Using some simple equations, we can define much more precisely how to measure potential and kinetic energy.
Potential Energy=mgh
Kinetic Energy =(1/2)mv²
m=mass
v=velocity
g=gravitational acceleration (9.8 m/s² on earth)
h=height
The units that these equations result in are Joules, the metric unit of energy (if you use kilograms for mass, 9.8 meters per second squared for g, meters per second for velocity, and meters for height).
All of the above examples can be redone to calculate the exact speed of the ball from its kinetic energy. Solve for the change in potential energy by using the difference between the heights for h in the potential energy equation. Then solve for v in the kinetic energy equation assuming the total difference was transferred to kinetic energy.
Problems
9. An airplane flying at 200 m/s has a mass of 300 kg. Another airplane is flying at 100 m/s and has the same amount of kinetic energy as the first plane. What is the mass of the second airplane?
10. Pretend you're swinging on the swing shown below. At the highest point of your swing, you are 3 meters above the ground. At the lowest point, you are 1 meter above the ground. What is your speed at the lowest point?