Total energy
The reason we are interested in energy is that the total energy in the universe is constant. When one object gains energy, it must have come from somewhere. This places a constraint on what can happen in any situation. In studying any event, physicists consider what happened to the energy as the first step in understanding the process.
Energy has many forms. Some are more obvious and easy to recognize than others. We have focused on energy due to gravity in the previous activities because it is uncomplicated and easy to measure.
Kinetic energy
Objects that are moving have a kind of energy called kinetic energy (which is Greek for "energy of motion"). Kinetic energy is related to mass and speed by
Kinetic Energy =1/2 mass x velocity2 .
The presence of the factor of mass means that a massive object has more kinetic energy than a less-massive object traveling at the same speed; changing the speed of a very massive object will require adding a lot of energy to it.
We can analyze the ball rolling down an incline in terms of energy, by observing that there is an unbalanced force on the ball that is transferring energy to it, and its kinetic energy is increasing correspondingly. Unfortunately, a rolling ball is not as simple as it appears: the part of the ball that is in contact with the track is temporarily not moving at all, and other parts of the ball are moving upwards or downwards, and with different speeds. The result is that the kinetic energy of the rolling ball is proportional to mv2 but the coefficient in front is not 1/2 (or we could say, the mass that appears in this equation is different from what we get when we weigh the ball). This complication is not present when we throw a ball, but now the ball is going too fast for us to measure the speed with a stopwatch over distances that will fit in a classroom.
Potential energy
When you lift a watermelon, you exert an upward force and the watermelon moves in the upward direction. Therefore you have transferred energy to it. Where is this energy? It hasn't gone far, because we can get it back by letting go! When the watermelon returns to its original height, it will have kinetic energy -- exactly the energy you gave it earlier.
But where was the energy in the meanwhile? The watermelon isn't hotter, or moving fast, or different in any visible way, except that it is higher. This points to the existence of a new kind of energy, called gravitational potential energy. It is a property of the interacting system consisting of the watermelon and the earth itself.
As you were lifting the watermelon, you were increasing the potential energy. Because the gravitational force is constant, the gravitational potential energy is just
Gravitational potential energy = weight x height
It may seem that there are two ways to use energy concepts to describe a falling object: