1. Work, Energy and Power

2. WORK Work is done whenever a force (F) is
exerted and whenever there is
displacement (s).
(s).
The amount of work done is proportional to
both the force and displacement. (W = F x s)
Work is measured in newton-meters.
newton-
1 joule of work = 1 newton of force x 1
meter of distance
James Prescott Joule

3. Units of Work

4. Force and displacement do not point in the
same direction
W = (F cos θ )s
the product of the component of force (F)
in the direction of the displacement (s) and
the magnitude of the displacement cos 0 = 1
o
produced by that force
cos 90 = 0
o
W= ( F cos θ ) s
θ = angle between the direction of F and
cos180 = −1 o
that of S

5. Work Done by a Constant Force
Example: Pulling a Suitcase-on-Wheels
Find the work done if the force is 45.0-N, the angle is 50.0
degrees, and the displacement is 75.0 m.
[ ]
W = (F cos θ )s = (45.0 N ) cos 50.0o (75.0 m )
= 2170 J

6. Work Done by a Constant Force
a. The weight lifter is bench
pressing a barbell whose
weight is 710 N.
b. He raises the barbell at a
distance of 0.65 m
W = (F cos 0)s = Fs
c. He lowers the barbell at the
same distance
W = (F cos180)s = − Fs

7. WORK

8. Working against Gravity
W = F x s; if F = mass x
gravity (9.8 m/s2)
Then: W = (mg) x d
Wgravity = mg (hf – hi)
(h
How much work against
gravity would a 50-kg person
50-
do if he climbs a flight of
stairs 3 meters high?

9. Energy
Ability to do work
No energy, no work
property of a body or system of bodies by which
work can be done or performed
The energy possessed by a body is equal to the total
work it can do (W = E)
Both are scalar quantity; same unit (joules)
Types
– Kinetic Energy: energy associated with moving objects
– Gravitational potential energy: form of energy waiting to be
released

10. Energy

11. Energy
1019 Joules
1027 Joules

12. Kinetic Energy
Two factors governing an object’s
kinetic energy:
energy:
– Kinetic energy is proportional to the
mass
– Kinetic energy increases as the square of
its velocity
Kinetic energy equals the mass of
the moving object times the square
of that object’s velocity, multiplied by
the constant ½.
Kinetic energy (joules) = ½ X mass (kg) x
[Velocity (in m/s)]2
KE = ½ mv2

13. Kinetic Energy (KE)
The KE of an object of mass m and speed v
If E = W; and W = F x s; then
F X s = ( ma) X (1/2 at2)
= 1/2 m X ( at) 2
since v = at
therefore KE = 1/2 m v 2

14. Sample Problem
Find the KE of a body with a mass of 10
kg and a speed of 10 m/s
500 joules
How much energy is required to
accelerate a 1000-kg car from rest to
1000-
30 m/sec, assuming no friction.
friction.
4.5 x 105 joules

15. Potential energy
Potential energy is the energy
that could result in the
exertion of a force over a
distance.
distance. Energy on account of
their position
Stored energy
Most common = gravitational PE

16. Gravitational Potential Energy
The gravitational potential energy PE is the
energy that an object of mass (m) has by
virtue of its position relative to the surface of
the earth.
The gravitational potential energy of an object
equals its weight (the force of gravity
exerted on the object) times its height above
the ground (the object has been lifted
above the surface of the earth).
Potential Energy (joules) =
mass (kg) x g (m/s2) x height (m)
PE = mgh

17. Sample Problem
Find the GPE of an object with
a mass of 100 kg raised to 2m
above ground? 1960 J
A 12-kg suitcase is lifted 0.75
12-
m above the ground. 88.2 J

18. Work and Conservative Force
Version 1 A force is conservative
when the work it does on a moving
object is independent of the path
between the object’s 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.
The track exerts a normal force but
the force is directed perpendicular to
the motion ,hence, no work is done

19. Work and Non - Conservative Force
A force is nonconservative if the work
it does on an object depends on the
path of the motion between the points
An example of a nonconservative
force is the kinetic frictional force.
When an object slides over a surface, the
kinetic frictional force points opposite to
the sliding motion and does negative work
W = (F cos θ )s = f k cos 180 o s = − f k s

20. Conservative and Nonconservative Forces
WORK – ENERGY THEOREM
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
W = Wc + Wnc
W = KE f − KE o = ∆KE
Wc = Wgravity = mgho − mgh f = PE o − PE f = −∆PE

21. Conservative Versus Nonconservative Forces
W = Wc + Wnc
∆KE = − ∆PE + Wnc
THE WORK-ENERGY THEOREM
Wnc = ∆KE + ∆PE
Wnc = Ef + Eo
Ef = Eo

22. Conservation of Energy
If there are no forces doing work on a system
(conserved), the total mechanical energy (E) of the
conserved), (E)
system (sum of the KE and PE) remains constant
E = KE + PE = constant
Principle of Conservation of Energy
E before = E after
Energy can neither be created not destroyed, but can
only be converted from one form to another.

23. Conservation of
Energy
As demonstrated by a pendulum
E = PE = mgh E = PE = mgh
E = KE = ½ mv2

24. Conservation of Energy:
Energy of a Falling Body
At the beginning of a fall just
before an object is released, its
energy is all potential.
As the object falls, potential
energy is gradually converted to
kinetic energy
The kinetic energy at the end of a
fall is equal to the potential
energy at the beginning.
Initial PE = Final KE
mgh = ½mv2
gh = ½v2 or v = √2gh

26. Food and Energy
Food: type of chemically stored energy
The energy content of food is in
kilocalories
1 kilocalorie = 4186 joules

27. Food and Energy
FOOD kcal/g ACTIVITY ENERGY
CONSUMPTION RATE
(kcal/min)
Apples 0.58
Sleeping 1.2
Avocado 1.67 Sitting in class 3.0
Beer 0.42 Walking slowly 3.8
Big Mac 2.89 Cycling 5.7
Butter 7.20 Playing tennis 6.3
Swimming 6.8
Chocolate 5.28
Climbing stairs 9.8
Eggs 1.63 Playing basketball 11.4
Sugar 4.00

28. Power
The rate at which work is done. The rate at which
done.
energy is expended.
expended.
Power is the amount of work done divided by the time
it takes to do it.
it.
Power is the energy expended divided by the time it
takes to expend it.
it.
Power (watts) = Work (joules) Power (watts) = Energy (joules)
Time (sec) Time (sec)
James Watt ; 1 horsepower = 550 ft-lb of work/second
= 746 watts or 0.746 kilowatt

29. Sample Problem
Calculate the amount of power generated by
a 60-kg person climbing a 2 m high flight of
60-
stairs in 7 sec.
sec.
P = W /t ; since W = mgh ,Then P = mgh
t
= (60 kg) ( 9.8 m/s2) ( 2 m )
7s
= 1176 J
7s
= 168 W

30. Sample Problem
If the cost per kilowatt hour is 50 cents,
what is the cost of running a 500-watt
500-
color TV set at 6 hours per day for 30
days?
P 45.00

31. Power

32. The rate of conversion of food
energy to some other form is
called metabolic rate.
The total energy conversion
rate of a person at rest is called
basal metabolic rate
BMR of an individual is related
to thyroid activity
The BMR is directly related to
the mass of the person.
Energy consumption is directly
proportional to oxygen
consumption