KINETIC ENERGY
 

Suppose that the object shown by the scenario in Fig. 1 is lifted a certain distance, imparting to it a potential energy E_p. What will happen if you let go of the rope, and the object falls back to the floor? First, the object might do damage, either to the floor or to itself, when it hits. Second, it will be moving, and in fact accelerating, when it hits. Third, all the potential energy that was imparted to the object in lifting it will be converted into other forms: vibration, sound, heat, and possibly the outward motion of flying chunks of concrete or linoleum.

Fig. 1. Work is done when a force is applied over a specific distance. In this case, the force is applied upward to an object against Earth’s gravity.

Now think of the situation an infinitesimal moment—an instant—before the object strikes the floor. At this moment the kinetic energy possessed by the object will be just equal to the potential energy imparted to it by lifting it. All this kinetic energy is about to be dissipated or converted in the violence of impact. The kinetic energy is
E_k = F_q = ma_gq = 9.8mq
where F is the force applied, q is the distance the object was raised (and thus the distance it falls), m is the mass of the object, and a_g is the acceleration of gravity. Here we are taking a_g to be 9.8 m/s², accurate to only two significant figures.
There is another way to express E_k for a moving object having a mass m. This is
E_k = mv²/2
where v is the speed of the object just before impact. We could use the formulas for displacement, but there’s no need. We already have a formula for kinetic energy in the example of Fig. 1. The mass-velocity formula is far more general and applies to any moving object, even if work is not done on it. Another note should be made here. You will notice that we use the notation m (lowercase italic m) for mass and m (lowercase nonitalic m) for meter(s). It is easy to get careless and confuse these. Don’t.