Download IP4.11.4 Work and energy

IP4.11.4 Work and energy
Work and energy
© Oxford University Press 2011
07/05/17
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IP4.11.4 Work and energy
Using graphs to summarise motion
D
1. Distances measured in one direction are ________, and in the other are _______
2. The _______ of an object is its ______ and the ________ of motion.
3. The velocity of an object moving in a straight line is ________ if it is moving in one
direction and ________ if it is moving in the opposite direction.
C
4. Sketch a velocity-time graph for an object that is:
a) stationary
b) moving in a straight line with constant speed
c) moving in a straight line with steadily increasing
1. Sketch a distance-time graph for an object that is:
a) stationary
b) moving at constant speed
A/B
speed
c
v
a
d
b
negative
t
direction
positive
b
velocity
a
negative
c
c) moving with increasing speed
t
distance /m
positive
2. Using the graph to the right
200
A
a) which is moving faster, A or B? A – steeper slope / gradient
100
B
b) Calculate the speed of B
Speed = gradient = (100-0) = 100 = 5 m/s
(20-0)
20
10
20
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time/s
IP4.11.4 Work and energy
Doing work:
When you push or pull something and make it move,
you do work.
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IP4.11.4 Work and energy
Energy and work
•
•
•
•
•
•
•
Whenever an object moves energy is used
This also means that work has been done
E.g you open a door
You have used force to open the door
You have used up energy to open the door
Therefore you have done work
The energy has been transferred to
opening the door
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IP4.11.4 Work and energy
• When an object is moved by a force, we say
work is done on the object by the force
• The work done on the object is equal to the
energy transferred to the object
• E.g. the energy you use to open the door is
transferred to the door (door moves)
• If the energy you used up to open the door was
20J then the work done was 20J
• Where does the energy come from?
• When you do work against friction, most of the
energy gets lost as heat and sometimes as
sound
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IP4.11.4 Work and energy
How much work?
Imagine pushing a car along a road.
• You must apply a force . . .
• . . . and you push the car a certain distance.
work done (in joules)
= force (in newtons)  distance (in metres)
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IP4.11.4 Work and energy
Work done, GPE and KE
LQ: Can I calculate the energy
used in different situations?
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IP4.11.4 Work and energy
An example
I push my car 30 m. I push with a force of 400 N.
work done = force  distance
= 400 N  30 m
= 12 000 J
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IP4.11.4 Work and energy
Lifting something
• If you lift something up, you must
exert enough force to balance the
force of gravity.
• The upward force is equal to the
weight of the object.
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IP4.11.4 Work and energy
Lifting something
If you lift something through a certain
distance
work done = force  distance
where
force = weight of the object lifted
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IP4.11.4 Work and energy
An example
A woman lifts up her baby from the floor.
The baby weighs 100 N.
The woman lifts the baby up by 2 m.
work done = force  distance
= weight  distance
= 100 N  2 m
= 200 J
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IP4.11.4 Work and energy
Work done = energy transferred
When someone does work, energy is transferred:
• from the person who exerts the force
• to other places.
amount of work done = amount of energy transferred
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IP4.11.4 Work and energy
Let’s look first at lifting
distance lifted
When you lift something up, you do
work.
work done = force  distance
= weight  distance lifted
The gravitational potential energy of the
object you lift has increased:
change in gravitational
potential energy
= weight  height gain
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IP4.11.4 Work and energy
Different paths?
What if you lift something, but not
straight up?
work done = force  distance moved
in the direction of the force
change in gravitational potential
energy = weight  vertical height gain
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IP4.11.4 Work and energy
1.
Hannah pushes a book 5m along the table with a force of
5N. She gets tired and decides to call it a day. How much
work did she do?
2. Courtney lifts a laptop 2m into the air with a force of 10N.
How much work does she do? What type of energy did the
laptop gain?
3. Tom does 200J of work by pushing a wheelbarrow with a
force of 50N. How far did he push it? What type of
energy did the wheelbarrow gain?
4. Dan cuddles his cat and lifts it 1.5m in the air. If he did
75J of work how much force did he use?
25J
20J, GPE
4m, KE
50N
5. Simon drives his car 1000m. If the engine was producing a
2MJ
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Oxford
University
Press 2011
driving force of 2000N how much work did the car do?
IP4.11.4 questions…
Work and energy
Some example
How much gravitational potential energy have the following
objects gained?:
1.
A brick that weighs 10N lifted to the top of a house
(10m),
100J
2. A 1,000kg car lifted by a ramp up to a height of 2m,
20KJ
3. A 70kg person lifted up 50cm by a friend.
350J
How much GPE have the following objects lost?:
1.
A 2N football dropping out of the air after being kicked
up 30m,
60J
2. A 0.5N egg falling 10m out of a bird nest,
5J
3. A 1,000kg car falling off its 200cm ramp.
20KJ
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IP4.11.4 Work and energy
© Oxford University Press 2011
IP4.11.4 Work and energy
© Oxford University Press 2011
IP4.11.4 Work and energy
© Oxford University Press 2011
IP4.11.4 Work and energy
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IP4.11.4 Work and energy
Work done = energy transferred
What happens if you push something
horizontally?
• Imagine pushing a cart with very
well-oiled wheels (no friction).
• The speed of the cart will increase
while the force acts.
work done = change in kinetic energy
of the cart
© Oxford University Press 2011
IP4.11.4 Work and energy
Calculating kinetic energy
The kinetic energy of a moving object depends on:
• its mass (how big it is)
• its speed (how fast it is moving).
The equation for calculating the kinetic energy of a
moving object is:
kinetic energy = ½ mass  (speed)2
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IP4.11.4 Work and energy
What if friction cannot be ignored?
Think about pushing a car.
As you push it, you transfer energy from your body to:
• the car – increasing its kinetic energy
• parts of the car (and the surroundings) – which heat up because of friction.
the amount of work you do = the amount of energy transferred
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IP4.11.4 Work and energy
Now let’s look at an example that brings several
of these ideas together. . .
. . . pushing a car up a slope.
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IP4.11.4 Work and energy
Pushing a car uphill
• If you push your car uphill, you do work:
work done = force  distance
• You increase the gravitational potential energy of your car:
change in gravitational potential energy
= weight  vertical height gain
• Are these the same? If not, why not?
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IP4.11.4 Work and energy
The calculation
work done in pushing
= force  distance
= 450 N  30 m
= 13 500 J
gain in gravitational potential energy
= weight  vertical height gain
= 900 N  1 m
= 9000 J
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IP4.11.4 Work and energy
So why the difference?
• Some of the energy is transferred to the
surroundings – heating them up.
• Only part of it goes to increasing the gravitational
potential energy of the car.
• If no energy is lost as heat you can assume that
kinetic energy = gravitational potential energy
(for falling objects only)
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A diver who has a mass of 50 kg dives off a diving board 3.0 metres above the water level. What is her kinetic energy when she reaches the w
IP4.11.4 Work and energy
• A diver who has a mass of 50 kg dives off
a diving board 3.0 metres above the water
level. What is her kinetic energy when she
reaches the water?
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IP4.11.4 Work and energy
• Kinetic energy gained = gravitational potential
energy lost
• Kinetic energy gained = weight × height
• You must calculate her weight to use in this
equation
• Weight = mass × gravitational field strength
• Weight = 50 kg × 10 N / kg
• Weight = 500 N
• Kinetic energy gained = weight × height
• Kinetic energy gained = 500 N × 3 m
• Kinetic energy gained = 1500 J
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IP4.11.4 Work and energy
• How fast is the diver moving when she
reaches the water?
• Ke = 0.5mv2
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IP4.11.4 Work and energy
• Put her kinetic energy (the 1500J you
have calculated) into the kinetic energy
equation together with her mass
• Kinetic energy = 1/2 × mass × speed2
• 1500 J = ½ × 50 × speed2 = 25 × speed2
• So speed2 = 1500/25 = 60 (This is not the
answer yet! It is speed2!)
• So her speed = square root of 60 = 7.7
m/s
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