![]() This relationship is called the work‐energy theorem: W net = K. The above derivation shows that the net work is equal to the change in kinetic energy. For example, a 2 kg mass moving with a speed of 3 m/s has a kinetic energy of 9 J. = (1/2) mv 2 Kinetic energy is a scalar quantity with the same units as work, joules (J). The right side of the last equation yields the definition for kinetic energy: K. ![]() Substitute the last expression for acceleration into the expression for work to obtain W = m ( v f 2 − v o 2) or W = (1/2) mv f 2 − (1/2) mv o 2. Consider a force applied parallel to the surface that moves an object with constant acceleration.įrom the definition of work, from Newton's second law of motion, and from kinematics, W = Fx = max and v f 2 = v o 2 + 2 ax, or a = ( v f 2 − v o 2)/2 x. The expression for kinetic energy can be derived from the definition for work and from kinematic relationships. Kinetic energy is the energy of an object in motion. For a gradually changing force, the work is expressed in integral form, W = ∫ F For example, in this case, the work done by the three successive forces is shown in Figure 1. The total work done is the total area between the curve and the x axis. The work performed on the object by each force is the area between the curve and the x axis. ![]() The force is increasing in segment I, is constant in segment II, and is decreasing in segment III. Figure shows the force‐versus‐displacement graph for an object that has three different successive forces acting on it. If work is done by a varying force, the above equation cannot be used. The SI unit for work is the joule (J), which is newton‐meter or kg m/s 2.
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