### Work Energy Theorem

**The net work done on an object is equal to the change in the object's kinetic energy **

OR

the work done on an object by a resultant (net) force is equal to the change in the object's kinetic energy.

**Equation:**

**Expanded equation:**

- This only works if you are calculating the NET work.
- This is very convenient since you can now calculate net work using mass and velocity

Question 1

**Study this diagram which shows a force F being applied to a 2kg box.
The box has a velocity of 3m.s**^{-1} and the velocity is increased to 8m.s^{-1}.

**Calculate the net work done by this force on the box.**

Since the force is not known, we cannot use the equation W = FΔx.

Instead we will use the mass-velocity method called the work-energy theorem.

From the work-energy theorem, net work is 55J.

Question 2

** Study the diagram. The net work done on the mass is 182J.**

**2.1.Calculate the magnitude of the final velocity. **

**2.2.Calculate the effective power involved if the time taken was 2s. **

Question 3

**An arrow of mass 80g strikes a tree trunk at a velocity of 60m.s**^{-1} and is brought to rest in a time of 0,1s.

**3.1. Calculate the magnitude of work done by the tree trunk in stopping the arrow.**

Calculate the loss in kinetic energy of the arrow.This would be the work done by the tree trunk. Convert the 80g to kg by dividing by 1000.
The final velocity of the arrow would be zero, since it was brought to rest.

Notice the brackets around the 60^{2}. The MINUS SIGN is NOT squared.

The tree trunk did 144J of work.

**3.2. Calculate the magnitude of power involved in stopping the arrow.**