Work, Energy, and Power!

Work = Force x Distance
or W = F(d)
The units of work are Newton meters (Nm), otherwise known as Joules (J).
We also learned about the Law of Conservation of Energy which states that in an isolated system energy cannot be created nor destroyed, it just changes forms. Therefore, change(in) = change(out).
There are two kinds of energies:
Gravitational Potential Energy (PEg) - Energy of Position
Gravitational potential energy = mass x gravity x height
PEg = mgh
and...
Kinetic Energy (KE) - Energy of Motion
Kinetic energy = 1/2 x mass x velocity squared
KE = 1/2mv^2
Power = change in energy/time
Power = work/time
The units of power are Joules/seconds, otherwise known as Watts.
When analyzing a force x distance graph, you should always remember: The area under the curve of a force x distance graph is WORK.

PEs = 1/2kd^2
where PEs is the elastic potential, k is the spring constant, and d is the distance stretched.
The bigger the spring constant, the harder it is to pull or stretch the spring. Therefore, with a larger spring constant, you need to apply more force.
When I was studying at Coffee Bean and Tea Leaf this afternoon, I accidentally dropped my pencil. I noticed that this was exactly like one of the problems that we discussed in class!
Let's say that my pencil with a mass of .4 kg fell to the floor from a table that was 2 m high. Can we find it's velocity?
Of course we can!
We first use the gravitational potential energy equation to find the amount of energy.
PEg = mgh
PEg = (0.2 kg)(10 m/s^2)(2 m)
PEg = 4 J
Then we use the kinetic energy equation to find the velocity.
KE = 1/2mv^2
4 J = 1/2 (0.5 kg)(v^2)
2 = (0.5 kg)(v^2)
1 = v^2
v = 1 m/s
Yay! We just did work!