Transcript Document

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P4 Explaining Motion
OCR 21st Century
W Richards
The Weald School
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P4.1 How can we describe motion?
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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
Distance vs Displacement
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“Distance” is how far you have gone, “displacement” is how far
you are from a point and can be positive or negative:
Distance =
Distance =
Displacement =
Displacement =
Start
-1 metre
1 metre
Distance
Distance
= =
Displacement
Displacement
= =
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Distance-time graphs
2) Horizontal line =
40
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
1) What is the speed during the first 20 seconds?
100
0.5m/s
2) How far is the object from the start after 60 seconds?
40m
3) What is the speed during the last 40 seconds?
1m/s
4) When was the object travelling the fastest?
40-60s
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
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Distance-time graph for changing speeds
40
Distance
(metres)
Object is
30
speeding up
here
Object is
slowing down
here
20
10
0
Time/s
20
40
60
80
100
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
Speed vs. Velocity
1) Is this car travelling at constant speed?
2) Is this car travelling at constant velocity?
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Speed vs. Velocity
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“Speed” means “how fast you are going”, “velocity” means “how
far you are going in a certain direction”. If the following
journeys take 1 second then work out:
Speed =
Speed =
Velocity =
Velocity =
Start
-1 metre
1 metre
Speed
Speed
= =
Velocity
Velocity
= =
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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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Acceleration
V-U
Acceleration = change in velocity (in m/s)
(in m/s2)
time taken (in s)
A
T
1) Will accelerates from standstill to 50m/s in 25 seconds.
What is his acceleration?
2m/s2
2) Pierre accelerates at 5m/s2 for 5 seconds. He started at
10m/s. What is his new speed?
35m/s
3) Elliott is in trouble with the police. He is driving up the A29
and sees a police car and brakes from 50m/s to a standstill.
His deceleration was 10m/s2. How long did he brake for?
5s
4) Another boy racer brakes at the same deceleration but only
for 3 seconds. What speed did he slow down to?
20m/s
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Velocity-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
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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
A higher tier question…
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20
10
Velocity
(metres)
0
-10
-20
20
40
60
80
1) When did the object have zero acceleration?
Time/s
100
2) What is the average acceleration from 0 to 40s?
3) What was the acceleration from 40 to 60s?
4) When did the object change direction?
20 - 40s
0.5m/s2
2m/s2
50s
P4.2 What are Forces?
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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
Air resistance/drag – a contact
force that acts against anything
moving through air or liquid
Friction – a contact force
that acts against anything
moving
Upthrust – keeps things afloat
Paired forces
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The Earth pulls Newton down with a
gravitational force of 700N.
direction
what
on
what
type
size
Newton pulls the Earth up with a
gravitational force of 700N.
Action and reaction are equal
and opposite!!
Free body force diagrams
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Consider a man on a sloping table:
Notice that the reaction force
always pushes up on the object
and the friction force always acts
up the slope!
Free body force diagrams
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1) Draw a free body force diagram
for a ladder against a wall.
2) A car pulls a caravan along the
M25. Draw a free body force
diagram for the caravan.
3) Draw a free body force diagram
for a 4-wheel drive car driving up
the M1.
4) Draw a free body force diagram
for a 2-wheel drive (engine at the
front) car driving up the M1 as well.
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Action and Reaction in Rockets
Consider a rocket leaving the Earth’s atmosphere:
A chemical reaction happens
inside the rocket that ______
out exhaust gases. There is an
equal and ______ reaction to
this force – this _______ acts
on the rocket and pushes it
_______. The same process
happens in ____ engines.
Words – jet, pushes, reaction,
upwards, opposite
P4.3 Forces and Movement
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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
Air Resistance
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Air resistance is a force that opposes motion through air. The
quicker you travel, the bigger the air resistance:
The same applies to a body falling through a liquid (called
“drag” or “upthrust”).
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
Resultant Force
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Calculate the resultant force of the following:
500N
100N
700N
600N
50N
700N
700N
200N
800N
800N
100N
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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
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Force and change in momentum
To calculate the change the momentum of an object you need
to know two things – how much force acts and how long it acts
for:
Force = Change in momentum (in kgm/s)
(in N)
mv-mu
Time (in s)
F
T
For example, Ronaldo 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
Let’s use this equation to explain how airbags work:
mv
F
T
Basically:
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
Terminal Velocity
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 VELOCITY
Words – increase, small,
constant, balance, accelerates
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Terminal Velocity
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 velocity, weight
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P4.4 Describing Motion with Energy Changes
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
1) Bex 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?
2) Emma rides her bike at a speed of 10m/s. If
the combined mass of Emma and her bike is
80kg what is her kinetic energy?
3) Rob 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?
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450,000J
4000J
5m/s
75kg
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
(Joules)
=
Weight
(newtons)
x
Change in height
(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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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.
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 he 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
book 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?
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25J
20J,
GPE
4m, KE
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?
50N
5. Simon drives his car 1000m. If the engine was producing a
driving force of 2000N how much work did the car do?
2MJ
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.
Amount of energy transferred =
work done
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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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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
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Energy Changes in Roller Coasters
1) Electrical energy is
transferred into gravitational
potential energy
3) Kinetic energy is
transferred back
into gravitational
potential energy
2) Gravitational potential
energy is transferred into
kinetic energy
Dropping objects
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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
mgh = ½mv2
gh = ½v2
10 x 1 = ½ x v2
v2 = 20
v = 4.5m/s
1m
Some Questions…
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1) Energy is always conserved, so what happens to the
electrical energy eventually?
2) If the height of the drop was 100m and assuming there was
a 100% conversion from gravitational to kinetic energy, how
fast was the car moving at the bottom of the ramp?