1. Work Transfers Energy Recall that energy and work have the same units
energy = kg x (m/s)2 = kg x m/s2 x m = Joules
work = N x m = kg m/s2 x m = Joules
In physics, this means they are two aspects of the same thing
Thus, in many situations, when a force is used to displace an object,
the energy of the object is changed
by an amount equal to the amount of work done

2. Work = ΔGPE
To lift an object, an upward force equal to the weight of the object must be applied
The work done on the object is that force times the distance it was raised W = (mg) x d
Before the object was moved, it had no GPE
After the object was moved, it had GPE = mgh
The change in GPE (final - initial) = mgh - 0 = mgh
Because d = h, W = ΔGPE; mg x d = mgh
The work transferred energy to the object

3. Work = ΔKE
When a moving car is brought to a stop, a braking force is applied throughout the stopping distance W = F x d
This work is negative because the displacement and force are in opposite directions
The change in KE = KEf - Kei ΔKE = 0 - ½ m v2
W = ΔKE F x d = -½ m v2
The work transferred (negative) energy to the car

4. Implications of Work = ΔKE
The W = ΔKE relationship allows us to
estimate the speed of a car in an accident based on the length of skid marks
estimate the speed of an arrow based on the force required to draw the bow and the length of the draw
estimate the force required to stop a roller coaster train in a given distance based on the train’s speed
We can also see that small changes in vehicle speed cause large changes in stopping distance