# 8.1 Energy

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## External and internal forces

In Grade 10, you saw that mechanical energy was conserved in the absence of external forces. It is important to know whether a force is an internal force or an external force in the system, because this is related to whether the force can change an object's total mechanical energy when it does work on an object.

When an external force (for example friction, air resistance, applied force) does work on an object, the total mechanical energy (KE + PE) of that object changes. If positive work is done, then the object will gain energy. If negative work is done, then the object will lose energy. The gain or loss in energy can be in the form of potential energy, kinetic energy, or both. However, the work which is done is equal to the change in mechanical energy of the object.

## Investigations : external forces

We can investigate the effect of external forces on an object's total mechanical energy by rolling a ball along the floor from point A to point B.

Find a nice smooth surface (e.g. a highly polished floor), mark off two positions, A and B, and roll the ball between them.

The total mechanical energy of the ball, at each point, is the sum of its kinetic energy (KE) and gravitational potential energy (PE):

$\begin{array}{ccc}\hfill {E}_{\mathrm{total},\mathrm{A}}& =& {\mathrm{KE}}_{\mathrm{A}}+{\mathrm{PE}}_{\mathrm{A}}\hfill \\ & =& \frac{1}{2}m{v}_{A}^{2}+mg{h}_{A}\hfill \\ & =& \frac{1}{2}m{v}_{A}^{2}+mg\left(0\right)\hfill \\ & =& \frac{1}{2}m{v}_{A}^{2}\hfill \end{array}$
$\begin{array}{ccc}\hfill {E}_{\mathrm{total},\mathrm{B}}& =& {\mathrm{KE}}_{\mathrm{B}}+{\mathrm{PE}}_{\mathrm{B}}\hfill \\ & =& \frac{1}{2}m{v}_{B}^{2}+mg{h}_{B}\hfill \\ & =& \frac{1}{2}m{v}_{B}^{2}+mg\left(0\right)\hfill \\ & =& \frac{1}{2}m{v}_{B}^{2}\hfill \end{array}$

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.

$\begin{array}{ccc}\hfill {v}_{A}& =& {v}_{B}\hfill \\ \hfill \frac{1}{2}m{v}_{A}^{2}& =& \frac{1}{2}m{v}_{B}^{2}\hfill \\ \hfill {E}_{\mathrm{total},\mathrm{A}}& =& {E}_{\mathrm{total},\mathrm{B}}\hfill \end{array}$

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 a large external frictional force, then the ball should be moving much slower at point B than at point A.

Let's now compare the total mechanical energy of the ball at points A and B:

$\begin{array}{ccc}\hfill {E}_{\mathrm{total},\mathrm{A}}& =& {\mathrm{KE}}_{\mathrm{A}}+{\mathrm{PE}}_{\mathrm{A}}\hfill \\ & =& \frac{1}{2}m{v}_{A}^{2}+mg{h}_{A}\hfill \\ & =& \frac{1}{2}m{v}_{A}^{2}+mg\left(0\right)\hfill \\ & =& \frac{1}{2}m{v}_{A}^{2}\hfill \end{array}$
$\begin{array}{ccc}\hfill {E}_{\mathrm{total},\mathrm{B}}& =& {\mathrm{KE}}_{\mathrm{B}}+{\mathrm{PE}}_{\mathrm{B}}\hfill \\ & =& \frac{1}{2}m{v}_{B}^{2}+mg{h}_{B}\hfill \\ & =& \frac{1}{2}m{v}_{B}^{2}+mg\left(0\right)\hfill \\ & =& \frac{1}{2}m{v}_{B}^{2}\hfill \end{array}$

However, in this case, ${v}_{A}\ne {v}_{B}$ and therefore ${E}_{\mathrm{total},\mathrm{A}}\ne {E}_{\mathrm{total},\mathrm{B}}$ . Since

$\begin{array}{ccc}\hfill {v}_{A}& >& {v}_{B}\hfill \\ \hfill {E}_{\mathrm{total},\mathrm{A}}& >& {E}_{\mathrm{total},\mathrm{B}}\hfill \end{array}$

Therefore, the ball has lost mechanical energy as it moves across the carpet. However, although the ball has lost mechanical energy, energy in the larger system has still been conserved. In this case, the missingenergy is the work 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 force does work on an object by an (for example, gravitational and spring forces), the total mechanical energy (KE + PE) of that object remains constant but the object's energy can change form. For example, as an object falls in a gravitational field from a high elevation to a lower elevation, some of the object's potential energy is changed into kinetic energy. However, the sum of the kinetic and potential energies remain constant. When the only forces doing work are internal forces, energy changes forms - from kinetic to potential (or vice versa); yet the total amount of mechanical energy is conserved.

#### Questions & Answers

Do polymers form restrictedly only if compound is saturated, only?
milani Reply
what is a free fall?
Beyanca Reply
is when The Only Force acting On an Object is Gravitational Force
Madman
Thats right
Beyanca
then Why ask when you Know the answer?
Madman
She's just helping those who forgot it...bro
Thato
guys I need help on Getting ready for a last minute test
Kenelioe Reply
what help you need
Neil
we'll I'm in grade 12 so we doing this topic about upac thing
Kenelioe
on What?
Madman
the organic molecule section
Kenelioe
IUPAC NAMING WHICH FUNCTIONAL GROUP YOU CANNOT NAME?SO I COULD HELP YOU
Madman
ester
Sboniso
you should also look at structural isomers. Its crucial that they might add that one. also try and write down the structural formula of all the given compounds on the table
milani
hi guys i can explain everything in terms of physics and chemistry
Neil Reply
😂😂😂😂😂
Madman
yes
Lucky
yea
Kenelioe
guys 2mrrow I'm writing a test in chemistry I need help
Kenelioe
Hi guys. Can anyone please tell me what a functional group is?
Samukelo
a functional group depends on how many bonds there are between carbon atoms, if there are single bonds all the way it's an alkane, if there is a presence of at least one double bond it's a Alkene and if there's at least one triple bond it's an alkyne.
Olive
which quantity is measured in Watt?
Saara Reply
work
Absai
explain for me absai
Sboniso
is Power Not Work work is Measured In Joules it has Energy
Madman
thanks
Saara
Pleasure
Madman
what is galvanic cell ?
Oratile Reply
is an electrochemical cell that derives electrical energy from spontaneous redox reactions taking place within the cell.
Hope
how to understand alkane names
Sboniso Reply
suffix Ane in the IUPAC NAMING
Madman
elaborate a little more plz
Kenelioe
Alkanes are Saturated Meaning they don't have Multiple Bonds between Carbon Atoms and When you are Naming THEM THEY MUST END WITH (-ANE ) GET ME?
Madman
What are hydrocarbons
Phelo Reply
are organic Compounds with only Carbon and Hydrogen Atoms
Madman
whats the difference between aldehydes and ketones
Angel Reply
definition of chain parent
Lea Reply
what is wave?
Agness Reply
when butane burns in an excess of oxygen ,the products are
Slay
CO2 and H2O
GARY
Carbon dioxide and Water...
Thato
what is hydrocarbon
Ntswaki Reply
Hydrocarbon is a compostion of mainy carbon and hydrogen
Tsion
hydrocarbon compound made up of carbon and hydrogen only
Thembelani
25 element of physics
musah Reply
an object will remain at rest or move at a constant velocity unless acted upon a net force
Lebogang Reply
thank you
Thabiso
law of inertia
Joan
an object resisting the change in velocity.
Thabiso
newton first law of motion
Tshepo
An object will remain at rest, unless an unbalanced force acts on it.
Anga
or uniform motion
Thato
What is a molecule
Thabiso Reply
a molecule is a simplest structure unite of an elements
Else
thank you
Thabiso
Plz remind me the 1st Newton's law
Thabiso

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Source:  OpenStax, Siyavula textbooks: grade 12 physical science. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11244/1.2
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