2. Work and Energy
Kinetic energy is defined as:
Ek = ½ mv2
If a particle is moving freely with no
unbalanced force acting on it:
NI tells us that it will move with constant
velocity.
This means that kinetic energy will also be
constant.
3. Work and Energy
What happens however if an unbalanced
force acts?
A constant unbalanced force produces:
a constant acceleration.
One of the kinematic equations that can
be used in this circumstance is:
4. Work and Energy
v2 – u2 = 2as
To find the K.E. multiply both sides by ½m.
½ mv2 - ½ mu2 = mas
From NII, F = ma
½ mv2 - ½ mu2 = Fs
6. Work and Energy
The work done by a constant unbalanced
force acting on a particle:
which is moving in one dimension is given by,
the product of the unbalanced force and,
the displacement produced.
W = Fs
7. Work and Energy
This equation shows us that if an unbalanced
force acts:
there will always be a change in kinetic
energy and,
an amount of work done.
A glider moving at constant velocity on an air
track has:
no unbalanced force acting on it.
8. Work and Energy
However, if it is on a slope;
there is an unbalanced force,
of gravity (weight),
acting on it and it will accelerate.
This weight can be resolved into two
components,
parallel and perpendicular to the motion.
10. Work and Energy
The perpendicular component of the
weight:
is balanced by the reaction force,
of the air track on the glider,
air on the glider.
11. Work and Energy
The unbalanced force is therefore the
parallel component of the weight.
This force:
multiplied by the displacement along the
track gives,
the work done on the glider.
12. Work and Energy
What part does the angle of inclination play in
calculating the work done?
13. Example
A Woolworths supermarket trolley (that
does move in the direction you push it), is
pushed with a force of 200 N acting at an
angle of 40o to the ground. Find the
effective horizontal force pushing the
trolley along.
16. Solution
FH is the effective force pushing the trolley
FH = F cos θ
FH = 200 x cos 40o
FH = 200 x 0.7660444
FH = 153 N Horizontally
17. Work and Energy
Work can be determined by studying a force-
displacement graph.
Force
(N)
Displacement
(m)
10
5
18. Work and Energy
Area under graph = height x length
Area under graph = Force x displacement
Force x displacement = Work
Area under graph = Work done
Area under graph = 5 x 10
Area under graph = 50 J
19. Work and Energy
Work is easy to calculate when the force is
constant.
What happens if the force is not constant?
Use a F vs. disp. graph.
21. Work and Energy
Work = Area under a F vs. Disp. Graph
Work = ½ (b x h)
Work = ½ (5 x 10)
Work = 25 J
22. Energy and Power
Kinetic Energy
Push an object and it can move.
If an object moves:
it is capable of doing work.
The object has energy associated with its
motion called:
Kinetic Energy
24. Energy and Power
As W = mas
W = ½mv2 – ½mu2
W = ∆½mv2
The quantity ∆½mv2 is called:
Kinetic Energy
a
uv
maW
2
22
−
=
25. Energy and Power
Kinetic Energy, Ek, can be defined as:
The product of half the object’s
mass m,
and the square of its speed v.
26. Energy and Power
Potential Energy
Kinetic energy is the
‘energy of motion’.
We can develop an
expression for the energy
that is dependent on
position;
potential energy.
27. Energy and Power
Consider an object that is dropped from a
height above the floor, ht:
where the floor is at height ho.
Displacement is given by s = ht - ho.
The unbalanced force is given by:
the weight of the object mg.
28. Energy and Power
As W = Fs
W = mg(ht - ho)
or W = mg∆h
This gives the work done in terms of the
objects position.
This quantity mgh, is defined as the
gravitational potential energy.
29. Energy and Power
P.E. = mgh
Work can also be defined as:
the change in gravitational potential energy.
When an object falls:
it loses gravitational potential energy,
and gains kinetic energy.
30. Energy and Power
Work can be calculated by the change in
either of these two terms.
Generally, work is defined as the change in
energy.
31. Energy and Power
The relationship between Ek, Ep and work
can be shown using a downhill skier.
32. Energy and Power
Energy transformation can be shown using a roller
coaster.
33. Energy and Power
Elastic Potential Energy
Consider a spring that has been
compressed.
When released for time t,
the spring will return to,
the uncompressed position.
34. Energy and Power
This means there must be an unbalanced
force acting.
This force is given by Hooke’s Law.
The restoring force in a spring is:
proportional to its extension or compression.
Graphically, it can be described as:
37. Energy and Power
The elastic potential energy can also be
calculated.
E.P.E. = ½kx2.
This suggests that as a spring is compressed
or extended:
the energy increases.
38. Energy and Power
Conservation of Energy
Consider a ball thrown vertically into the air.
It begins its motion with kinetic energy.
As it reaches it’s highest point:
The Ek is zero.
39. Energy and Power
At the same time, the G.P.E. has:
increased.
The loss of one type of energy:
is balanced by the gain in another.
Total Energy = mgh + ½mv2.
If a glass of whisky is pushed along a bar to a
waiting gunslinger:
is energy conserved?
40. Energy and Power
In this case,
the G.P.E. has not increased:
when the K.E. has decreased.
This however is not an isolated system.
Energy has been lost to friction.
The total energy in any isolated system:
is constant.
42. Energy and Power
A 3 kg cart moves down the hill.
Calculate the Ep lost and Ek gained.
43. Energy and Power
Ep = mgh
Ep = 3 x 9.8 x (0.40 – 0.05)
Ep = 10.3 J
Ek = ½ mv2
Ek = ½ x 3 x 2.622
Ek = 10.3 J
Energy is conserved.
44. Energy and Power
Energy can be expended to perform a
useful function.
A device that turns energy into some useful
form of work is called a:
Machine
45. Energy and Power
Machines cannot turn all the energy used
to run the machine into useful work.
In any machine, some energy goes to:
atomic or molecular kinetic energy.
This makes the machine warmer.
Energy is dissipated as heat.
46. Energy and Power
The amount of energy converted into:
useful work by the machine is called,
The efficiency.
An example of a simple machine is:
A pulley system.
We can do 100 J of work.
47. Energy and Power
Friction turn the pulleys which in turn rub on the
axles.
This may dissipate 40 J of energy as heat.
The system is 60% efficient.
48. Energy and Power
Efficiency can be expressed mathematically:
inputworktotal
outputworkuseful
efficiency =
50. Energy and Power
The work in this equation could be:
the change in kinetic energy or,
the work done on a mass that has been
lifted.
It does not matter what form the energy
takes:
it is just the rate at which work is done.
51. Energy and Power
A 100W light globe produces 100 J of
energy every second.
To give an idea of the size of 1 W,
a jumping flea produces 10-4 W,
a person walking 300 W and,
a small car 40 000 W.
