Kinetic energy

If a constant force F acts through a displace­ment ∆x, it does work W = F ∆ x = ma ∆ x on the particle. Since the acceleration is constant, we may use Eq.3.12, , to replace a∆x in the expression for W:

(4.7)

The quantity

(4.8)

is a scalar and is called the kinetic energy of the particle. Kinetic energy is energy that a particle possesses by virtue of its motion. Equation 4.7 may be written in the form

W _NET = ∆ K (4.9)

where W _NET is the work done by the resultant of all the forces acting on the particle. Equation 4.9 is called the work-energy theorem. It states that the net work done on a particle is equal to the resulting change in its (translational) kinetic energy. From Eq. 4.9 we see that the kinetic energy of an object is a measure of the amount of work needed to increase its speed from zero to a given value. Equivalently, the translational kinetic energy of an object is the work it can do on its surroundings in coming to rest. This fits the idea of energy as the capacity to do work.

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