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ForcesForces
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Distance, Speed Distance, Speed and Timeand Time
Speed = distance (in metres)
time (in seconds)
D
TS
1) Seb walks 200 metres in 40 seconds. What is his speed?
2) Lucy covers 2km in 1,000 seconds. What is her speed?
3) How long would it take Freddie to run 100 metres if he runs at 10m/s?
4) Sue travels at 50m/s for 20s. How far does he go?
5) Hannah drives her car at 85mph (about 40m/s). How long does it take her to drive 20km?
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Distance-time graphsDistance-time graphs
40
30
20
10
0 20 40 60 80 100
4) Diagonal line downwards =
3) Steeper diagonal line =1) Diagonal line =
2) Horizontal line =
Distance(metres)
Time/s
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40
30
20
10
0 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?
Distance(metres)
Time/s
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Distance-time graph for non-uniform motionDistance-time graph for non-uniform motion
40
30
20
10
0 20 40 60 80 100
Distance(metres)
Time/s
Object is accelerating up to here
Object is now decelerating
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Speed vs. VelocitySpeed vs. Velocity
Speed is simply how fast you are travelling…
Velocity is “speed in a given direction” (a “vector quantity”)…
This car is travelling at a speed of 20m/s
This car is travelling at a velocity of 20m/s east
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AccelerationAcceleration V-U
TAAcceleration = change in velocity (in m/s)
(in m/s2) time taken (in s)
1) A cyclist accelerates from 0 to 10m/s in 5 seconds. What is her acceleration?
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?
3) A car accelerates from 10 to 20m/s with an acceleration of 2m/s2. How long did this take?
4) A rocket accelerates from 1,000m/s to 5,000m/s in 2 seconds. What is its acceleration?
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Velocity-time graphsVelocity-time graphs
80
60
40
20
0 10 20 30 40 50
Velocitym/s
T/s
1) Upwards line =
2) Horizontal line = 3) Upwards line =
4) Downward line =
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80
60
40
20
0
1) How fast was the object going after 10 seconds?
2) What is the acceleration from 20 to 30 seconds?
3) What was the deceleration from 30 to 50s?
4) How far did the object travel altogether?
10 20 30 40 50
Velocitym/s
T/s
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Speed-time graph for non-uniform motionSpeed-time graph for non-uniform motion
40
30
20
10
0 20 40 60 80 100
Distance(metres)
Time/s
Object’s acceleration is increasing
Object’s acceleration is decreasing
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Some subtle differences…Some subtle differences…“Distance” is how far you have gone, “displacement” is how far you are and can be positive or negative:
Start
1 metre-1 metre
Distance =
Displacement =
Distance =
Displacement =
Distance =
Displacement =
Distance =
Displacement =
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Some subtle differences…Some subtle differences…“Distance” is how far you have gone, “displacement” is how far you are and can be positive or negative:
Start
1 metre-1 metre
Speed =
Velocity =
Speed =
Velocity =
Speed =
Velocity =
Speed =
Velocity = “Speed” is how fast you go. “Velocity” is how fast in a given direction.
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Vector vs. scalarVector vs. scalarScalar quantities have size only and no direction.Vector quantities have both size and direction.
Scalar or vector???
Scalar Vector
1. Mass2. Distance
3. Displacement4. Speed
5. Velocity
6. Energy
8. Power
7. Time
9. Momentum
10. Current11. Force
12. Acceleration
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Balanced and unbalanced forcesBalanced and unbalanced forces
Consider a camel standing on a road. What forces are acting on it?
Weight
Reaction
These two forces would be equal – we say that they are BALANCED. The camel doesn’t move anywhere.
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Balanced and unbalanced forcesBalanced and unbalanced forces
What would happen if we took the road away?
Weight
Reaction
The camel’s weight is no longer balanced by anything, so the camel falls downwards…
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Introduction to ForcesIntroduction to ForcesA 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
Upthrust – keeps things afloat_____ – a contact force that acts against anything moving
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Air ResistanceAir ResistanceAir 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”).
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Examples of Air ResistanceExamples of Air Resistance
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Facts on Air ResistanceFacts on Air ResistanceAir Resistance is the force that acts ___________ anything that moves through the ______:
It can be reduced by using a more “__________” (aerodynamic) shape:
It gets _______ when you move faster:
Streamlining also works when travelling through _______:
Words – water, air, larger, against, streamlined
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Balanced and unbalanced forcesBalanced and unbalanced forces
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Balanced and unbalanced forcesBalanced and unbalanced forces
1) This animal is either ________ or moving with _____ _____…
4) This animal is…
2) This animal is getting _________…
3) This animal is getting _______….
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Resultant ForceResultant ForceCalculate the resultant force of the following:
500N 100N 700N 600N
700N 700N
200N
800N 800N
100N
50N
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Force and accelerationForce and acceleration
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
AM
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Force, mass and accelerationForce, mass and acceleration1) 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
AM
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Terminal VelocityTerminal VelocityConsider 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 VelocityTerminal VelocityConsider 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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Velocity-time graph for terminal velocity…Velocity-time graph for terminal velocity…
Velocity
Time
Speed increases…
Terminal velocity reached…
Parachute opens – diver slows down
New, lower terminal velocity reached
Diver hits the ground
On the Moon
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A closer look at motion graphsA closer look at motion graphsConsider a bouncing ball:
Displacement
Time
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A closer look at motion graphsA closer look at motion graphsConsider a bouncing ball:
Velocity
Time
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A closer look at motion graphsA closer look at motion graphsConsider a bouncing ball:
Acceleration
Time
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Equations of MotionEquations of MotionIf we’re talking about any object travelling in a straight line with constant acceleration then we can use these 4 “golden equations”…
Golden equation #1Golden equation #1 Golden equation #1Golden equation #2
Vel
Tu
v
Ave
Ave. velocity = (u + v) / 2
Therefore x = u + v
2 t
Vel
Tu
v
Acc = (v – u) / t
Therefore v = u + at
v-u
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Equations of MotionEquations of MotionGolden equation #1Golden equation #3 Golden equation #1Golden equation #4
Vel
Tu
v
From equation #2 (v-u) = at
Therefore x = ut + ½at2 Therefore v2 = u2 + 2ax
v-u
ut
t(v-u)/2
Therefore x = ut + t/2 x at
From eqn #2 t = (v-u) / a
From eqn #1 x = t(u+v) / 2
So x = (v-u) (v+u)2a
2ax = v2 – u2
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Equations of MotionEquations of Motion
x = u + v
2 t
v = u + at
x = ut + ½at2
v2 = u2 + 2ax
They’re golden!
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Example questionsExample questions1) Ben drops a ball on Dan’s foot. How long does the ball take
to fall 1m? 2m? Why is the second answer not twice the first?
2) Ryan flies to Belgium. His aeroplane has a maximum acceleration on the ground of 3.4ms-2. What is the minimum length of runway needed to reach its take off speed of 110ms-1 and how long will this take?
3) Luke likes watching kangaroos. A kangaroo jumps to a vertical height of 2.8m. For how long was it in the air?
4) Tom likes baseball. A baseball pitcher can release a ball at 40ms-1 after accelerating through a distance of 2.5m. Calculate the average acceleration of the ball.
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Example questionsExample questions5) Andrew wants to play with the air track. The air track is
slightly tilted. He pushes a trolley up the track with a speed of 1ms-1 and its acceleration due to the tilt is 0.5ms-2 down the track. How long does it take to drop 1m below the starting point?
6) Howard travels in a rocket powered sledge and accelerates from rest to 284ms-1 in 5s and then comes to a rest in 1.5s. Calculate his acceleration in both stages.
7) Harry has a good chance of surviving a car crash with a seatbelt on if his deceleration does not exceed 30g. Calculate the distance by which the front end of the car must collapse in if a crash occurs at 70mph.
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Vertical ProjectionVertical ProjectionIf I throw this ball upwards with a speed of
40ms-1 how high will it go?
Use v2 = u2 + 2ax
0 = 402 + (2 x -9.81 x x)
0 = 1600 – 19.62x
1600 = 19.62x
x = 1600/19.62
x = 81.5m
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Practice QuestionsPractice Questions1) How far will a cricket ball go if it is thrown upwards with an
initial velocity of 10ms-1?
2) How far will a table tennis ball go if it is thrown upwards with an initial velocity of 5ms-1?
3) A human cannonball is projected vertically upwards and she reaches a vertical height of 20m before coming back down. How fast was she going when she left the cannon?
4) A test tube falls off the table. If the table is 1m high how fast was the test tube going when it hit the floor?
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Measuring gMeasuring gConsider the equation x = ut + ½at2…
If we consider a ball being dropped then u=0, so x = ½at2
We also know that a = g, therefore…
x = ½gt2
x
½t2
y = m x + c
x = ½ g t2
x
x
x
x
Gradient = g
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Projectile MotionProjectile MotionAha! If I let go of the branch when he fires his gun I’ll be safe because
the bullet will go above me…
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Projectile MotionProjectile Motion
50m
1.5m
Question – how long did this take and how fast was the bullet?
1) Use x = ut + ½at2 vertically to find the time
2) Then use speed = distance / time horizontally to get the speed
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Example questionsExample questions1) Ben throws a bowling ball at Tom and it lands on his foot.
If the ball started 1.2m above Tom’s foot and the distance between them was 2m calculate both the time taken and the initial velocity of the ball.
2) Rob fires a gun and the bullet leaves the barrel at a speed of 200ms-1. If it landed on the ground 500m away calculate how long the journey took and how high up Rob was holding the gun from ground level.
3) Andrew likes knocking test tubes off the table. If he hits one with an initial velocity of 2ms-1 and the table is 1m high calculate the time taken for the test tube to hit the floor and how far away from the table it landed.
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Recap questionsRecap questions1) Andrew Murray hits a tennis ball and it passes horizontally
over the net and lands just inside the baseline of the court. The net has a height of 1.07m and is 11.9m from the baseline. Find the horizontal speed of the ball.
2) David Beckham takes a free kick and it flies into the top corner horizontally. If the corner is 2.4m above the ground and the goal is 18m away calculate the time taken for the ball to reach the goal.
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Newton 1642-1727
Newton’s 1Newton’s 1stst Law of Motion Law of MotionBasically, a body will remain at rest or
continue to move with constant velocity as long as the forces acting on it are balanced.
An unbalanced forwards force will make me
accelerate…
…and an unbalanced backwards force will make
me slow down…
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Newton’s 2Newton’s 2ndnd Law of Motion Law of Motion
Newton 1642-1727
The acceleration of a body is proportional to the resultant force causing its
acceleration and is in the same direction.
In other words…
force = mass x accelerationF
AM
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Revision questionsRevision questions1) 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 1.5ms-2. How heavy is the car?
3) A car accelerates at a rate of 5ms-2. 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
AM
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Testing Newton’s 2Testing Newton’s 2ndnd Law LawFor each version of the experiment:
1) Draw a diagram of how you set it up
2) Describe your method
3) Describe what equipment you used to get the results and how you analysed them (you only need to do this once as they’re both the same).
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Newton’s 3Newton’s 3rdrd Law of Motion Law of Motion
Newton 1642-1727
When body A exerts a force on body B, body B exerts an equal and opposite force
on body A.
My third law says that if I push to the right I will
move backwards as well.
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Newton’s 3Newton’s 3rdrd Law of Motion Law of Motion
What will happen if I push this satellite away from me?
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Types of ForcesTypes of ForcesGravitational (W=mg)
Electromagnetic/electrostatic
+++++
Nuclear (2 types)
+++++
-
Describe each force, including a comment on the
distance it works over, whether it repels or attracts and other important points
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Free body force diagramsFree body force diagrams
The Earth pulls Newton down with a gravitational force of 700N.
Newton pulls the Earth up with a gravitational force of 700N.
what on what
direction
type
size
This is a Newton III pair of forces
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Free body force diagrams 2Free body force diagrams 2Consider a man standing on a table on the Earth:
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Newton I vs. Newton IIINewton I vs. Newton IIIThese two forces are acting on the same body, they’re two different types of force and the man is in equilibrium as long as the forces balance – this is a “Newton I pair of forces”.
These two forces are acting on different bodies, they’re both the same type and they are always equal and opposite – this is a “Newton III pair of forces”.
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SummarySummaryNewton I Newton III
A law about the forces on _ _____ ____
A law about the forces on ____ _______ _____
Concerns any _____ of forces Always concerns ____ forces only
The forces can be ______ types
Both forces are ___ ______ type
If there are two forces and the body is in equilibrium the forces are _____ and ________
The two forces are ALWAYS ______ and ________
Newton I only applies when the body is in ________
Newton III ______ applies
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Random recap questionsRandom recap questions1) Nick runs the last 100m of a 200m race over 15s. If he
was accelerating at a rate of 1ms-2 during those 15s how fast was he running when he passed the 100m mark?
2) Ben throws a ball from the 1st floor at Ryan below. If the ball travels for 1.5s before hitting Ryan how far above Ryan is Ben? If Ryan is 20m away from the building how fast did Ben throw it?
3) Dan is swinging a conker around on a piece of string. Draw a free body force diagram for each object (you may find it easier to draw both on the same diagram).
4) For each of the forces in the previous two diagrams identify the Newton III pair and describe what the force is, what is acts on and its direction.
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VectorsVectors
100ms-1
5ms-1
10km
10km
14.1km
100.1ms-1
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Resolving VectorsResolving VectorsConsider a diagonal push:
F
θ
This force is given by:
F1 = F sin θ
This force is given by:
F2 = F cos θ
F1
F2
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Resolving Vectors – example questionsResolving Vectors – example questionsCalculate the horizontal and vertical components of the following:
1)
3) 4)
2)
50O35O
80O
10N 20N
10N8N
Work out the size and direction of the resultant force:
50O 45O
15N20N
30O
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Free body force diagrams 3Free body force diagrams 3Consider a man on a sloping table:
Reaction (a contact force) is perpendicular to the surface. Friction (a tangential contact force) goes up the slope. Let’s combine the forces…
Resultant force is zero, so no acceleration
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Free body force diagramsFree body force diagrams1) 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.
4) Draw a free body force diagram for a 2-wheel drive (engine at the front) car driving up the M1 as well.
3) Draw a free body force diagram for a 4-wheel drive car driving up the M1.
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Stopping a car…Stopping a car…
Braking distance
Too much alcoholThinking
distance(reaction time)
Tiredness
Too many drugs
Wet roads
Driving too fast
Tyres/brakes worn out
Icy roads
Poor visibility
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Weight vs. MassWeight vs. MassEarth’s Gravitational Field Strength is 10N/kg. In other words, a 1kg mass is pulled downwards by a force of 10N.
W
gM
Weight = Mass x Gravitational Field Strength
(in N) (in kg) (in N/kg)
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?
3) Dave weighs 700N. What is his mass?
4) On the moon the gravitational field strength is 1.6N/kg. What will Dave weigh if he stands on the moon?
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Work doneWork doneWhen 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 movedin J in N in m W
DF
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Example questionsExample questions1. Bori pushes a book 5m along the table with a force of 5N.
He gets tired and decides to call it a day. How much work did he do?
2. Alicia lifts a laptop 2m into the air with a force of 10N. How much work does she do?
3. Martin does 200J of work by pushing a wheelbarrow with a force of 50N. How far did he push it?
4. Chris cuddles his cat and lifts it 1.5m in the air. If he did 75J of work how much force did he use?
5. Carl drives his car 1000m. If the engine was producing a driving force of 2000N how much work did the car do?
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Elastic Potential EnergyElastic Potential Energy
Elastic potential energy is the energy stored in a system when work is done to change its shape, e.g:
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Kinetic energyKinetic energyAny 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 squaredin J in kg in m/s
KE = ½ mv2
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Example questionsExample questions1) Nicole 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) Shanie rides her bike at a speed of 10m/s. If the combined mass of Shanie and her bike is 80kg what is her kinetic energy?
3) Dan is running and has a kinetic energy of 750J. If his mass is 60kg how fast is he running?
4) George 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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Random questions…Random questions…1) Sophie tries to run 100m in 12 seconds and succeeds. How fast did she
run?
2) Tommy accelerates at a rate of 2m/s2 for 3 seconds. If he started at 10m/s what was his final speed?
3) Charlie decides to lift his book up into the air. His book has a mass of 100g and he lifts it 50cm. Calculate the work done.
4) Lewis accelerates from 0 to 10m/s in 5 seconds. If his mass is 70kg how much force did his legs apply?
5) Rachel rides 1km at a speed of 20m/s. How long did the journey take?
6) Claire thinks it’s funny to push James with a force of 120N. If James has a mass of 60kg calculate his acceleration.
7) Lauren slams on the brakes on her bike and her brakes do 20,000J of work. If the combined mass is 100kg what speed was she travelling at?
8) Tom has a mass of 75kg. If he accelerates from 10 to 20m/s in 2s how much force did he apply?
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Random questions…Random questions…9) Georgina amuses herself by throwing things at Sarah. If she throws a
ball with a speed of 20m/s and the distance between her and Sarah is 5m how long will it take to reach her?
10) Mr Richards throws calculators around the room with a force of 20N. If each calculator has a mass of 200g calculate the acceleration.
11) Sam has a mass of 70kg. What is his weight on Earth, where the gravitational field strength is 10N/kg?
12) Zak does some work by pushing a box around with a force of 1N. He does 5J of work and decides to call it a day. How far did he push it?
13) On the moon Matt might weigh 112N. If the gravitational field strength on the moon is 1.6N/kg what is his mass? What will he weigh on Earth?
14) Dan likes bird watching. He sees a bird fly 100m in 20s. How fast was it flying?
15) How much kinetic energy would Richard have if he travelled at a speed of 5m/s and has a mass of 70kg?
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MomentumMomentumAny object that has both mass and velocity has MOMENTUM. Momentum (symbol “p”) is simply given by the formula:
Momentum = Mass x Velocity (in kgms-1) (in kg) (in ms-1)
P
VM
What is the momentum of the following?
1) A 1kg football travelling at 10ms-1
2) A 1000kg Ford Capri travelling at 30ms-1
3) A 20g pen being thrown across the room at 5ms-1
4) A 70kg bungi-jumper falling at 40ms-1
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Conservation of MomentumConservation of MomentumIn any collision or explosion momentum is conserved (provided that there are no external forces have an effect). Example question:
Two cars are racing around the M25. Car A collides with the back of car B and the cars stick together. What speed do they move at after the collision?
Mass = 1000kg Mass = 800kg
Speed = 50ms-1 Speed = 20ms-1
Momentum before = momentum after…
…so 1000 x 50 + 800 x 20 = 1800 x V…
…V = 36.7ms-1
Mass = 1800kg Speed = ??ms-1
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Momentum in different directionsMomentum in different directionsWhat happens if the bodies are moving in opposite directions?
Speed = 50ms-1
Mass = 1000kg
Speed = 20ms-1
Mass = 800kg
Momentum is a VECTOR quantity, so the momentum of the second car is negative…
Total momentum = 1000 x 50 – 800 x 20 = 34000 kgms-1
Speed after collision = 34000 kgms-1 / 1800 = 18.9ms-1
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Another exampleAnother exampleConsider the nuclear decay of Americium-241:
Am24195
α42
If the new neptunium atom moves away at a speed of 5x105 ms-1 what was the speed
of the alpha particle?
Np23793
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More questions…More questions…1) A white snooker ball moving at 5m/s strikes a red ball and pots it.
Both balls have a mass of 1kg. If the white ball continued in the same direction at 2m/s what was the velocity of the red ball?
2) A car of mass 1000kg heading up the M1 at 50m/s collides with a stationary truck of mass 8000kg and sticks to it. What velocity does the wreckage move forward at?
3) A defender running away from a goalkeeper at 5m/s is hit in the back of his head by the goal kick. The ball stops dead and the player’s speed increases to 5.5m/s. If the ball had a mass of 500g and the player had a mass of 70kg how fast was the ball moving?
4) A gun has a recoil speed of 2m/s when firing. If the gun has a mass of 2kg and the bullet has a mass of 10g what speed does the bullet come out at?
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Force and momentumForce and momentumNewton’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
TF
Force = Change in momentumTime(in N)
(in kgm/s)
(in s)
For example, David Beckham 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
Also called “impulse”
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Example questionsExample questions1) Ben 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.
2) Nick thinks it’s funny to hit tennis balls at Tom. He 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.
3) Dan 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.
4) Simon strikes a 200g golf ball away at 50m/s. If he applied a force of 50N calculate how long his club was in contact with the ball for.
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Safety featuresSafety featuresLet’s use Newton’s Second Law to explain how airbags work:
∆mv
TF
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
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Car Safety FeaturesCar Safety Features
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Energy loss in collisionsEnergy loss in collisions
We’ve also said that in a collision momentum is conserved (unless an external force acts). The same cannot usually be said for kinetic energy…
For example, consider the following collision. How much kinetic energy is lost?
Kinetic energy = ½ x mass x velocity squared
in J in kg in m/s
In the “Forces” module we looked at how to calculate an object’s kinetic energy:
Mass = 1000kg Mass = 800kg
Speed = 50m/s Speed = 20m/s
Before
Mass = 1000kg Mass = 800kgSpeed = 20m/s Speed = 30m/s
After
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Energy loss in collisionsEnergy loss in collisionsConsider a head-on collision where the cars stick together. How much kinetic energy is lost in this example? Where does all the energy go?
In this example more kinetic energy was lost. We say it was a “less elastic collision”. An “elastic collision” is one where the kinetic energy is conserved.
Speed = 10m/s
Before
After
Speed = 50m/s Speed = 30m/s
m=800Kg m=3000Kg
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Conservation of EnergyConservation of EnergyConsider a bouncing ball:
Gravitational Potential Energy
Time
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Conservation of EnergyConservation of EnergyConsider a bouncing ball:
Kinetic Energy
Time
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Conservation of EnergyConservation of EnergyNow put these graphs together:
Kinetic Energy
Time
Total energy of the ball
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Finding the Centre of MassFinding the Centre of Mass
Q. How would you find the centre of mass of this object?
Definition: The Centre of mass of an object is the point at which all the mass of the object is centred.
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StabilityStability1. Centre of mass is within the wheelbase – no problem!
2. Centre of mass is directly above the edge of the wheelbase –car is on the point of toppling
3. Car falls over
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Turning MomentsTurning MomentsA moment is a “turning force”, e.g. trying to open or close a door or using a spanner. The size of the moment is given by:
Moment (in Nm) = force (in N) x PERPENDICULAR distance from pivot (in m)
Calculate the following turning moments:
100 Newtons
5 metres
200 Newtons
2 metres
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Turning MomentsTurning Moments
100 Newtons200 Newtons
2 metres 2 metres
Total ANTI-CLOCKWISE turning moment = 200x2 =
400Nm
Total CLOCKWISE turning moment = 100x2 = 200Nm
The anti-clockwise moment is bigger so the seesaw will turn anti-clockwise
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An example questionAn example question
5 metres
2000 Newtons 800 Newtons
? metres
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Calculate the missing quantityCalculate the missing quantityThe following are all balanced:
2N
4m 2m
??N
5N 3N
2m ??m
4m??m
2m
5N 5N 15N
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Balanced or unbalanced?Balanced or unbalanced?
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1m
A hard question…A hard question…Consider a man walking along a plank of wood on a cliff.
3m
Man’s weight = 800N
Plank’s weight = 200N
How far can he walk over the cliff before the plank tips over?Aaarrgghh
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A recap questionA recap questionCalculate the mass of man in the example given below:
30kg
1.2m0.4m
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Centripetal forceCentripetal forceConsider a ball of Pleistocene attached to some string:
The ball is kept in its path by the tension in the string – an example of a CENTRIPETAL FORCE. This force also produces the change in velocity due to the direction constantly changing.
This force is INCREASED if you increase the mass of the object, its speed or decrease the radius of the circle.
Other examples of centripetal
forces:Orbits Electrons
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Centripetal force and The EarthCentripetal force and The Earth
Notice that the orbit path is slightly elliptical
Gravity (and the fact that the Earth is moving at high speeds) keeps the Earth in orbit.
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Different OrbitsDifferent Orbits
Mercury
MarsJupiter
Saturn
NeptuneUranus
Pluto
VenusEarth
Mercury = 88 days
Mars = 687 days
Pluto = 90,500 days
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GravityGravityGravity is an attractive force that affects anything with mass:
Note that this force goes both ways – the Earth
is attracted to us.
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Gravity on different Gravity on different planets:planets:
Jupiter – gravitational field strength = 25N/Kg
Earth – gravitational field strength = 9.8N/Kg
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More information on gravityMore information on gravity
F
F/9
F/4
If you double the distance the gravitational
force divides by 4…
If you triple the distance the force
divides by 9…
The amount of gravity attracting an object decreases the further out the object is…
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DensityDensity
Density =Mass
Volumeρ =
m
V
1) What is the density of a piece of wood of volume 2m3 and mass 1200kg?
2) Air only has a density of 1.3kg/m3. What is the mass of 0.2m3 of air?
3) Carbon dioxide is more dense and the same volume would have a mass of 0.38kg. What is its density?
4) The mercury in a thermometer has a volume of 5x10-5m3. If the density of the mercury is 13600kg/m3 what mass of mercury is in the thermometer?
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FloatingFloatingWhether or not an object will float depends on its DENSITY. For example:
The metal block will ____ because it is ______
dense than water
The wooden block will ____ because it is
______ dense than water
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Pressure – some basic ideasPressure – some basic ideasDescribe and draw experiments for each of the following
ideas:
1) Pressure increases with depth2) Pressure is the same in all directions at a certain depth
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PressurePressure
Explain how the following work:
1) A sharp knife is easier to use then a blunt knife
2) A drawing pin
3) A woman with stilettos on might damage a floor more than an elephant would
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PressurePressurePressure depends on two things:
1) How much force is applied, and
2) How big (or small) the area on which this force is applied is.
Pressure can be calculated using the equation:
Pressure (in N/m2) = Force (in N)
Area (in m2)
F
APOR in cm2 and N/cm2
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Some pressure questionsSome pressure questions
1) Calculate the pressure exerted by a 1000N elephant when standing on the floor if his feet have a total area of 1m2.
2) A brick is rested on a surface. The brick has an area of 20cm2. Its weight is 10N. Calculate the pressure.
3) A woman exerts a pressure of 100N/cm2 when standing on the floor. If her weight is 500N what is the area of the floor she is standing on?
4) (Hard!) The pressure due to the atmosphere is 100,000N/m2. If 10 Newtons are equivalent to 1kg how much mass is pressing down on every square centimetre of our body?
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Some examples of pressureSome examples of pressure
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Gas PressureGas Pressure
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Hydraulic systemsHydraulic systems
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LeversLevers
Load
Effort
Pivot
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3 types of lever3 types of lever
Load is on other side of pivot (e.g.
seesaw)
Load is “outside” the effort, (e.g.
biceps)
Load is “inside” the effort (e.g.
wheelbarrow)
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Circular MotionCircular Motion
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Circular MotionCircular Motion
1) Is this car travelling at constant speed?
2) Is this car travelling at constant velocity?
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Centripetal AccelerationCentripetal AccelerationIf the velocity is changing then it must be accelerating...
Va
Vb
ΔV
This change in velocity is towards the centre of the circle so the acceleration and is towards the centre if the circle –
“Centripetal Acceleration”
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RadiansRadiansTo further understand circular motion we need to use a different system for measuring angles:
Old method New method
rs
Angle = 300 Angle = s/r rad
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RadiansRadiansCalculate the following angles in radians:
1)
3) 4)
2)
2cm
5mm 8m
6cm
1.5cm15cm
2.05cm 50.24m
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Centripetal AccelerationCentripetal AccelerationConsider a circle:
r
θ
v1
v2
θv1
v2
Δv
If we assume θ is very small then v1 = v2 = v
Therefore θ = Δv/v
v
v
Also θ = vΔt/r
Therefore Δv/v = vΔt/r
Δv/Δt = v2/r
a = v2/r
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More Exciting EquationsMore Exciting EquationsFrom the last slide a = v2/r but F=ma so centripetal force F = mv2/r
The “angular speed” is the “angular distance” divided by time, or ω = θ/t
The total time period T for one revolution must therefore be the time taken to complete 2π revolutions, or ω = 2π/T
“Frequency” is how often something happens every second, so T = 1/f. Therefore ω = 2πf
For a whole circle, v = 2πr/T. However, T = 2π/ω. Therefore v = rω
Acceleration a = v2/r, therefore a = rω2
Finally, this must mean that F = mrω2
F = mv2/r
ω = θ/t
ω = 2π/T
ω = 2πf
v = rω
a = rω2
F = mrω2
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Example questionsExample questions1) A disc spins twice per second. Calculate its angular speed.
2) Estimate the angular speed of the Earth.
3) Scoon spins a conker around his head using a 50cm long string. The conker has a mass of 0.1kg and he spins it with a velocity of 2ms-1. Calculate the centripetal force.
4) Calculate the velocity of a satellite moving with an angular speed of 7x10-5 rads-1 and at an altitude of 700km above the Earth (radius 6370km).
5) Tom drives his car in circles. If he drives with an angular speed of 1 rads-1 how many times will he make a complete turn in 10 seconds?
6) If the combined mass of Tom and his car is 1000kg calculate the centripetal force if his turning circle has a radius of 3m.
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Simple Harmonic MotionSimple Harmonic Motion
Definition: simple harmonic motion is when acceleration is proportional to displacement and is always directed towards equilibrium.
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Simple Harmonic MotionSimple Harmonic MotionConsider a pendulum bob:
Let’s draw a graph of displacement against time:
Displacement
Time
Equilibrium position “Sinusoidal”
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SHM GraphsSHM Graphs
Time
Displacement
Velocity
Acceleration
Time
Time
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The Maths of SHMThe Maths of SHM
Time
Displacement
As we’ve already seen, SHM graphs are “sinusoidal” in shape:
Therefore we can describe the motion mathematically as:
x = x0cosωt
v = -x0ωsinωt
a = -x0ω2cosωt
a = -ω2x
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The Maths of SHMThe Maths of SHM
Definition: simple harmonic motion is when acceleration is proportional to displacement and is always directed towards equilibrium.
Recall our definition of SHM:
a = -ω2x
This agrees entirely with the maths: a
x
Important – remember ω = 2π/T
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SHM questionsSHM questionsa
x
5
2
1) Calculate the gradient of this graph
2) Use it to work out the value of ω
3) Use this to work out the time period for the oscillations
4) Howard sets up a pendulum and lets it swing 10 times. He records a time of 20 seconds for the 10 oscillations. Calculate the period and the angular speed ω.
5) The maximum displacement of the pendulum is 3cm. Sketch a graph of a against x and indicate the maximum acceleration.
a
x
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SHM Maximum ValuesSHM Maximum Valuesx = x0cosωt
v = -x0ωsinωt
a = -x0ω2cosωt
Consider our three SHM equations:
Clearly, the maximum value that sinωt can take is 1, therefore:
amax = -ω2x0
xmax = x0 (obviously)
vmax = -x0ω (or max speed = ωx0)
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SHM periods: Two examplesSHM periods: Two examples
For a pendulum the only thing that affects the period is the length of the string:
T = 2π √ lg
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SHM periods: Two examplesSHM periods: Two examplesFor a spring there are two things that affect the period – the mass and the spring constant:
T = 2π √ mk
Where k is defined as “the force needed to extend the spring by a given number of metres” (units Nm-1):
F = -kΔx
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More questionsMore questions1) Define simple harmonic motion.
2) A pendulum in a grandfather clock has a period of 1 second. How long is the pendulum?
3) Luke sets up a 200g mass on a spring and extends it beyond its equilibrium. He then releases it and enjoys watching it bounce up and down. If the period is 10s what is the spring constant?
4) Nick is envious of this and sets up another system with a spring constant of 0.1Nm-1. If the spring oscillates every 8 seconds how much mass did he use?
5) Simon sets up a pendulum and records the period as being 3 seconds. He then lengthens the pendulum by 1m and does the experiment again. What is the new period?
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SHM recap questionsSHM recap questions1) Define SHM and state “the golden SHM equation”
2) A body is performing SHM and is temporarily at rest at time t=0. Sketch graphs of its displacement, velocity and acceleration.
a
x
10
5
3) A body is performing SHM as shown on this graph. Calculate its angular speed and its time period T.
4) What is this body’s maximum speed?
5) A 1kg mass is attached to a spring of spring constant 10Nm-1. The mass is pulled down by 5cm and released. It performs SHM. Calculate the time period of this motion.
6) Describe the energy changes in this system as it bounces up and down.
7) Calculate the length of a pendulum if it oscillates with a period of 5s.
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SHM: Energy changeSHM: Energy change
Equilibrium position Energy
Time
GPE
K.E.