TOPIC 5: Work, Energy

1
TOPIC 5Work, Energy Power
2
WORK

• Definition of Work
• When a force causes a displacement of an object
• Components of the force need to be in the
  direction of the displacement

3
Net Work done by a Constant Net Force

• Work Force (F) x Displacement (x)
• W Fx
• W Fx (Fcos?)x
• Only the component of the force in the
  direction of the displacement, contributes to
  work

4
Units of Work

• Work Force x Displacement
• Newtons x meters
• Newton x meter ? Joule (J)
• Joule is named after James Prescott Joule
  (1818-1889) who made major contributions to the
  understanding of energy, heat, and electricity

5
Work

• Work
• Scalar quantity
• Can be positive or negative
• Positive work ? Exists when the force
  displacement vectors point in the same direction
• Negative work ? Exists when the force
  displacement vectors point in opposite directions

6
Problem

• How much work is done on a vacuum cleaner
  pulled 3 m by a force of 50 N at an angle of 30
  above the horizontal?
• W (Fcos?)x W ? F 50N
• d 3m ? 30
• W (50N)(cos30)(3m)
• 130 J

7
ENERGY

• Kinetic Energy
• Energy associated with an object in motion
• Depends on speed and mass
• Scalar quantity
• SI unit for all forms of energy Joule (J)
• KE ½ mv2
• KE ½ x mass x (velocity)2

8
Kinetic Energy

• If a bowling ball and a soccer ball are
  traveling at the same speed, which do you think
  has more kinetic energy?
• KE ½ mv2
• Both are moving with identical speeds
• Bowling ball has more mass than the soccer
  ball ? Bowling ball has more kinetic energy

9
Kinetic Energy Problem

• A 7 kg bowling ball moves at 3 m/s. How fast must
  a 2.45 g tennis ball move in order to have the
  same kinetic energy as the bowling ball?
• Velocity of tennis ball 160 m/s

10
Work-Kinetic Energy Theorem

• Work-kinetic Energy Theorem
• Net work done on a particle equals the change in
  its kinetic energy (KE)
• W ?KE

11
PROBLEM

• What is the soccer balls speed immediately after
  being kicked? Its mass is 0.42 kg.

12
PROBLEM

• What is the soccer balls speed immediately after
  being kicked? Its mass is 0.42 kg.
• W F ?x
• W (240 N) (0.20 m) 48 J
• W ?KE 48 J
• KE ½ mv2 48 J
• v2 2(48 J)/0.42 kg
• v 15 m/s

13
Work-Kinetic Energy Theorem

• On a frozen pond, a person kicks a 10 kg sled,
  giving it an initial speed of 2.2 m/s. How far
  does the sled move if the coefficient of kinetic
  friction between the sled and the ice is 0.10?
• m 10 kg vi 2.2 m/s vf 0 m/s µk
  0.10
• d ?

14
Work-Kinetic Energy Theorem

• Wnet Fnetdcos?
• Net work done of the sled is provided by the
  force of kinetic friction
• Wnet Fkdcos? ? Fk µkN ? N mg
• Wnet µkmgdcos?
• The force of kinetic friction is in the
  direction opposite of d ? ? 180
• Sled comes to rest ? So, final KE 0
• Wnet ? KE ½ mv2f ½ mv2i
• Wnet -1/2 mv2i

15
Work-Kinetic Energy Theorem

• Use the work-kinetic energy theorem, and solve
  for d
• Wnet ?KE
• - ½ mv2i µkmgdcos?
• d 2.5 m

16
POWER

• POWER
• A quantity that measures the rate at which
  work is done or energy is transformed
• Power work / time interval
• P W/?t
• (W Fx ? P Fx/?t ? v x/?t)
• Power Force x speed
• P Fv

17
POWER

• SI Unit for Power
• Watt (W) ? Defined as 1 joule per second (J/s)
• Horsepower Another unit of power
• 1 hp 746 watts

18
POWER PROBLEM

• A 193 kg curtain needs to be raised 7.5 m, in
  as close to 5 s as possible. The power ratings
  for three motors are listed as 1 kW, 3.5 kW, and
  5.5 kW. What motor is best for the job?

19
POWER PROBLEM

• m 193 kg ?t 5s d 7.5m
• P ?
• P W/?t
• Fx/?t
• mgx/?t
• (193kg)(9.8m/s2)(7.5m)/5s
• 280 W ? 2.8 kW
• Best motor to use 3.5 kW motor. The 1 kW
  motor will not lift the curtain fast enough, and
  the 5.5 kW motor will lift the curtain too fast

20
POTENTIAL ENERGY

• Potential Energy
• Stored energy
• Associated with an object that has the
  potential to move because of its position
  relative to some other location
• Example
• Balancing rock- Arches National Park, Utah
• Delicate Arch- Arches National Park, Utah

21
(No Transcript)
22
(No Transcript)
23
GRAVITATIONAL POTENTIAL ENERGY-
Definition Gravitational potential energy PEg is
the energy an object of mass m has by virtue of
its position relative to the surface of the
earth. That position is measured by the height h
of the object relative to an arbitrary zero level
PEg mgh SI Unit Joule (J)
24
Problem

• What is the buckets gravitational potential
  energy?

25
Problem

• What is the buckets gravitational potential
  energy?
• PE mgh
• PE (2.00 kg)(9.80 m/s2)(4.00 m)
• PE 78.4 J

26
Gravitational Potential Energy
Example A Gymnast on a Trampoline The gymnast
leaves the trampoline at an initial height of
1.20 m and reaches a maximum height of 4.80 m
before falling back down. What was the initial
speed of the gymnast?
27
Gravitational Potential Energy
28
Elastic Potential Energy

• Energy stored in any compressed or stretched
  object
• Spring, stretched strings of a tennis racket or
  guitar, rubber bands, bungee cords, trampolines,
  an arrow drawn into a bow, etc.

29
Springs

• When an external force compresses or stretches a
  spring ? Elastic potential energy is stored in
  the spring
• The more stretch, the more stored energy
• For certain springs, the amount of force is
  directly proportional to the amount of stretch or
  compression (x)
• Constant of proportionality is known as the
  spring constant (k)
• Fspring k x

30
Hookes Law

• If a spring is not stretched or compressed ? no
  potential energy is being stored
• Spring is in an Equilibrium position
• Equilibrium position Position spring naturally
  assumes when there is no force applied to it
• Zero potential energy position

31
Hookes Law

• Special equation for springs
• Relates the amount of elastic potential energy
  to the amount of stretch (or compression) and the
  spring constant
• PE elastic ½kx2
• k Spring constant (N/m)
• Stiffer the spring ? Larger the spring constant
• x Amount of compression relative to the
  equilibrium position

32
Potential Energy Problem

• A 70 kg stuntman is attached to a bungee cord
  with an unstretched length of 15 m. He jumps off
  the bridge spanning a river from a height of 50m.
  When he finally stops, the cord has a stretched
  length of 44 m. Treat the stuntman as a point
  mass, and disregard the weight of the bungee
  cord. Assuming the spring constant of the bungee
  cord is 71.8 N/m, what is the total potential
  energy relative to the water when the man stops
  falling?

33
Potential Energy Problem

• Zero level for gravitational potential energy
  is chosen to be the surface of the water
• Total potential energy ? sum of the
  gravitational elastic potential energy
• PEtotal PEg PEelastic
• mgh ½ kx2
• Substitute the values into the equation
• PEtotal 3.43 x 104 J

34
Potential Energy

• The energy stored in an object due to its
  position relative to some zero position
• An object possesses gravitational potential
  energy if it is positioned at a height above (or
  below) the zero height
• An object possesses elastic potential energy if
  it is at a position on an elastic medium other
  than the equilibrium position

35
Linking Work to Mechanical Energy

• WORK is a force acting upon an object to cause a
  displacement
• When work is done upon an object, that object
  gains energy
• Energy acquired by the objects upon which work is
  done is known as MECHANICAL ENERGY

36
Mechanical Energy

• Objects have mechanical energy if they are in
  motion and/or if they are at some position
  relative to a zero potential energy position

37
Total Mechanical Energy

• Total Mechanical Energy The sum of kinetic
  energy all forms of potential energy
• 1. Kinetic Energy (Energy of motion)
• KE ½ mv2
• 2. Potential Energy (Stored energy of position)
• a. Gravitational
• PEg mgh
• b. Elastic
• PEelastic ½ kx2

38
Mechanical Energy

• CONSERVATION OF MECHANICAL ENERGY
• In the absence of friction, mechanical energy
  is conserved, so the amount of mechanical energy
  remains constant
• MEi MEf
• Initial mechanical energy final mechanical
  energy
• (in the absence of friction)
• PEi KEi PEf KEf
• mghi ½ mvi2 mghf ½ mvf2

39
Conservation of Energy Problem

• Starting from rest, a child zooms down a
  frictionless slide from an initial height of 3 m.
  What is her speed at the bottom of the slide?
  (Assume she has a mass of 25 kg)

40
Conservation of Energy Problem

• hi 3m m 25kg vi 0 m/s
• hf 0m vf ?
• Slide is frictionless ? Mechanical energy is
  conserved
• Kinetic energy potential energy only forms of
  energy present
• KE ½ mv2 PEg mgh
• Final gravitational potential energy zero
  (Bottom of the slide) ? PEgf 0
• Initial gravitational potential energy ? Top of
  the slide ? PEgi mghi ? (25kg)(9.8m/s2)(3m)
  736 J

41
Conservation of Energy Problem

• hi 3m m 25kg vi 0 m/s
• hf 0m vf ?
• Initial Kinetic Energy 0, because child starts
  at rest
• KEi 0
• Final Kinetic Energy
• KEf ½ mv2 ? ½ (25kg)v2f
• MEi MEf
• PEi KEi PEf Kef
• 736 J 0 J 0 J (1/2)(25kg)(v2f)
• vf 7.67 m/s

42
Mechanical Energy ? Ability to do Work

• An object that possesses mechanical energy is
  able to do work
• Its mechanical energy enables that object to
  apply a force to another object in order to cause
  it to be displaced
• Classic Example ? Massive wrecking ball of a
  demolition machine

43
(No Transcript)
44
(No Transcript)
45
Mechanical Energy is the ability to do work

• An object that possesses mechanical energy
  (whether it be kinetic energy or potential
  energy) has the ability to do work
• That is its mechanical energy enables that
  object to apply a force to another object in
  order to cause it to be displaced

46
Mechanical Energy

• Work is a force acting on an object to cause a
  displacement
• In the process of doing work ? the object which
  is doing the work exchanges energy with the
  object upon which the work is done
• When work is done up the object ? that object
  gains energy

47
Mechanical Energy

• A weightlifter applies a force to cause a barbell
  to be displaced
• Barbell now possesses mechanical energy- all in
  the form of potential energy
• The energy acquired by the objects upon
  which work is done is known as mechanical energy

48
Mechanical Energy is the ability to do work

• Examples on website
• Massive wrecking ball of a demolition machine
• The wrecking ball is a massive object which is
  swung backwards to a high position and allowed to
  swing forward into a building structure or other
  object in order to demolish it
• Upon hitting the structure, the wrecking ball
  applies a force to it in order to cause the wall
  of the structure to be displaced
• Mechanical energy ability to do work

49
Work- Energy Theorem

• Categorize forces based upon whether or not
  their presence is capable of changing an objects
  total mechanical energy
• Certain types of forces, which when present
  and when involved in doing work on objects, will
  change the total mechanical energy of the object
• Other types of forces can never change the
  total mechanical energy of an object, but rather
  only transform the energy of an object from PE to
  KE or vice versa
• Two categories of forces ? Internal External
  

50
Work- Energy Theorem

• External Forces
• Applied force, normal force, tension force,
  friction force and air resistance force
• Internal Forces
• Gravity forces, spring forces, electrical
  forces and magnetic forces

51
Work- Energy Theorem

• THE BIG CONCEPT!!
• When the only type of force doing net work
  upon an object is an internal force
  (gravitational and spring forces)
• ? Total mechanical energy (KE PE) of that
  object remains constant
• ? Objects energy simply changes form ?
  Conservation of Energy
• Ex) As an object is forced from a high
  elevation to a lower elevation by gravity ? Some
  of the PE is transformed into KE (Yet, the sum of
  KE PE remains constant)

52
Work- Energy Theorem

• THE BIG CONCEPT!!
• If only internal forces are doing work ?
  energy changes forms (KE to PE or vice versa) ?
  total mechanical energy is therefore conserved
• Internal forces referred to as
  conservative forces
• Quick Quiz

53
Work-Energy Relationship

• Analysis of situations in which work is
  conserved ? only internal forces are involved
• TMEi WEXT TMEf
• (Initial amount of total mechanical energy
  (TMEi) plus the work done by external forces
  (WEXT) ? equals the final amount of total
  mechanical energy (TMEf))
• KEi PEi Wext KEf PEf
• KEi PEi KEf Pef
• Website

54
Work- Energy Theorem

• THE BIG CONCEPT!!
• Forces are categorized as being either
  internal or external based upon the ability of
  that type of force to change an objects total
  mechanical energy when it does work upon an
  object
• Net work done upon an object by an external
  force ? Changes the total mechanical energy (KE
  PE) of the object
• ? Positive work object gained energy
• ? Negative work object lost energy

55
Work- Energy Theorem

• THE BIG CONCEPT!!
• Gain or loss in energy can be in the form of
• ? PE, KE, or both
• Under such circumstances, the work which is
  done is equal to the change in mechanical energy
  of the object
• External forces ? capable of changing the
  total mechanical energy of an object
  (Nonconservative forces)

56
Work-Energy Relationship

• Analysis of situations involving external
  forces
• TMEi WEXT TMEf
• (Initial amount of total mechanical energy
  (TMEi) plus the work done by external forces
  (WEXT) ? equals the final amount of total
  mechanical energy (TMEf))
• KEi PEi Wext KEf PEf
• Practice Problems

57
DEFINITION OF A CONSERVATIVE FORCE Version 1 A
force is conservative when the work it does on a
moving object is independent of the path between
the objects initial and final positions. Version
2 A force is conservative when it does no work
on an object moving around a closed path,
starting and finishing at the same point.
58
Conservative Versus Nonconservative Forces
59
Conservative Versus Nonconservative Forces
Version 1 A force is conservative when the work
it does on a moving object is independent of the
path between the objects initial and final
positions.
60
Conservative Versus Nonconservative Forces
Version 2 A force is conservative when it does
no work on an object moving around a closed
path, starting and finishing at the same point.
61
Conservative Versus Nonconservative Forces
An example of a nonconservative force is the
kinetic frictional force.
The work done by the kinetic frictional force is
always negative. Thus, it is impossible for the
work it does on an object that moves around a
closed path to be zero.
The concept of potential energy is not defined
for a nonconservative force.
62
Conservative Versus Nonconservative Forces
In normal situations both conservative and
nonconservative forces act simultaneously on an
object, so the work done by the net external
force can be written as
63
Conservative Versus Nonconservative Forces
THE WORK-ENERGY THEOREM
64
The Conservation of Mechanical Energy
If the net work on an object by nonconservative
forces is zero, then its energy does not change
65
The Conservation of Mechanical Energy
THE PRINCIPLE OF CONSERVATION OF MECHANICAL
ENERGY
The total mechanical energy (E KE PE) of an
object remains constant as the object moves,
provided that the net work done by external
nonconservative forces is zero.
66
The Conservation of Mechanical Energy
67
The Conservation of Mechanical Energy
Example A Daredevil Motorcyclist A
motorcyclist is trying to leap across the canyon
by driving horizontally off a cliff at 38.0 m/s.
Ignoring air resistance, find the speed with
which the cycle strikes the ground on the
other side.
68
The Conservation of Mechanical Energy
69
The Conservation of Mechanical Energy
70
Nonconservative Forces and the Work-Energy Theorem
THE WORK-ENERGY THEOREM
71
Nonconservative Forces and the Work-Energy Theorem
Example Fireworks Assuming that the
nonconservative force generated by the burning
propellant does 425 J of work, what is the final
speed of the rocket. Ignore air resistance. The
mass of the rocket is 0.2kg.
72
Nonconservative Forces and the Work-Energy Theorem
73
POWER

• POWER
• A quantity that measures the rate at which
  work is done or energy is transformed
• Power work / time interval
• P W/?t
• W Fd ?P Fd/?t ? v d/?t
• Power Force x speed
• P Fv

74
POWER

• SI Unit for Power
• Watt (W) ? Defined as 1 joule per second (J/s)
• Horsepower Another unit of power
• 1 hp 746 watts

75
POWER PROBLEM

• A 193 kg curtain needs to be raised 7.5 m, in
  as close to 5 s as possible. The power ratings
  for three motors are listed as 1 kW, 3.5 kW, and
  5.5 kW. What motor is best for the job?

76
POWER PROBLEM

• m 193 kg ?t 5s d 7.5m
• P ?
• P W/?t
• Fd/?t
• mgd/?t
• (193kg)(9.8m/s2)(7.5m)/5s
• 280 W ? 2.8 kW
• Best motor to use 3.5 kW motor. The 1 kW
  motor will not lift the curtain fast enough, and
  the 5.5 kW motor will lift the curtain too fast

77
(No Transcript)
78
THE PRINCIPLE OF CONSERVATION OF ENERGY Energy
can neither be created nor destroyed, but can
only be converted from one form to another.
Disclaimer This powerpoint presentation is a
compilation of various works.
79
(No Transcript)
80
Question

• 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 3.0 kg and the height of the seat top is
  0.45 meters, then what is the potential energy of
  the loaded cart at the height of the seat-top?
• PE mgh
• PE (3 kg ) (9.8 m/s/s) (0.45m) PE
  13.2 J

81
Question

• If a force of 14.7 N is used to drag the loaded
  cart (from previous question) along the incline
  for a distance of 0.90 meters, then how much work
  is done on the loaded cart?
• W F d cos Theta
• W 14.7 N 0.9 m cos (0 degrees)
• W 13.2 J 
• (Note The angle between F and d is 0 degrees
  because the F and d are in the same direction)