1. Work,
EnErgy &
PoWEr
Objectives:
to begin developing a concept of energy – what it is, how
it is transformed and transferred.
show an understanding of the concept of work in terms
of the product of a force and displacement in the direction
of the force
2. Work, EnErgy & PoWEr
• Objectives:
calculate the work done in a
number of situations including the
work done by a gas that is
expanding against a constant
external pressure:
W = p ΔV
5. Concept of Energy
An analogy:
ability to purchase
good and services
=
ENERGY
ability to do
work (simple
but inadequate)
Work, energy and power
6. Concept of Energy
Kinetic energy is
analogous to cash
just like energy, can
be transformed and
transferred in
various ways
Potential energy is
analogous to savings
account
Work is analogous to
getting a paycheck (+) or
paying bills (making
purchases) ( - )
Work, energy and power
7. Work, EnErgy & PoWEr
So what then
is WORK?
-it is the mechanical transfer of
energy to or from the system by
the pushes and pull of external
forces
- it is the product of force and
distance in the same direction of
the force.
8. Work, EnErgy & PoWEr
Calculating work done
2 factors are involved
External force, F must be
applied
S = distance moved
Object must move in the
direction of the force, s
9. Work, EnErgy & PoWEr
W=Fxs
The work done by a force is
defined as the product of the
force and the distance moved in
the direction of the force.
the magnitude of the force F – the bigger the force,
the greater the amount of work you do.
the distance s you push the car – the further you
push it, the greater the amount of work done.
10. Work, EnErgy & PoWEr
work done W = F x s
= 300 x 5.0
= 1500 J
= 1.5 kJ
S = distance moved
F = 300 N
s = 5.0 m
11. Work, EnErgy & PoWEr
Doing work
Pushing a car to start it moving: your
force transfers energy to the car. The
car’s K.E. (i.e. movement energy)
increases.
Lifting weights: you are doing work as
the weights move upwards. The GPE of
the weights increases.
Not doing work
Pushing a car but it does not budge: no
energy is transferred, because your
force does not move. The car’s K.E.
does not change.
Holding the weights above your head:
you are not doing work on the weights
because the force you apply on them is
not causing it to move. The GPE of the
weights is not changing
Writing an essay: you are doing work
Reading an essay: this may seem like
because you need a force to move your “hard work”, but no force is involved,
pen across the page, or to press the
so you are not doing any work.
keys on the keyboard
12. Work, EnErgy & PoWEr
work done = energy transferred
Doing work is a way of
transferring energy.
1 Joule = 1 newton metre
1J=1Nm
The Joule is defined as the amount of work done
when a force of 1 Newton moves an object a
distance of 1 metre in the direction of the force
13. Work, EnErgy & PoWEr
work done = energy transferred
The Joule is also defined as the amount of
energy transferred when a force of 1 Newton
moves an object a distance of 1 metre in the
direction of the force
14. Work, EnErgy & PoWEr
Test yourself
1. In each of the following examples, explain whether or not any
work is done by the force mentioned.
a) You pull a heavy sack along the ground. YES
b) The force of gravity pulls you downwards when you fall.YES
c) The tension in a string pulls on a stone when you whirl it
around at a steady speed. NO
d) The contact force of the bedroom floor stops you from
falling into the room below. NO
2. A man of mass 70 kg climbs stairs of vertical height 2.5 m.
Calculate the work done against the force of gravity.
1716.75 = 1.7 kJ
15. Work, EnErgy & PoWEr
Test yourself
3. A stone of weight 10 N falls from the top
of a 250 m high cliff.
a) Calculate how much work is done
by the force of gravity in pulling the stone to
the foot of the hill.
2500 J
b) How much energy is transferred to
the stone? 2500 J
16. Work, EnErgy & PoWEr
Force, distance and direction
For force to do work, there must be movement
in the direction of the force
17. Work, EnErgy & PoWEr
Fx = F cos 30o
= 50 cos 30o
= 43. 301270189
horizontal
component (Fx)
of 50 N
Work done = (Fx) x s
= 43. 301270189 x 10
= 433.01270189
= 4.3 x 102 J
18. Work, EnErgy & PoWEr
Doing work against gravity
A 80.0 kg man is climbing
a stair as shown in the
diagram on the right. Given
the dimensions calculate
for the work done by the
man upon reaching the last
step above.
20. Work, EnErgy & PoWEr
Quick review: Doing/Not Doing work????
F
d
21. Work, EnErgy & PoWEr
F
=
0
12
N
Θ = 35o
Fx = ?
An airport passenger is
pulling his luggage with a
force F = 120 N along a
level floor. The pulling
force makes an angle of
35o measured from the
floor and the passenger
moves through a distance
d of 6.0 m, what is the
work done on the
luggage?
d = 6.0 m
22. Work, EnErgy & PoWEr
A stunt person slides down a cable that is attached between a tall
building and the ground.
The stunt person has a mass of 85 kg. The speed
of the person when reaching the ground
is 20 m s−1. Calculate:
a)the change in gravitational potential energy of
the person
b) the final kinetic energy of the person
c) the work done against friction
d) the average friction acting on the person.
23. Work, EnErgy & PoWEr
The figure on
the right shows
the forces
acting on a
box which is
being pushed
up a slope.
100 N
70 N
30 N
100 N
45o
Calculate the work done by each force if the box
moves up 0.5 m up the slope.
24. Work, EnErgy & PoWEr
Try these:
1. Calculate how much gravitational potential
energy (GPE) is gained if you climb a flight of
stairs. Assume that you have a mass of 52 kg
and that the height you lift yourself is 2.5 m.
2. A climber of mass 100 kg (including all the
equipment he is carrying) ascends from sea level
to the top of a mountain 5500 m high. Calculate
the change in her gravitational potential energy
(GPE)
25. Work, EnErgy & PoWEr
3. Calculate the increase in kinetic energy of
a mass 800 kg when it accelerates from 20
m/s to 30 m/s. Change in KE = 200 kJ
4. Calculate the change in KE of a ball of
mass 200 g when it bounces. Assume that it
hits the ground with a speed of 15.8 m/s
and leaves it at 12.2 m/s.
Change in KE = 10 J
26. Work, EnErgy & PoWEr
movable piston
Work done by gas
P=
force
_____
area
force exerted by
the gas when it
expands
F=p A
work done is
W=pAs
A s ???
Change in
volume, ΔV
W=pΔV
27. Work, EnErgy & PoWEr
When the gas EXPANDS,
work is done BY the gas.
When the gas
CONTRACTS, then work
is done ON the gas.
28. Work, EnErgy & PoWEr
Study the sample
problems on pages
76, 80, & 82 and
answer the “Now it’s
your turn” questions.
Check your answers
against the answers
from the book.
29. Work, EnErgy & PoWEr
The diagram shows a child on a swing. The
mass of the child is 35 kg. The child is
raised to point A and then released. She
swings downwards through point B.
a) Calculate the change in
gravitational potential energy of the
child between A and B.
b) Assuming that air resistance is
negligible, calculate the speed of the
child as she passes through the
equilibrium position B.
c) The rope stays taut throughout.
Explain why the work done by the
tension in the rope
is zero.
30. Work, EnErgy & PoWEr
A bullet of mass 30 g and travelling at a
speed of 200 m s−1 embeds itself in a
wooden block. The bullet penetrates a
distance of 12 cm into the wood. Using
the concepts of work done by a force and
kinetic energy, determine the average
resistive force acting on the bullet.
Work done by resistive force = initial kinetic energy of bullet
1
× 0.030 × 200 2
2
0.030 × 200 2
F=
= 5.0 × 10 3 N (5.0 kN)
2 × 0.12
F × 0.12 =
31. Work, EnErgy & PoWEr
The diagram shows a 50 kg crate
being dragged by a cable up a ramp
that makes an angle of 24° with the
horizontal.
The crate moves up the ramp at a constant speed and travels a
total distance of 20 m up the ramp. Determine the magnitude of
the friction between the crate and the surface of the ramp.
32. Work, EnErgy & PoWEr
Gain in gravitational potential energy = mgh
= 50 × 9.81 × 20 sin 24°
= 3.99 × 103 J
Work done by tension in the rope = F cos θ × x
= 350 × cos 30° × 20
= 6.06 × 103 J
33. Work, EnErgy & PoWEr
Work done against friction = 6.06 × 103 − 3.99 × 103
= 2.07 × 103 J
Since work done is given by:
work done = force × distance
we have:
3
friction
2.07 × 10
=
= 104 N ≈ 100 N
20
34. Work, EnErgy & PoWEr
An object of mass m passes a point X with a
velocity v and slides up a frictionless incline to stop
at point Y which is at a height h above X
v
Y
h
X
A second ball of mass 0.5m passes X with a
velocity of 0.5v. To what height will it rise?
35. Work, EnErgy & PoWEr
10.0 m
1.0 m
A body of mass 1.0 kg initially at rest slides down an incline
plane that is 1.0 m high and 10.0 m long. If the body
experiences a constant resistive force of 0.5 N over the slope,
what is the KE of the body at the base of the plane?
Gain in KE = loss in PE – Work against resistive force
4.8J
36. Work, EnErgy & PoWEr
Power
work done
Power =
time taken
Watts (W)
- is the rate of working 1
joule per second ( scalar
just like energy )
J
s
37. Work, EnErgy & PoWEr
It’s common to say that a strong person is
“powerful”
In Physics, strength, or force, and power are NOT
the same.
Large forces may be exerted w/o any movement
and thus NO WORK is done and the power is zero.
Large rock resting on the ground is not moving and
yet exerts a large amount of force.
38. Work, EnErgy & PoWEr
Consider a force F which
moves a distance x at
constant speed v in the
direction of the force, in
time t
W=Fs
W=Fs
t
t
Dividing both
sides by t
but W/t = power
and s/t = speed
P=Fv
Power = force x speed
39. Work, EnErgy & PoWEr
Study the sample problem from page 103, then
solve “Now it’s your turn” problems 1-3
