Everything Science Grade 12

8.3 CHAPTER 8. WORK, ENERGY AND POWER

Etotal,A = KEA+ PEA

=

1

2

mv^2 A+ mghA

=

1

2

mv^2 A+ mg(0)

=

1

2

mv^2 A

Etotal,B = KEB+ PEB

=

1

2

mvB^2 + mghB

=

1

2

mvB^2 + mg(0)

=

1

2

mvB^2

In the absence of friction and other external forces, the ball should slide

along the floor and its speed should be the same at positions A and B. Since

there are no external forces acting on the ball,its total mechanical energy at

points A and B are equal.

vA = vB

1

2

mv^2 A =

1

2

mv^2 B

Etotal,A = Etotal,B

Now, let’s investigate what happens when there is friction (an external force)

acting on the ball.

Roll the ball along a rough surface or a carpeted floor. What happens to the

speed of the ball at point A compared to point B?

If the surface you are rolling the ball along is very rough and provides alarge

external frictional force,then the ball should bemoving much slower atpoint

B than at point A.

Let’s compare the total mechanical energy of theball at points A and B:

Etotal,A = KEA+ PEA

=

1

2

mv^2 A+ mghA

=

1

2

mv^2 A+ mg(0)

=

1

2

mv^2 A

Etotal,B = KEB+ PEB

=

1

2

mvB^2 + mghB

=

1

2

mvB^2 + mg(0)

=

1

2

mvB^2

However, in this case, vA�= vBand therefore Etotal,A�= Etotal,B. Since

vA > vB

Etotal,A > Etotal,B

Therefore, the ball has lost mechanical energy asit moves across the carpet.

However, although theball has lost mechanical energy, energy in thelarger

system has still been conserved. In this case, the missing energy is thework

done by the carpet through applying a frictional force on the ball. In this case

the carpet is doing negative work on the ball.

When an internal forcedoes work on an objectby an (for example, gravitational and
spring forces), the total mechanical energy (KE +PE) of that object remains constant but
the object’s energy canchange form. For example, as an object falls in agravitational
field from a high elevation to a lower elevation,some of the object’s potential energy
is changed into kinetic energy. However, the sumof the kinetic and potential energies
remain constant. Whenthe only forces doing work are internal forces, energy changes
forms - from kinetic topotential (or vice versa); yet the total amountof mechanical
energy is conserved.