Conservation of energy
The law of conservation of energy states that the total energy in an isolated system is constant. Energy is not created or destroyed; it changes form. For our purposes, total energy is the sum of kinetic and potential energies.
When a ball is thrown upwards, it is gaining potential energy and losing kinetic energy joule for joule. When it starts falling back down, the trade occurs in reverse. Mathematically,
.
When we substitute those energy changes, we can rearrange to get
.
This looks very similar to the eighth and final equation that we derived in the section on the equations of motion of the first unit.
If we were instead considering a situation where kinetic energy was converted to elastic energy (a ball hits a spring and compresses it), our equation would be .
Example
A 2.5 kg block is dropped from 7.5 m above the floor. What is its speed as it hits the floor?
We can used the equation that I just mentioned:
.
Solving for , we have
,
therefore the final speed is 12 m/s.