CK-12-Physics - Intermediate

6.2. Energy http://www.ck12.org

FIGURE 6.11

From our kinetic energy formula, the initial kinetic energy is^12 mvi^2 , while the final kinetic energy is^12 mvf^2. Com-

bining this with the previous kinematic equation, we have:

KEf=^12 mvf^2 =^12 m(vi^2 + 2 a∆x) =^12 mvi^2 +(ma)∆x

We know from Newton’s Second Law thatΣF=Fnet=ma, so this final term is justF∆x, which is thenet workdone

on the object.

The equationWnet=∆KEis referred to as theWork-Energy Principle.

What we have learned from the above is that the change in kinetic energy can easily be found by computing the work

done. The change in kinetic energy of the race car is therefore:

W=F x= (ma)x= (900kg)(5m/s^2 )(60m) = 270 ,000 J

Check Your Understanding

1a. Let’s revisit Example 6.1.4, where we’re told that the man is pulling a tire with a force of 300 N. We’ll assume

he is pulling the tire at a constant speed in a fixed direction. If so, what is the net work done on the tire? SeeFigure

6.12.

Answer:If the speed remains constant, then the change in kinetic energy is zero by the Work-Energy Principle and

therefore the net work done on the tire must be zero.

1b. True or False: Since the net work done on the tire is zero, there must be negative work done on the tire.

Answer:True

1c. What force is responsible for doing negative work on the tire?

Answer:Friction

1d. Explain how friction does negative work.