also changes the potential energy (U) of an object. We can, therefore, define the potential energy of a spring; note that, as the displacement is squared, this expression is applicable for both compressed and stretched springs. Gravitational potential energy: Only changes in potential energy are physically significant; therefore, the point where U = 0 may be chosen for convenience. We observe that, once all forms of energy are accounted for, the total energy of an isolated system does not change. This is the law of conservation of energy: The total energy of an isolated system is always conserved. We define a conservative force: A force is said to be conservative if the work done by it in moving an object is independent of the object’s path. So, what types of forces are conservative? Gravity is one; the work done by gravity depends only on the difference between the initial and final height, and not on the path between them. Similarly, a nonconservative force: A force is said to be nonconservative if the work done by it in moving an object does depend on the object’s path. The quintessential nonconservative force is friction. Another way of describing a conservative force: A force is conservative if the work done by it in moving an object through a round trip is zero. We define the total mechanical energy: For a conservative force: Many kinematics problems are much easier to solve using energy conservation. All three of these balls have the same initial kinetic energy; as the change in potential energy is also the same for all three, their speeds just before they hit the bottom are the same as well. In a conservative system, the total mechanical energy does not change, but the split between kinetic and potential energy does. If a nonconservative force or forces are present, the work done by the net nonconservative force is equal to the change in the total mechanical energy. The average power is the total amount of work done divided by the time taken to do the work. If the force is constant and parallel to the displacement, Mechanical efficiency: The efficiency of any real system is always less than 100%. Work done by a constant force is the displacement times the component of force in the direction of the displacement. Kinetic energy is the energy of motion. Work–energy theorem: the net work done on an object is equal to the change in its kinetic energy. Potential energy is the energy of position or configuration. The total energy of the universe, or of an isolated system, is conserved. Total mechanical energy is the sum of kinetic and potential energy. It is conserved in a conservative system. The net work done by nonconservative forces is equal to the change in the total mechanical energy. Power is the rate at which work is done.

• published: 19 Nov 2014
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