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type. The amount of energy transformed (∆E) is called work W. The body losing energy does work, the body gaining energy has work done on it. Work is given by the force multiplied by the displacement through which the force acts, or: where F = force (N), d = displacement (m) KE = ½ mv2 Work = Change in Energy = Force × displacement
The scientific definition of work reveals its relationship to energy—whenever work is done, energy is transferred. For work, in the scientific sense, to be done, a force must be exerted and there must be motion or displacement in the direction of the force.
Work - Definition • There are only two relevant variables in one dimension: the force, F x, and the displacement, Δx. Work W is the energy transferred to or from an object by means of a force acting on the object. Energy transferred to the object is positive work, and energy transferred from the object is negative work. W =F x
Net work is defined to be the sum of work done by all external forces—that is, net work is the work done by the net external force \(F_{net}\). In equation form, this is \(W_{net} = F_{net}d \, cos \, \theta\), where \(\theta\) is the angle between the force vector and the displacement vector.
To understand energy and conservation of energy, we must first define some terms: work, kinetic energy (KE), and potential energy (PE). We’ll get to PE in the next Chapter.
When we drop the rock the force of gravity causes the rock to fall, giving the rock kinetic energy. When work done on an object increases only its kinetic energy, then the net work equals the change in the value of the quantity 1 2 m v 2 1 2 m v 2. This is a statement of the work–energy theorem, which is expressed mathematically as
Objectives: To describe the conditions under which positive and negative work are done and to use the work equation to calculate the amount of work done. To define potential energy, to identify the two forms and the variables that affect the amount of each form, and to calculate the potential energy possessed by an object.
