1 Work, Energy and Power
Reference Text: All About Physics – Chapter 7 (pg. 164).
Knowledge you should gain in this section:
•
Define work as the product of a force and distance moved in the direction
of the force
•
Solve problems using the equation W=F.s
•
Recall that the unit of work is the joule (J)
•
Understand that doing work on an object means energy is transferred to
that object
•
Define kinetic energy as the energy due to motion
•
Calculate kinetic energy using 𝐸𝐾 = 2 𝑚𝑣 2
•
Define gravitational potential energy as the energy due to vertical height
•
Calculate gravitational potential energy using 𝐸𝑃 = 𝑚𝑔ℎ
•
Describe elastic potential energy and chemical potential energy
•
State the law of conservation of energy
•
Define mechanical energy as the sum of kinetic energy and potential
1
energy at a point
•
Solve simple problems using the knowledge that mechanical energy, 𝐸𝑀 =
𝐸𝐾 + 𝐸𝑃 , must be a constant (problems must be scaffolded)
•
Identify how energy is transferred from one form to another
•
List other types of energy: electrical energy, thermal energy, light, sound,
nuclear
•
Describe heat as energy transferred
•
Relate temperature to the kinetic energy of particles
1.1 Definitions
a)
Work - product of force and distance moved parallel to the force
b)
Power - rate at which work is done
c)
Energy - ability to do work
d)
Kinetic energy - energy due to motion
e)
Potential energy - stored energy due to position or shape
1.2 Symbols and units
Quantity label
Quantity
symbol
Unit label
Unit symbol
Work
W
Joules
J
Potential energy
Ep
Joules
J
Kinetic energy
Ek
Joules
J
Power
P
Watts
W
s
m.s-1
m/s
kg
Mass
m
Meters per
second
kilograms
Force
F
Newtons
N
Distance
s
meters
m
Speed
1.3 Calculations
You will need to be able to use the following equations and state your answers with
the correct units. Ensure that you can change the subject of the formula.
W = F s (units and manipulation)
P = W / t (including efficiency calculations)
Ep = m g h
Ek = ½ m v2
Emech = Ep + Ek
1.4 Relationship between work and power
1.5 Conservation of Energy
Law of Conservation of Energy
Energy cannot be created or destroyed, only changed from one
form into another.
Read All About Physics page 141 – 142 and answer the questions that follow:
1) Discuss the different conversions which you encounter in your daily lives.
2) If FRICTION IS IGNORED, then total mechanical energy, Emech of a body is
conserved (remains unchanged)
Refer to Phet animation – energy skate park
3) You will also need to consider the mechanical energy of a falling body WHILE
IT IS IN MOTION, not only at the top and bottom of its fall.
Refer to Experiments 6 page 7 in your practical book
Activity
1. What are the sources of energy used by the body? What forms of energy are
generated by the body? What form of energy is lost during this conversion process?
Sources are food, sunlight, chemical energy. Transformed into kinetic, sound,
heat and potential energy. Lost as sound, friction.
2. Compare the energy you used to get up the stairs to the nutritional information on
a food packet. What is the kilojoules content for the food? If you ate this food item,
how much work would it give your body to do?
45g Doritos packet 906 kJ = 906 000 J
My work = 1274J. Equivalent to 726.5 runs up the stairs
3. Now compare your power to the power needed to light a globe. How many 60 W
light bulbs could your body power when walking and running?
My power = 10,6W
Powers about 1/6 of a bulb.
4. If you were to run up the stairs for 4 hours per day for five days, how many
kilo-watt hours would you produce? (tip: number of kWh = P (in kW) X t (in hr) )
W=Pxt
= 0,0283 x 4 x 5
= 0,5662 kWh
All About Physics Page 146
Questions
1.
2.
3.
4. B:
C:
D:
E:
Worksheet
1)
A force of 20 N is applied horizontally to a box to slide it 5 m along the floor.
Calculate the work done in sliding the box.
W=Fxd
= 20 x 5
= 100 J
2)
A brick of mass 2 kg is lifted through a height of 5 m.
a. Calculate the work done in lifting the brick.
W=Fxd
=mxgxd
= 2 x 9,8 x 5
= 98 J
b. How much gravitational potential energy did the brick gain?
Ep = mgh = 98 J
3)
A stone of mass 500 g is dropped from a height of 3 m. (ignore air resistance)
Calculate:
a. The potential energy as the stone is held at 3 m above the ground.
W=Fxd
=mxgxd
= ½ x 9,8 x 3
= 14,7 J
b. The kinetic energy of the stone the moment before it hits the ground.
Ek bottom = Ep top = 14,7 J
c. The speed of the stone just as it hits the ground.
d. After the stone has fallen 2 m, calculate the potential energy and the
kinetic energy.
4)
A 65 kg boy is swinging on a rope. At the bottom of the swing he is traveling at
2 m/s.
a. Calculate his kinetic energy at the bottom of the swing.
b. What potential energy will the boy possess at the top of the swing?
Ep top = Ek bottom = 130 J
c. Calculate how high above the ground the boy will swing.
5)
A skateboarder is traveling at 3 m/s and has a kinetic
energy of 450 J. The skateboarder then goes up a small
hill.
a. How much potential energy does the skateboarder
have as he comes to rest at the top of the hill?
(ignore friction).
Ek bottom = Ep top
= 450 J
b. How high is the top of the hill?
c. If there was friction, would the skateboarder get to the top of the hill?
Explain.
No. Some of this energy would be used up overcoming the friction, so
you would have insufficient energy to get to the top of the hill.
6)
A pendulum bob of mass 200 g is lifted to a height of 1 m above its lowest
position and then released. Ignoring air resistance, calculate
a. The maximum potential energy of the bob
Ep = mgh
= 0,2 x 9,8 x 1
= 1,96 J
b. The maximum kinetic energy of the bob.
Ek bottom = Ep top
= 1,96 J
c. The maximum velocity of the bob.
d. The total mechanical energy of the bob
Emech = Ep top = Ek bottom = 1,96 J
7)
A brick, of mass 1 kg, is dropped and strikes the ground at 5 m/s. Ignore air
resistance.
a. Calculate the kinetic energy as it strikes the ground.
b. What is the maximum potential energy of the brick?
Ep max = Ek max = 12,5 J
c. Calculate the height from which the brick was dropped.
d. Calculate the potential energy of the brick when it’s velocity is 2 m/s.
e. Calculate the height at which it had a velocity of 2 m/s.
8)
A boy of mass 65 kg runs up a flight of stairs in 8 s. There are 24 steps and
each step is 20 cm high. Calculate the power of the boy.
9)
How much work is done on a go-cart when a force of 30 N pushes it for 15 m?
W=Fxd
= 30 x 15
= 450 J
10) Calculate the work done by a force of 25 N in pushing a book 80 cm across
the table.
W=Fxd
= 25 x 0,8
= 20 J
11)
A hiker of mass 65 kg climbs a hill as shown in the diagram.
1800 m
600 m
a.
Calculate the work done by the hiker in climbing the hill.
W=Fxd
= mgd
= 65 x 9,8 x 600
= 382 200 J
b.
12)
How much potential energy does the hiker gain by climbing the hill?
Ep = 382 200 J
A box of mass 5 kg is lifted by a force of 70 N to a height of 4 m.
a.
Calculate the work done by the 70 N force.
W=Fxd
= 70 x 4
= 280 J
b.
Calculate the potential energy gained by the box.
Ep = mgh = 5 x 9.8 x 4
= 196 J
c.
Compare your values for work done and potential energy.
Work done is larger than Ep.
d.
What has happened to the difference in energy?
The energy has been converted into sound and heat energy. Box gets lifted
faster
Homework:
Answer Multiple Choice Questions 1 – 10 in All About Physics pg. 155
Practice questions 1-5, 9. Use g = 9,8 N.kg-1
Multiple choice
1. D
2. D
3. C
4. C
5. C
6. C
7. C
8. D
9. C
10. A
Structured questions
1. a.
b.
2. a.
b.
3. a. Ep = mgh
= 80 x 9,8 x (80 – 20)
b.i. Ek = 47040 x 0,75
= 35 280 J
= 47 040 J
ii.
4.
a.
b.
c.
5. a. Ep = mgh
= 0,2 x 9,8 x 10
= 19,6 J
b. Ep = mgh
= 0,2 x 9,8 x 4
= 7,84 J
c. E lost = 19,6 – 7,84
= 11,76 J
Energy is lost to friction (or heat / sound)
d.
9.a. W = F x d
= 40 x 90
= 3 600 J
b.
1.6 Past Paper Question
[14 Marks]
One of the tallest and fastest roller coasters in the world is the Steel Dragon in
Japan. The ride includes a vertical drop of 93,5 m. The loaded coaster has a mass of
500 kg and a speed of 9,0 m.s-1 at the top of the drop (A).
9 m.s-1
A
8 m.s-1
93,5 m
B
2.1
State the law of “Conservation of Energy”.
(2)
Energy cannot be created or destroyed, only changed from one form into
another.
2.2
Calculate the gravitational potential energy of the roller coaster at point A.
Take the potential energy at B to be zero.
(3)
Ep = mgh
= 500 x 9,8 x 93,5
= 458 150 J
2.3
Calculate the kinetic energy of the roller coaster at point A.
Ek = ½ mv2
= ½ 500 x 92
(3)
= 20250 J
2.4
Hence, calculate the total mechanical energy at point A.
Emech = Ep + Ek
= 458 150 + 20250
= 478 400 J
(2)
2.5
Calculate the velocity of the roller coaster when it reaches point B.
Emech top = Ek bottom
478 400 = ½ mv2 ✓
= ½ 500 v2
v2 = 2 x 478 400 ✓
500
v = 43.74 m.s-1
(4)