1. MECHANICAL ENERGY

2. MECHANICAL ENERGY: The total mechanical energy of anything is simply the sum of its gravitational potential energy and its kinetic energy.
We will discuss each of these types separately and combine them later.

3. GRAVITATIONAL POTENTIAL ENERGY
Observe the ball of mass m sitting on the floor beside a table of height h. Because the floor is the lowest
possible position for the ball, we call this level the ground or the zero of potential.

4. Now suppose that someone lifts the ball up at constant speed
and places it on the table. This requires that work be done.
A force (the ball’s weight) must be applied through a distance
(the table’s height) to do the job

5. Therefore the work done on the ball = W = Fd = mgh
But this work represents the energy that the person has given
to the ball. The ball has this energy merely because of its
elevated position above the ground.
It is now capable of falling and doing some work that it
previously could not do.
This energy of position is called gravitational potential energy
and is given by the equation.
Ep = mgh

6. Be sure to keep your units straight – mass in kilograms, gravity in newtons per kilogram, and height in metres.
For example in the example described above, the mass of the ball was 1.5 kg and the table height was 0.75 m, then the gravitational potential energy of the ball on the table would be
Ep = mgh = (1.5 kg)(9.8 N/kg)(0.75 m) = 11 J

7. The ball is now capable of doing 11 J of work that it couldn’t do while on the floor.
Remember that you must know where the ground or zero of potential is before you can calculate the gravitational potential energy of anything

8. A coconut of mass 1 kg hangs from a tree as shown.
If you were asked to calculate the gravitational potential energy
of this coconut, you must first identify where the ground
or zero of potential is located. If you consider that the
base of the tree is the ground, then the gravitational
potential energy of the coconut would be
Ep = mgh = (1 kg)(9.8 N/kg)(5 m) = 49 J

9. However if the head of the person in the boat is taken as the ground, then the coconut has a lot more gravitational potential energy than before.
Ep = mgh
= (1 kg)(9.8 N)(25 m)
= 245 J
 If the coconut were to fall, it could do much more work on the person’s head (ouch!) than it could on the ground at the base of the tree.