Transcript P3 Forces for Transport

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P3: Forces for Transport
OCR Gateway Additional Science
W Richards
P3a Speed
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Distance, Speed
and Time
D
Speed = distance (in metres)
time (in seconds)
S
T
1) Freddie walks 200 metres in 40 seconds. What is his
speed?
5m/s
2) Hayley covers 2km in 1,000 seconds. What is her
speed?
2m/s
3) How long would it take Lauren to run 100 metres if she
runs at 10m/s?
4) Jake travels at 50m/s for 20s. How far does he go?
5) Izzy drives her car at 85mph (about 40m/s). How long
does it take her to drive 20km?
10s
1000m
500s
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Distance, Speed
and Time
D
Speed = distance (in metres)
time (in seconds)
S
T
1) Sarah walks 2000m in 50 minutes. What is her speed in
m/s?
0.67m/s
2) Jack tries to walk the same distance at a speed of 5m/s.
How long does he take?
400s
3) James drives at 60mph (about 100km/h) for 3 hours. How
far has he gone?
4) The speed of sound in air is 330m/s. Molly shouts at a
mountain and hears the echo 3 seconds later. How far
away is the mountain? (Careful!)
300km
495m
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How speed cameras work
Speed cameras work by recording the
position of the car at a certain time
apart. What is the speed of the trolley
in the lab example done below?
After 0s
After 1.5s
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Average Speed
It is common to see “average speed
cameras” near roadworks. They work
by recording how long you take to
cover a certain distance and then
working out your average speed.
u+v
s=
2 t
1) Two cameras are 1km apart and a car takes 50s to travel
between them. What was the car’s average speed?
20m/s
2) A car accelerates from 10 to 20m/s for 50s. How far has
it gone?
750m
3) How long would it take to travel 10km if you started at a
speed of 30m/s and ended up at 50m/s after the 10km?
250s
Distance-time graphs
2) Horizontal line =
40
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4) Diagonal line
downwards =
30
Distance
(metres)
20
10
0
Time/s
20
1) Diagonal line =
40
60
80
100
3) Steeper diagonal line =
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40
Distance
(metres)
30
20
10
0
Time/s
20
40
60
80
100
1) What is the speed during the first 20 seconds?
2) How far is the object from the start after 60 seconds?
3) What is the speed during the last 40 seconds?
4) When was the object travelling the fastest?
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Distance-time graph for non-uniform motion
40
Distance
(metres)
Object is
accelerating
up to here
30
Object is now
decelerating
20
10
0
Time/s
20
40
60
80
100
40
Distance
(metres)
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30
20
10
0
Time/s
20
40
60
80
100
1) What was the velocity in the first 20 seconds?
1.5m/s
2) What was the velocity between 20 and 40 seconds?
0.5m/s
3) When was this person travelling the fastest?
80-100s
4) What was the average speed for the first 40 seconds?
1m/s
P3b Changing Speed
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Acceleration
V-U
Acceleration = change in velocity (in m/s)
(in m/s2)
time taken (in s)
A
1) A cyclist accelerates from 0 to 10m/s in 5 seconds.
What is her acceleration?
T
2m/s2
2) A ball is dropped and accelerates downwards at a rate of
10m/s2 for 12 seconds. How much will the ball’s velocity
increase by?
120m/s
3) A car accelerates from 10 to 20m/s with an acceleration
of 2m/s2. How long did this take?
5s
4) A rocket accelerates from 1,000m/s to 5,000m/s in 2
seconds. What is its acceleration?
2000m/s2
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Speed-time graphs
1) Upwards line =
80
Velocity
m/s
4) Downward line =
60
40
20
0
10
2) Horizontal line =
20
30
40
50
3) Upwards line =
T/s
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80
60
Velocity
m/s
40
20
0
T/s
10
20
30
40
50
1) How fast was the object going after 10 seconds?
40m/s
2) What is the acceleration from 20 to 30 seconds?
2m/s2
3) What was the deceleration from 30 to 50s?
3m/s2
4) How far did the object travel altogether?
1700m
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Speed-time graph for non-uniform motion
40
Distance
(metres)
Object’s
acceleration
is increasing
30
Object’s
acceleration
is decreasing
20
10
0
Time/s
20
40
60
80
100
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80
60
Velocity
m/s
40
20
0
T/s
10
20
30
40
50
1) How fast was the object going after 10 seconds?
10m/s
2) What is the acceleration from 20 to 30 seconds?
4m/s2
3) What was the deceleration from 40 to 50s?
6m/s2
4) How far did the object travel altogether?
1500m
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80
60
Velocity
m/s
40
20
0
T/s
10
20
30
40
50
This velocity-time graph shows Coryn’s journey to school.
How far away does she live?
2500m
Speed vs. Velocity
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Speed is simply how fast you are travelling…
This car is travelling at a
speed of 20m/s
Velocity is “speed in a given direction”…
This car is travelling at a
velocity of 20m/s east
Circular Motion
1) Is this car travelling at constant speed?
2) Is this car travelling at constant velocity?
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P3c Forces and Motion
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Force and acceleration
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If the forces acting on an object
are unbalanced then the object will
accelerate, like these wrestlers:
Force (in N) = Mass (in kg) x Acceleration (in m/s2)
F
M
A
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Force, mass and acceleration
1) A force of 1000N is applied to push
a mass of 500kg. How quickly does
it accelerate?
2) A force of 3000N acts on a car to
make it accelerate by 1.5m/s2. How
heavy is the car?
3) A car accelerates at a rate of
5m/s2. If it weighs 500kg how
much driving force is the engine
applying?
4) A force of 10N is applied by a boy
while lifting a 20kg mass. How
much does it accelerate by?
F
M
A
2m/s2
2000kg
2500N
0.5m/s2
Stopping a car…
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What two things must the driver of the car do in order to stop
in time?
Tiredness
Stopping a car…
Thinking
distance
Too many
drugs
(reaction time)
Too much
alcohol
Poor
visibility
Wet roads
Icy roads
Tyres/brakes
worn out
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Braking
distance
Driving too
fast
Total Stopping Distance = Thinking Distance + Braking Distance
Stopping Distances
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This diagram (taken from drivingtestsuccess.com) shows the thinking and
braking distances for different speeds. What patterns do you notice?
Thinking distance increases
linearly
Braking distance increases in
a squared relationship
P3d Work and Power
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Weight vs. Mass
Earth’s Gravitational Field Strength is 10N/kg. In other
words, a 1kg mass is pulled downwards by a force of 10N.
W
Weight = Mass x Gravitational Field Strength
(in N)
(in kg)
(in N/kg)
M
1) What is the weight on Earth of a book with mass 2kg?
2) What is the weight on Earth of an apple with mass 100g?
g
20N
1N
3) James weighs 700N on the Earth. What is his mass?
70kg
4) On the moon the gravitational field strength is 1.6N/kg.
What will James weigh if he stands on the moon?
112N
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Work done
When any object is moved around work will need to be
done on it to get it to move (obviously).
We can work out the amount of work done in moving an
object using the formula:
Work done = Force x distance moved
in J
in N
W
in m
F
D
Example questions
1.
Jessie 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. Hayley 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. James 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?
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25J
20J,
GPE
4m, KE
4. Jack cuddles his cat and lifts it 1.5m in the air. If he did
75J of work how much force did he use?
50N
5. Freddie drives his car 1000m. If the engine was producing
a driving force of 2000N how much work did the car do?
2MJ
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A Practical Example of Doing Work
Consider a rocket re-entering the Earth’s atmosphere:
The rocket would initially have
a very high _______ energy.
This energy would then _____
due to friction caused by
collisions with _______ in the
atmosphere. These collisions
would cause the rocket to ____
up (_____ is “being done” on
the rocket). To help deal with
this, rockets have special
materials that are designed to
lose heat quickly.
Words – work, kinetic,
particles, heat, decrease
Energy and Power
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The POWER RATING of an appliance is simply how much
energy it uses every second.
In other words, 1 Watt = 1 Joule per second
E
E = Energy (in joules)
P = Power (in watts)
T = Time (in seconds)
P
T
Some example questions
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1) What is the power rating of a light bulb that transfers
120 joules of energy in 2 seconds?
60W
2) What is the power of an electric fire that transfers
10,000J of energy in 5 seconds?
2KW
3) Tanner runs up the stairs in 5 seconds. If he transfers
1,000,000J of energy in this time what is his power
rating?
0.2MW
4) How much energy does a 150W light bulb transfer in a)
one second, b) one minute?
150J,
9KJ
5) Pierre’s brain needs energy supplied to it at a rate of
40W. How much energy does it need during a 50 minute
physics lesson?
120KJ
6) Levi’s brain, being more intelligent, only needs energy at a
rate of about 20W. How much energy would his brain use
in a normal day?
1.73MJ
An example with cars
Citroen Saxo, 60bhp
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Audi R8, 423 bhp
What are the advantages and disadvantages of each car?
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Power
Power (in watts) is “the rate of doing work”:
W
P=W
t
P
Also, using our “work done” equation:
P = W = FxD
t
t
t
W = FxD
…therefore
P = Fv
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Random questions on work and power
1) Jordan pushes Tom in the direction of a cliff. If he
uses a force of 40N and he moves Tom 10m in 4s
calculate the work done and Jordan’s power rating.
400J,
100W
2) Chris runs up some stairs and has a power rating of
600W while he does so. If he does it in 5 seconds and
his weight is 750N calculate how high the stairs are.
4m
3) A man pulls a block of wood and uses a force of 50N.
If the distance travelled horizontally is 5m calculate
the work done by the man and his power if the journey
lasted 10 seconds.
250J,
25W
50N
P3e Energy on the Move
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Kinetic energy
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Any object that moves will have kinetic energy.
The amount of kinetic energy an object has can be found using
the formula:
Kinetic energy = ½ x mass x velocity squared
in J
in kg
KE =
½
in m/s
mv2
Example questions
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1) Shannon drives her car at a speed of 30m/s.
If the combined mass of her and the car is
1000kg what is her kinetic energy?
450,000J
2) Issy rides her bike at a speed of 10m/s. If
the combined mass of Issy and her bike is
80kg what is her kinetic energy?
4000J
3) Will is running and has a kinetic energy of
750J. If his mass is 60kg how fast is he
running?
4) Josh is walking to town. If he has a kinetic
energy of 150J and he’s walking at a pace of
2m/s what is his mass?
5m/s
75kg
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Stopping Distances revision
Recall the patterns we observed in this data:
Thinking distance increases
linearly
Braking distance increases in
a squared relationship
Stopping a car…
What happens inside the car when it stops?
In order to stop this car the brakes must
“do work”. This work is used to reduce the
kinetic energy of the vehicle and the
brakes will warm up – this is why the
braking distance depends on speed2
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An example question…
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This car can apply a maximum braking
force of 10,000N. If the car’s mass
is 1000Kg how far is its stopping
distance when it is travelling at a
speed of 15m/s (roughly 30mph) and
30m/s (roughly 60mph)?
15m/s = 11.25m stopping distance
30m/s = 45m stopping distance (4 times greater)
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Different ways of fuelling cars
What are the advantages and disadvantages of each of the following fuels?
Fuel consumption
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How do the following features help or hinder fuel economy?
Having an aerodynamic shape
Having a roof box
Having a
“deflector”
Having a
window open
P3f Crumple Zones
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Momentum
Any object that has both mass and
velocity has MOMENTUM. Momentum
(symbol “p”) is simply given by the formula:
P
Momentum = Mass x Velocity
(in kgm/s)
(in kg)
(in m/s)
M
V
What is the momentum of the following?
1) A 1kg football travelling at 10m/s
2) A 1000kg Ford Capri travelling at 30m/s
3) A 20g pen being thrown across the room at 5m/s
4) A 70kg bungi-jumper falling at 40m/s
10kgm/s
30,000kgm/s
0.1kgm/s
2800kgm/s
Force and momentum
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Newton’s second law of motion says that the force acting on an
object is that object’s rate of change of momentum. In other
words…
mv
Force = Change in momentum (in kgm/s)
(in N)
Time (in s)
Also called “impulse”
F
T
For example, Rooney takes a free kick by kicking a stationary football with
a force of 40N. If the ball has a mass of 0.5kg and his foot is in
contact with the ball for 0.1s calculate:
1) The change in momentum of the ball (its impulse),
2) The speed the ball moves away with
Example questions
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1) Paddy likes playing golf. He strikes a golf ball with a force
of 80N. If the ball has a mass of 200g and the club is in
contact with it for 0.2s calculate a) the change in
momentum of the golf ball, b) its speed.
16Kgm/s,
80m/s
2) Courtney thinks it’s funny to hit tennis balls at Kit. She
strikes a serve with a force of 30N. If the ball has a
mass of 250g and the racket is in contact with it for 0.15s
calculate the ball’s change in momentum and its speed.
4.5Kgm/s,
18m/s
3) Tom takes a dropkick by kicking a 0.4kg rugby ball away at
10m/s. If his foot was in contact with the ball for 0.1
seconds calculate the force he applied to the ball.
40N
4) Jenny strikes a 200g golf ball away at 50m/s. If she
applied a force of 50N calculate how long her club was in
contact with the ball for.
0.2s
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Safety features
How do air bags and crumple zones
work?
mv
Basically:
F
T
1) The change in momentum is the same with or without an
airbag
2) But having an airbag increases the time of the collision
3) Therefore the force is reduced
Car Safety Features
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These objects all help reduce injury by basically absorbing
energy.
Cars also have ABS brakes which
prevent them from skidding by
automatically pumping off and on
to avoid the brakes locking.
P3g Falling Safely
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Introduction to Forces
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A force is a “push” or a “pull”. Some common examples:
Weight (mg) – pulls
things towards the
centre of the Earth
Friction – a contact force
that acts against anything
moving
Air resistance/drag – a contact
force that acts against anything
moving through air or liquid
Upthrust – keeps things afloat
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Examples of Air Resistance
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Balanced and unbalanced forces
Consider a camel standing on a road.
What forces are acting on it?
Reaction
These two forces would be equal –
we say that they are BALANCED.
The camel doesn’t move anywhere.
Weight
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Balanced and unbalanced forces
Reaction
What would happen if we took the
road away?
Weight
Balanced and unbalanced forces
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Balanced and unbalanced forces
1) This animal is either
________ or moving
with _______ _____…
2) This animal is getting
________…
3) This animal is getting
_______….
4) This animal is also
either _______ or moving
with ________ ______..
Words - Stationary, faster, slower or constant speed?
Summary
Complete these sentences…
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If an object is stationary and has NO resultant force on it the object
will…
If an object is stationary and a resultant force acts on it the object will…
If an object is already moving and NO resultant force acts on it the
object will…
If an object is already moving and a resultant force acts on it the object
will…
…accelerate in the direction of the
resultant force
…continue to move at the same
speed and the same direction
…continue to stay stationary
…accelerate in the direction of the
resultant force
Terminal Speed
Consider a skydiver:
1) At the start of his jump the air
resistance is _______ so he
_______ downwards.
2) As his speed increases his air
resistance will _______
3) Eventually the air resistance will be
big enough to _______ the
skydiver’s weight. At this point
the forces are balanced so his
speed becomes ________ - this is
called TERMINAL SPEED
Words – increase, small,
constant, balance, accelerates
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Terminal Speed
Consider a skydiver:
4) When he opens his parachute the
air resistance suddenly ________,
causing him to start _____ ____.
5) Because he is slowing down his air
resistance will _______ again until
it balances his _________. The
skydiver has now reached a new,
lower ________ _______.
Words – slowing down, decrease,
increases, terminal speed, weight
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Velocity-time graph for terminal velocity…
Parachute opens –
diver slows down
Velocity
Speed
increases…
Terminal
velocity
reached…
Time
New, lower terminal
velocity reached
Diver hits the ground
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Acceleration due to Gravity
Notice that the skydiver’s weight didn’t change at any point.
Or did it?
In reality, every object
that is close to the
_____ has the same
gravitational _______.
However, if you drop an
object from the top of
Mt Everest its
acceleration will be
slightly ______!
Also, if you take out __ ______, objects would fall with the
same acceleration (like the skydiver on the _____).
Words – acceleration, Earth, moon, air resistance, smaller
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P3h The Energy of Games and Theme rides
Gravitational Potential Energy
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To work out how much gravitational potential energy (GPE) an
object gains when it is lifted up we would use the simple
equation…
GPE = Mass x Acceleration of free-fall x Change in height
(Joules) (newtons)
(=10N/kg)
(metres)
GPE
(Remember - W=mg)
mg
H
Some example questions…
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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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Energy changes for a skydiver
Recall our skydiver:
If the skydiver has reached terminal speed explain what
happens to his…
1) Kinetic energy
2) Gravitational potential energy
…while he is falling.
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Understanding Kinetic Energy
KE =
If the mass of the object
is doubled what effect
would this have on the
object’s kinetic energy?
½
mv2
If the speed of the object
is doubled what effect
would this have on the
object’s kinetic energy?
Roller Coasters
1) Electrical energy is
transferred into gravitational
potential energy
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3) Kinetic energy is
transferred back
into gravitational
potential energy
2) Gravitational potential
energy is transferred into
kinetic energy
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Using conservation of energy when dropping objects
If I drop this ball 1m how fast will it be going
when it hits the floor?
Use GPE at top = Kinetic energy at bottom
mgh = ½mv2
gh = ½v2
h=
v2
2g
v2 = 2 x 10 x 1
v2 = 20
v = 4.5m/s
1m
An example question…
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If the height of the drop was 100m and assuming there was a
100% conversion from gravitational to kinetic energy, how
fast was the roller coaster car moving at the bottom of the
ramp?