Kinetic Energy:

Assume that the object shown by the scenario in figure below is lifted a certain distance, informing to it a potential energy Ep. What will occur if you let go of the rope, and the object falls reverse to the floor? At first, the object may do damage, either to the floor or to itself, whenever it hits. Secondly, it will be moving, and however accelerating, whenever it hits. Thirdly, all the potential energy which was informing to the object in lifting it will be transformed into other forms: sound, vibration, heat, and possibly the outward motion of flying chunks of linoleum or concrete.

Figure: Work is done whenever a force is applied over a particular distance. In this situation, the force is applied upward to an object against Earth's gravity.

Now think of the case an infinitesimal moment-an immediate-before the object strikes the floor. At this moment the kinetic energy overcome by the object will be just equivalent to the potential energy informing to it by lifting it. All this kinetic energy is about to be degenerated or transformed in the violence of impact. The kinetic energy is

E_k = F_q = ma_gq = 9.8mq

Here F is the force applied, q is the distance the object was elevated (and therefore the distance it falls), a_g is the acceleration of gravity, and m is the mass of the object. At this time we are taking a_g to be 9.8 m/s², accurate to only two major figures.

There is another way to state E_k for a moving object containing a mass m, as follows:

E_k = mv²/2

Here v is the speed of the object just before the impact. We could use the formulas for speed, displacement, and acceleration to compute the instant speed of the object whenever it hits the floor, although there is no requirement. We already contain a formula for kinetic energy in the illustration of figure shown above. The mass-velocity formula is far more common and applies to any moving object, even when work is not completed on it.

The other note must be made here. You will observe that we use the notation m (lowercase italic m) for mass and m (lowercase non-italic m) for meter.

PROBLEM:

Assume that the object has mass m = 1.0 kg and is elevated to 4.0 m. Compute the kinetic energy it achieves the instant before it strikes the floor, according to the force/displacement technique. Use a_g = 9.8 m/s², the acceleration of gravity.

SOLUTION:

This is completed according to the formula F = ma_gq.

Here, m = 1.0 kg, ag = 9.8 m/s², and q = 4.0 m. Hence:

E_k = 1.0 kg x 9.8 m/s² x 4.0 m

     = 39.2 kg . m²/s²

     = 39.2 J

We are given each input value to only two major figures; therefore we must round this off to E_k = 39 J.