Transcript Slide 1

CLB 10102
PHYSICS
CHAPTER 4
Work, Energy and
Power
Ahmad Azahari Hamzah
[email protected]
F2F
WEEK
TOPIC
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DELIVERY
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METHOD/
ASSESSMENT
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Physical Quantities and Dimensions
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Forces Acting at a Point
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Newton’s Laws of Motion and Friction
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Work, Energy and Power
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* TEST 1
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Optics
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Simple Machines
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* Mini project
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*Assignment 2
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The Effects of Forces on Materials
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Heat Energy
Thermal Expansion
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
4.1 Work
Work is the product of the force in the
direction of the motion and the displacement.
W = Fd
The work done by an agent exerting a
constant force (F) and causing a
displacement (d) equals the magnitude of the
displacement, times the component of along
the direction of.
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
In Figure 4.1, the work done by is:
W = Fd cos θ
F
θ
F cos θ
d
Figure 4.1: Work
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
Scenario A
A force acts rightward upon an object as it is
displaced rightward. In such an instance, the
force vector and the displacement vector are
in the same direction. Thus, the angle
between F and d is 0o.
F
d
θ = 0o
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
Scenario B
A force acts leftward upon an object which is
displaced rightward. In such an instance, the
force vector and the displacement vector are
in the opposite direction. Thus, the angle
between F and d is 180o.
F
d
θ = 180o
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
Scenario C
A force acts upward upon an object as it is
displaced rightward. In such an instance, the
force vector and the displacement vector are
at right angles to each other. Thus, the angle
between F and d is 90o.
F
θ = 90o
d
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
If d = 0 ➱W = 0. (i.e: no work is done when
holding a heavy box, or pushing against a
wall).
W = 0 if F ┴ d (i.e: no work is done by
carrying a bucket of water horizontally).
The sign of W depends on the direction of F
relative to d:
a) W > 0 when component of F along d is in
the same direction as d.
b) W < 0 when it is in the opposite direction.
If F acts along the direction of d
then W = Fd since cos θ = cos 0 = 1.
The SI units of work are Joules (J)
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
Examples:
A teacher applies a force to a wall and
becomes exhausted.
➦ This is not an example of work because
the wall is not displaced.
A book falls off a table and free falls to the
ground.
➦ There is a force (gravity) which acts on
the book which causes it to be displaced in a
downward direction.
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
A waiter carries a tray full of meals above his
head by one arm across the room.
➦ This is not an example of work because
there is a force ( the waiter pushes up the
tray), and there is a displacement (the tray
is moved horizontally across the room) but
the force does not cause the displacement.
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
Calculating of Work Done by Forces
When a force acts to cause an object to be
displaced, 3 quantities must be known in
order to calculate the work:
o Force
o Displacement
o Angle between the force and
displacement
The work is subsequently calculated as:
Force x Displacement x Cosine θ
where θ = angle between the force and the
displacement vectors.
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
Example:
Diagram
F = 100 N
15 kg
F = 100 N
30o
15 kg
F
15 kg
Statement of the problem
A 100 N force is applied to
move a 15 kg object a
horizontal distance of 5 m at
constant speed.
Solution
W = Fd cos θ
= (100 N)(5 m) cos 0o
= 500 Nm
= 500 J
A 100 N force is applied at
W = Fd cos θ
an angle 30o to the
= (100 N)(5 m) cos 30o
horizontal to move a 15 kg
object at a constant speed
= 433 Nm
for a horizontal distance of 5
= 433 J
m.
An upward force is applied
to lift a 15 kg object to a
height of 5 m at constant
speed.
W = Fd cos θ
= (150 N)(5 m) cos 0o
= 750 Nm
= 750 J
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
4.2 Energy
 Energy is the capacity or ability to do work.
 It is a scalar quantity and has the units of
Joules, (J).
 There are various types of energy, such as
mechanical, thermal, electrical and chemical
energy.
 Mechanical energy of a body or a system is
due to its position, its motion or its internal
structure.
 There are two kinds of mechanical energy:
i) Potential energy, EP
ii) Kinetic energy, EK
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
4.3 Potential Energy
Potential energy is the stored energy of a
body due to its internal characteristics or
its position.
 Water behind a dam
 Hammer over head
 Food on the plate
Potential energy:
 Gravitational potential energy
 Elastic potential energy
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
The gravitational potential energy
acquired by a weight, mg, in lifting it a
distance, h, above the ground is equal to the
work done in lifting the weight, i.e., mgh.
EP = mgh
Where m = mass
g = gravitational force
h = height
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
 Elastic potential energy is the energy
stored in elastic materials as the result of
their stretching or compressing.
 Can be stored in rubber bands, bungee
chords, trampolines, springs, an arrow
drawn into a bow, etc.
 The amount of elastic potential energy
stored in such a device is related to the
amount of stretch of the device - the more
stretch, the more stored energy.
 A force is required to compress a spring; the
more compression there is, the more force
which is required to compress it further.
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
For certain springs, the amount of force is
directly proportional to the amount of stretch
or compression (x); the constant of
proportionality is known as the spring
constant (k).
Elastic potential energy:
EP spring = ½kx2
Where k = spring constant
x = amount of compression
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
Example:
A cart is loaded with a brick and pulled at
constant speed along an inclined plane to
the height of a seat-top. If the mass of the
loaded cart is 4.0 kg and the height of the
seat top is 0.55 meters, then what is the
potential energy of the loaded cart at the
height of the seat-top?
EP = mgh
= (4.0 kg)(9.8 ms-2)(0.55 m)
= 21.56 J
CLB 10102 Physics
4.4 Kinetic Energy
Kinetic energy is the energy of
motion.
An object which has motion whether it be vertical or
horizontal motion - has kinetic
energy.
CHAPTER 4 Work, Energy & Power
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
There are many forms of kinetic energy:
• Vibrational (the energy due to vibrational
motion)
• Rotational (the energy due to rotational
motion)
• Translational (the energy due to motion
from one location to another).
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
The amount of translational kinetic energy
which an object has depends upon two
variables:
 mass (m)
 speed (v)
The following equation is used to represent
the kinetic energy (EK) of an object.
EK = ½mv2
This equation reveals that the kinetic energy
of an object is directly proportional to the
square of its speed.
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
That means:
 for a twofold increase in speed, the kinetic
energy will increase by a factor of 4;
 for a threefold increase in speed, the
kinetic energy will increase by a factor of 9.
The kinetic energy is dependent upon the
square of the speed.
Example:
Determine the kinetic energy of a 1000 kg roller
coaster car that is moving with a speed of 20.0 m/s.
EK = ½mv2
= ½(1000 kg)(20.0 m/s)2 = 200 000 J
= 200 kJ
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
4.5 WORK-ENERGY THEOREM
• Forces can be categorized as:
 Internal forces
 External forces
Internal Forces
External Forces
Gravitational Force, Fgrav Applied Forces, Fapp
Spring Forces, Fspring
Frictional Forces, Ffrict
Air Resistance Forces, Fair
Tensional Forces, Ftens
Normal Forces, Fnorm
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
• When work is done upon an object by an
external force, the TME = (EK + EP) of that
object is changed.
• If the work is "positive work“ ( +ve)
 the object will gain energy.
• If the work is "negative work“ ( -ve)
 the object will lose energy.
• The gain or loss in energy can be in the
form of potential energy, kinetic energy, or
both.
EKo + EPo + Wext = EK + EP
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
• When work is done upon an object by an
internal force, the TME = (EK + EP) of that
object remains constant.
• When the only forces doing work are internal
forces, energy changes forms or transform
from EK to EP (or vice versa);
 the sum of the EK + EP remain constant.
 the TME is conserved.
• In these situations, the sum of the EK + EP is
everywhere the same.
EKo + EPo = EK + EP
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
EXAMPLE:
• As an object falls from rest, its EP is
converted to EK.
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
4.6 Principle of Conservation of
Energy
Energy cannot be created or destroyed;
it may be transformed from one form into
another, but the total amount of energy
never changes.
At any point, the total mechanical energy
is given by:
E = Ek + Ep = ½mv2 + mgh
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
Description of Motion
EK to EP / EP to EK?
1. A ball falls from a height of
2 meters in the absence of air
resistance.
EP to EK
2. A skier glides from
location A to location B
across the friction free ice.
EP to EK
3. A bungee cord begins
to exert an upward force
upon a falling bungee
jumper.
EK to EP
4. The spring of a dart gun exerts
a force on a dart as it is launched
from an initial rest position.
EP to EK
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
4.7 Power
 Power is the rate of doing work.
P = Work =
Time
W
t
 The unit for power is Watt.
CLB 10102 Physics
CHAPTER 4 Work, Energy & Power
Example:
An escalator is used to move 20 passengers every
minute from the 1st floor of a department store to the
second. The 2nd floor is located 5 meters above the
1st floor. The average passenger's mass is 60 kg.
Determine the power requirement of the escalator in
order to move this number of passengers in this
amount of time.
Work done to lift 1 passenger
= (60 kg)(9.8 ms-2)(5 m) = 2940 J
Work done to lift 20 passenger
= 20 x 2940 J = 58800 J
Power = W/t = 58800 J = 980 Watts
60 s