Chapter 5 matriculation STPM
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Work, energy and power...
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CHAPTER 5
WORK, ENERGY AND POWER
CHAPTER 5: Work, Energy and Power (3 Hours)
CHAPTER 5
WORK, ENERGY AND POWER
Learning Outcome: 5.1 Work (1 hour) At the end of this chapter, students should be able to: (a)Define and use work done by a force.
W F s
(b)) Dete (b Determ rmin ine e work done from the forcedisplacement graph.
CHAPTER 5 5.1
WORK, ENERGY AND POWER
Work, W
Work done by a constant force
is defined as the product of the component of the force parallel to the displacement times the displacementt of a body. displacemen body. OR is defined as the scalar (dot) product between force and displacement of a body. body.
CHAPTER 5 Mathematically :
WORK, ENERGY AND POWER
W F s
W F cos θ s Fs cos θ Where,
F : magnitude of force
the bo body s : displacement of the
θ : the the angle betwee between n F and s
CHAPTER 5
WORK, ENERGY AND POWER
It is a scalar quantity. scalar quantity.
Dimension :
W F s W ML2T 2
The S.I. unit of work is kg m2 s
2
or joule joule (J). (J).
The joule The joule (1 J) is defined as the work done by a force of 1 N which results in a displacement of 1 m in the direction of the force. force.
1 J 1 N m 1 kg m 2 s 2
CHAPTER 5
WORK, ENERGY AND POWER
Work done by a variable force Figure 5.1 shows a force, F whose magnitude changes with the displacement, displacement, s . For a small displacement, s the force remains 1 almost constant at F 1 and work done therefore becomes W 1 = F 1 s . 1
CHAPTER 5
WORK, ENERGY AND POWER F/N F N
F 4 F 1 0 s1
Figure 5.1 W 1 s1
s4
s2 s s N
To find the total work done by a variable force, W when the displacement changes from s=s1 to s=s2, we can divide the displacement into N small successive displacements : s1 , s2 , s3
,
Thus
…, …,
s N
W F s F s
F s
CHAPTER 5
WORK, ENERGY AND POWER
When N
W
,
s2
s1
s 0, therefore
Fds
F/ N
Work = Area
0 s1
s2 s/ m
CHAPTER 5
WORK, ENERGY AND POWER
Applications of work’s equation Case 1 :
Work done by a horizontal force, F on an object (Figure 4.2).
F
Figure 5.2
W W Fs
Fs cos θ and
s
θ 0
Case 2 :
Work done by a vertical force, F on an object (Figure 4.3).
F
Figure 5.3
W Fs cos θ and θ 90 W 0 J s
CHAPTER 5
WORK, ENERGY AND POWER
Case 3 :
Work done by a horizontal forces, F 1 and F 2 on an object (Figure 5.4). F
1
Figure 5.4
W W W F s F s W F F s s F F F 1
2
1
2
nett
1
and
2
nett
1
s F nett s
Work done by a force, F and frictional force, force , f on an object (Figure 5.5). F
f
s W nett F nett s s and F nett F cos θ f ma W F cos cos f s s OR W mas Figure 5.5
s
W W
Case 4 :
F 2
W 1 F 1 s cos 0 W 2 F 2 s cos 0
2
CHAPTER 5
WORK, ENERGY AND POWER
Caution :
Work done on an object is zero when F = 0 or s = 0 and = 90 .
CHAPTER 5
Sign for work.
WORK, ENERGY AND POWER
W Fs cos
If 0 0 (positive)
work done on the system ( by the external force) where energy is transferred to the system.
If 90
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