Work and Energy presentation

1. WORK
KINETIC ENERGY
POTENTIAL ENERGY
and POWER
Mechanics

2. WORK and KINETIC ENERGY
OUTLINE
• Work
– Force in the direction of
displacement
– Force at an angle to
displacement
– Positive, negative and zero
work
– Constant force and variable
force
• Kinetic energy
• Work-energy theorem
• Potential energy
• Power
d
F
cos
Fd
W






2
mv
2
1
K 
2
i
2
f
total mv
2
1
mv
2
1
K
W 



t
W
P 
Mgh
GPE 
2
2
1
kx
ElasticPE 

3. WORK and KINETIC ENERGY
OBJECTIVES
• understand the concepts of work and kinetic energy
• be able to calculate the work done by constant forces and
approximate the work of variable forces
• be able to determine the kinetic energy of a moving object
• understand the concept of potential energy
• be able to apply the principle of the conservation of mechanical
energy
• know how to calculate the average power delivered when work
is done
• understand Law of conservation of energy

4. Reminders
• Work , in physics,: measure of energy transfer .
• Kinetic Energy: the energy acquired by the object when it is in
motion.
• Potential Energy: the energy acquired by the object because of
its position.
2
mv
2
1
K 
Mgh
GPE 

5. Reminders
• Potential Energy appear whenever we have a force acting on the
object (more specifically when we have a conservative force).
• Potential Energy can be gravitational and can be elastic.
• Average Power is delivered whenever work is done or energy is
transferred which is defined as the rate (divided by time) at
which work is done or energy is transferred.
𝑃 =
𝑊
𝑡
=
𝐸
𝑡

6. WORK DONE BY A CONSTANT FORCE
Force in the direction of the displacement
W=Fd
SI unit: newton-meter (N m) = joule, J
1 joule = 1J = 1 N m = 1 (kg m/s2) m = 1 kg m2 / s2

7. HEADING FOR THE ER
An intern pushes a 72-kg patient on a 15-kg gurney, producing an
acceleration of 0.60 m/s2. How much work does the intern do by
pushing a patient and gurney through a distance of 2.5 m?
  
   J
130
m
5
.
2
N
52
Fd
W
N
52
s
/
m
60
.
0
kg
15
kg
72
ma
F 2








10. POSITIVE, NEGATIVE and ZERO WORK

12. GRAVITATIONAL WORK

13.  
 
f i
f i
2
i
2
i
i f i i f i
f i f i
2 2
f i
v v
v v
1
d v t gt
2
F mg
1
W Fd mg v t gt
2
1 1 1
W m v m v v v v
gt
gt
gt v
2 2 2
1 1
m v v v v
2 2
1 1
W mv mv
2 2
gt
 
 
 

 
  
 
 
   
     
   
   
 
  
 
 
 

14. KINETIC ENERGY
2
mv
2
1
K 
SI units: kg m2/s2 = joule, J

16. 2
i
2
f
total mv
2
1
mv
2
1
K
W 




17. A 4.1kg box of books is lifted vertically from rest a distance of 1.6 m by an
upward applied force of 60.0 N.
Find (a) the work done by the applied force, (b) the work done by gravity, and (c)
the final speed of the box.
    J
96
m
6
.
1
1
N
0
.
60
y
0
cos
F
W app
app 


 
     J
64
m
6
.
1
1
s
/
m
81
.
9
kg
1
.
4
y
180
cos
mg
W
2
g





 
  s
/
m
9
.
3
kg
1
.
4
J
32
2
m
W
2
v
mv
2
1
mv
2
1
mv
2
1
W
J
32
J
64
J
96
W
W
W
total
f
2
f
2
i
2
f
total
g
app
total











(a)
(b)
(c)

18. Graphical representation of the work
done by a constant force

19. Work done by a non-constant force

20. Work done by a continuously varying force

21. KINETIC ENERGY
SI units: kg m2/s2 = joule, J
Mgh
GPE 

22. Work to stretch or compress a spring a
distance x from equilibrium
2
2
1
kx
ElasticPE
W 


23. POWER
how quickly is work done?
t
W
P 
SI units: J / s = watt, W
1 watt = 1 W =1 J/s
1 horsepower = 1 hp =746 W
**1KW.h is a unit of energy and not a unit of power
1KW.h= 1000Wx3600s=3.6 x106 J

24. CONSERVATIVE AND
NONCONSERVATIVE FORCES
Conservative forces conserve the mechanical
energy of a system. Thus in a conservative
system the total mechanical energy remains
constant.
Non conservative forces convert mechanical
energy into other forms of energy (e.g. heat), or
convert other forms of energy into mechanical
energy.

25. CONSERVATIVE AND
NONCONSERVATIVE FORCES
When a conservative force acts, the work it
does is stored in the form of energy that can be
released at a later time

26. EXAMPLES
Conservative forces
• Gravity
• Spring
Nonconservative forces
• Friction
• Air resistance
• Tension in ropes or cables
• Forces exerted by muscles
• Forces exerted by motors

27. CONSERVATIVE AND
NONCONSERVATIVE FORCES
Work against gravity
Gravity is a conservative force
Work against friction
Friction is a nonconservative force

28. THE WORK DONE BY A CONSERVATIVE FORCE
IS ZERO ON ANY CLOSED PATH
1
2
3
1
3
3
1
1
2
2
1
W
W
W
W
W
0
W
W
W
W
0
W
W












29. CONSERVATIVE FORCE
• A conservative force does zero total work on a
closed path
• The work done by a conservative force in going
from an arbitrary point A to an arbitrary point B
is independent from the path from A to B

30. POTENTIAL ENERGY, U
When a conservative force does an amount of work Wc
(subscript c for conservative), the corresponding
potential energy is changed according to the definition:
  PE
PE
PE
PE
PE
W i
f
f
i
c 







SI units: joule, J

31. • The work done by a conservative force is equal to the negative of
the change in potential energy.
• When an object falls, gravity does a positive work on it and its
potential energy decreases. When an object is lifted, gravity
does a negative work and the potential energy is increased.
• The definition of potential energy determines only the difference
in potential energy, not the actual value of the potential energy.
Hence we are free to choose the place where the potential
energy is zero (PE=0).

32. GRAVITATIONAL POTENTIAL ENERGY
mgy
PE
PE
PE
mgy
PE
mgy
W
PE
PE
PE
mgy
Fd
W
f
f
i
c
f
i
c












0
Choice: PE=0 at water level
(y=0)
mgy
PE 
0

PE

33. GRAVITATIONAL POTENTIAL ENERGY
   
J
m
s
m
kg
mgy
PE
1900
3
/
81
.
9
65 2



Find the gravitational
potential energy of a 65 kg
person on a 3.0 m high
diving board. Let U=0 be at
water level.
mgy
PE 
0

PE

34. CONVERTING FOOD ENERGY INTO
MECHANICAL ENERGY
• A chocolate bar has a calorie
content of 210.0 kcal which is
equivalent to an energy of
8.791x105 J. If a 82 kg mountain
climber eats this chocolate bar and
magically converts it all into
potential energy, what gain in
altitude would be possible?
   1093m
9.81m/s
82kg
J
10
8.791
mg
PE
h
mgh
PE
2
5






35. SPRING POTENTIAL ENERGY
2
2
1
kx
PE 
x
Choice: U=0 at equilibrium position (x=0)
Spring stretched by x Equilibrium position (x=0)
f
i
c PE
PE
kx
W 

 2
2
1
SPRING POTENTIAL ENERGY
X

36. SPRING POTENTIAL ENERGY
m
0.0350
cm
3.50
x
m
0.0225
cm
2.25
x






x
Find the potential energy of a
spring with force constant
k=680 N/m if it is (a) stretched
by 2.25 cm or (b) compressed
by 3.50 cm
X
  
   J
0.416
m
0.0350
N/m
680
2
1
kx
2
1
PE
J
0.172
m
0.0225
N/m
680
2
1
kx
2
1
PE
2
2
2
2







(a)
(b)
2
2
1
kx
PE 

37. MECHANICAL ENERGY
K
PE
E 

KINETIC ENERGY
POTENTIAL ENERGY

38. CONSERVATION OF MECHANICAL ENERGY
In a system with
conservative forces, the
mechanical energy E is
conserved: i.e.
E=PE+K=constant
constant


















E
E
E
K
PE
K
PE
PE
PE
K
K
PE
PE
PE
W
W
W
K
K
K
W
i
f
i
i
f
f
f
i
i
f
f
i
c
c
tot
i
f
tot

39. GRAVITY IS A CONSERVATIVE FORCE

40. Solving a kinematics problem using conservation of energy
What is the velocity of the keys?
gh
v
gh
v
v
gh
mv
mgh
K
PE
K
PE
E
E
f
f
i
i
f
i
2
2
2
1
2
1
0
0
2
2
2











41. A 55 kg skateboarder enters a ramp moving horizontally with a speed of 6.5 m/s,
and leaves the ramp moving vertically with a speed of 4.1 m/s. (a) Find the height
of the ramp assuming no energy loss to frictional forces. (b) What is the
skateboarder’s maximum height?
   
 
m
h
s
m
s
m
s
m
g
v
v
h
mv
mgh
mv
mv
mgh
mv
mg
K
PE
K
PE
E
E
f
i
f
i
f
i
f
f
i
i
f
i
3
.
1
/
81
.
9
2
/
1
.
4
/
5
.
6
2
2
1
2
1
2
1
2
1
0
2
2
2
2
2
2
2
2















(a)
(a)

42. summary
CONSERVATIVE FORCES
A force is conservative if the work it does on an object
moving between two points is independent of the path
the object takes between the points
– The work depends only upon the initial and final positions of the object
– A conservative force does zero total work on a closed path
– Any conservative force can have a potential energy function associated
with it
– When a conservative force acts, the work it does is stored in the form of
potential energy that can be released at a later time

43. summary
CONSERVATION OF MECHANICAL ENERGY
• Conservation in general
– To say a physical quantity is conserved is to say that the
numerical value of the quantity remains constant
• In Conservation of Energy, the total mechanical energy
remains constant
– In any isolated system of objects that interact only through
conservative forces, the total mechanical energy of the
system remains constant.