forces - revision.paigntononline.com · introduction to forces 21/11/2017 a force is a “push”...
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Forces AQA Physics topic 5
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5.1 – Forces and their Interactions
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Vector vs. scalar Scalar quantities have size (“magnitude”) only and no direction.
Vector quantities have both size and direction.
Scalar or vector???
Scalar Vector
1. Mass 2. Distance
4. Speed
5. Velocity
6. Energy
8. Power
7. Time
9. Force
3. Acceleration
21/11/2017
Vectors
100ms-1
5ms-1
10km
10km
14.1km
100.1ms-1
Here’s a man walking 10km north and then 10km east. Notice that we can replace his two movements with a “displacement vector”. Note the length and direction of this vector:
The same can be applied to velocity vectors:
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Introduction to Forces A force is a “push” or a “pull”. What forces do these pictures represent?
Which of these forces would you describe as “contact forces” and which ones are “non-
contact forces”?
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Contact or non-contact forces?
Contact Non-contact
1. Friction
2. Air resistance
3. Gravitational forces
4. Tension
5. Electrostatic forces
6. Reaction
7. Magnetic forces
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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
g M
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) Charles weighs 700N on the Earth. What is his mass?
4) On the moon the gravitational field strength is 1.6N/kg. What will Charles weigh if he stands on the moon?
20N
1N
70kg
112N
You need to learn this equation!!
More information about Weight 21/11/2017
1) How much does 1kg weigh on the Earth? 2) How much does 2kg weigh? 3) How much does 3kg weigh? 4) What are you noticing about your answers?
Whatever mass goes up by, weight goes up by the same ratio. For example, if you double mass you double weight. This is called “proportionality”:
Centre of Mass 21/11/2017
The centre of mass is defined as “the point at which an object’s mass is centred on”. Where is the centre of mass for these objects?
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Resultant Force A “resultant force” is a single force that can replace all of the other forces acting on something. Calculate and draw the resultant force of the following:
500N 100N 700N 600N
700N 700N
200N
800N 800N
100N
50N
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Higher Tier – Resultant Force 1. Draw the resultant force for these people and describe where the person will go:
500N 100N 700N 600N
200N
50N
700N 800N
2. If you were going to describe these resultant forces as the resultant of two other forces, what forces would you draw?
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Higher Tier – Drawing Resultant Force Here are two forces acting on a person. How can we work out the resultant force and its direction?
500N
200N We can represent these forces
as a “vector diagram”
Higher Tier - Vector Diagrams 21/11/2017
500N
200N
You can now use a ruler and protractor to measure the size and angle of this resultant force
Higher Tier – Example Questions 21/11/2017
Use squared or graph paper to find the resultant vector for these forces:
8N
300N
4N
800N
Magnitude = 8.9N Angle to vertical = 63O
Magnitude = 854N Angle to (upwards) vertical = 159O
21/11/2017 21/11/2017 5.2 – Work Done and Energy Transfer
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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 in m W
s F You need to learn this equation!!
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Example questions 1. Amy 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. Jodie lifts a laptop 2m into the air with a force of 10N. How much work does she do?
3. Ronnie 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. Julian cuddles his cat and lifts it 1.5m in the air. If he did 75J of work how much force did he use?
5. Travis drives his car 1000m. If the engine was producing a driving force of 2000N how much work did the car do?
25J
20J
4m, heat and
kinetic energy
50N
2MJ
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Recap questions on Weight and work done
1) Matt weighs 600N on the Earth. What is his mass in kg?
2) Chris pushes Gabriel with a force of 20N. If Gabriel moves 2m how much work did Chris do on him?
3) Matt weighs 120N on the moon, where g=1.6N/Kg. What is his mass and what would he weigh on the Earth?
4) Rebecca does 100J of work by pushing her pencil case across the table. If she applied a force of 5N how far did she push it?
5) If you push a book with a force of 1N a distance of 1m, how much work did you do? In other words, what is 1 Joule in terms of Newton metres?
60kg
40J
75kg, 750N
20m
1J = 1Nm
21/11/2017 21/11/2017 5.3 – Forces and Elasticity
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Force and Extension
Consider a mass on a spring:
When a force is applied to this spring it will change
shape and extend.
What happens when a mass is added?
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Investigating Force and Extension Task: Find an expression that relates extension to the amount of weight added.
Force = Spring constant x extension
F = ke
Weight added (N)
Extension (cm)
1
2
3
4
5
6
You need to learn this equation!!
Q. What is the spring constant for
your spring?
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Force-Extension Graph for a spring Force/N
Extension/mm
The “limit of proportionality”.
Force is proportional to extension as long as you don’t
go past the “limit of proportionality”. There is a linear relationship up to this
point.
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Elastic and Inelastic Deformation Force/N
Extension/mm
If you don’t use too much force on the spring you can take the force off and the spring returns to it’s original shape – this is “elastic deformation”.
If you put too much force on the spring it “stretches” – in other words, when you remove the force the spring does not go back to its original length. This is “inelastic deformation”.
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Force and compression
Consider some springs:
The force-compression graphs for objects like these can be determined and plotted.
Example questions:
1) A stiff spring has a spring constant of 10N/m. How much will it compress by if a force of 20N is applied to it?
2) Another spring compresses by 2cm when a force of 50N is applied. What is its spring constant?
2m
2500N/m
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Elastic Potential Energy
Consider a mass on a spring:
When a force is applied to this spring it will change shape and extend. The spring will have “stored elastic potential energy”
What happens when a mass is added?
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Elastic Potential Energy
Elastic potential energy is the energy stored in a system when work is done to change its shape, e.g:
Describe the energy changes when the mass is:
1) At the top of it’s movement
2) In the middle
3) At the bottom
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Elastic Potential Energy Task: Calculate how much stored EPE there is in your springs
Stored EPE = ½ke2
F = ke Weight
added (N) Extension
(m) Stored EPE (J)
1
2
3
4
5
6
21/11/2017 21/11/2017 5.4 – Moments, levers and gears (PHYSICS ONLY)
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Balanced or unbalanced?
21/11/2017 Turning Moments A 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
You need to learn this equation!!
21/11/2017
Turning Moments
100 Newtons 200 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 question
5 metres
2000 Newtons 800 Newtons
? metres
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Calculate the missing quantity The following are all balanced:
2N
4m 2m
??N
5N 3N
2m ??m
4m ??m
2m
5N 5N 15N
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1m
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 question
Calculate the mass of man in the example given below:
30kg
1.2m 0.4m
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How do Levers work?
Load
Effort
Pivot
Consider a simple lever – the nutcracker:
Notice how the distance between the effort and the pivot is much larger than the distance between the load and the pivot. Larger distance = less force needed
How do Gears work? 21/11/2017
Can you explain how gears work using turning moments?
If the smaller wheel is turned, it turns the larger one slower but with more force (i.e. the distance to the pivot has been increased).
21/11/2017 21/11/2017 5.5 – Pressure and Pressure Differences in Fluids (PHYSICS ONLY)
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Pressure in Gases and Liquids Particles in a liquid or a gas (“fluids”) move around randomly, a little like this:
Every time the particles hit the side of the container the particles exert a force at right angles on the container – this is called “pressure”.
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Pressure Pressure 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
A P OR in cm2 and N/cm2
You need to learn this equation!!
21/11/2017
Some pressure questions
1) Calculate the pressure exerted by a 1000N elephant when standing on the floor if his feet have a total area of 2m2.
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?
500 Pa
0.5 N/cm2
5cm2
Around 1kg per
cm2!
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Pressure in Fluids Consider a column of fluid:
h Density ρ
Area A
The pressure at the base of this column would be given by:
Pressure = ρhg
…where ρ = the density of the liquid, h = the height of the container and g = gravitational field strength.
You DON’T need to learn this equation!!
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Example questions
1) Calculate the pressure at the bottom of a 2 litre bottle of water of height 40cm (density of water = 1000kg/m3and g = 10N/kg).
2) What is the pressure at the bottom of a can of coke if the density of coke is 1000kg/m3 and the can is 15cm tall?
3) If the density of seawater is 1027kg/m3 what depth would you need to be at to experience a pressure of 50,000Pa?
4000Pa
1500Pa
4.87m
Pressure vs. Depth 21/11/2017
What does this demonstration tell you?
Pressure increases with ____. This is because the water at the ______ of this container is pushed on by the ______of the water further up, which causes it to be under higher ________.
Words – pressure, bottom, weight, depth
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Why do objects float? Whether 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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Floating in more detail Consider a floating object:
How does the pressure at the bottom of this object compare to the pressure at the top of the object?
This difference in pressure causes the force called “upthrust”.
If weight equals upthrust the object will ____. This is because the object displaces a weight of fluid _____ to its own weight. If weight is greater than upthrust the object will ____. This is because the object is ______to displace a weight of liquid equal to its own weight.
Words – equal, unable, sink, float
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Atmospheric Pressure Recall our earlier explanation of how collisions cause air pressure:
Every time the particles hit the side of the container the particles exert a force at right angles on the container – this is called “pressure”.
Atmospheric Pressure 21/11/2017
Why does atmospheric pressure decrease when you go up a mountain?
Less air molecules = fewer collisions = less pressure!
There are less air molecules up here
… than down here
5.6 - Forces and Motion 21/11/2017
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Distance vs Displacement “Distance” is how far you have gone, “displacement” is how far you are from a point and can be positive or negative:
Start
1 metre -1 metre
Distance =
Displacement =
Distance =
Displacement =
Distance =
Displacement =
Distance =
Displacement =
Which one is a scalar quantity and which one is a vector quantity?
Some questions on Displacement 21/11/2017
1) A man walks 10km north and then 10km west. a) What distance has he covered? b) How would you measure his
displacement? c) What angle would his
displacement be at compared to north?
2) A car drives around in a circle. What
is its displacement after it has completed one circle?
10km
10km
Speed 21/11/2017
Speed is a scalar quantity. What does this mean?
Typical values for speed:
Walking ≈ 1.5m/s
Running ≈ 3m/s
Cycling ≈ 6m/s
What about cars? Aeroplanes?
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Speed of sound The speed of sound in air is around 330m/s. Notice that the speed can vary as well:
0
1000
2000
3000
4000
5000
Air Water Brick IronMaterial
Speed of sound
(in m/s)
Conclusion – the denser the material, the faster sound travels through it.
Q. Would sound travel faster or slower at the top of a mountain?
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Distance, Speed and Time
Speed = distance (in metres)
time (in seconds)
s
t v
1) Oli walks 200 metres in 40 seconds. What is his speed?
2) Ella covers 2km in 1,000 seconds. What is her speed?
3) How long would it take Grace to run 100 metres if she runs at 10m/s?
4) Alex runs to the shop to buy the new Fallout game and travels at 50m/s for 20s. How far does he go?
5) Jasmine drives her car at 85mph (about 40m/s). How long does it take her to drive 20km?
5m/s
2m/s
10s
1000m
500s
You need to learn this equation!!
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Distance, Speed and Time (higher)
Speed = distance (in metres)
time (in seconds)
D
T S
1) Matilda walks 2000m in 50 minutes. What is her speed in m/s?
2) James tries to walk the same distance at a speed of 5m/s. How long does he take?
3) Greg drives at 60mph (about 100km/h) for 3 hours. How far has he gone?
4) The speed of sound in air is 330m/s. Evie shouts at a mountain and hears the echo 3 seconds later. How far away is the mountain? (Careful!)
0.67m/s
400s
300km
495m
21/11/2017 21/11/2017 Speed vs. Velocity
Speed (a SCALAR quantity) is simply how fast you are travelling…
Velocity (a VECTOR quantity) is “speed in a given direction”…
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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Speed vs Velocity
1) Is this car travelling at constant speed?
2) Is this car travelling at constant velocity?
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Distance-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
0.5m/s
40m
1m/s
40-60s
21/11/2017
Distance-Time graphs
Task: Produce a distance-time graph for the following journey:
1) Charlie walks 50m in 20 seconds.
2) She then stands still for 10 seconds
3) She then runs away from Harry and covers 100m in 30 seconds.
4) She then stands still and catches her breath for 20 seconds.
5) She then walks back to the start and covers the total 150m in 50 seconds.
21/11/2017 40
30
20
10
0 20 40 60 80 100
1) Who was travelling the fastest?
2) Who was travelling the slowest (but still moving)?
3) Who didn’t move?
Distance
(metres)
Time/s
G B N
Y
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40
30
20
10
0 20 40 60 80 100
1) What was the velocity in the first 20 seconds?
2) What was the velocity between 20 and 40 seconds?
3) When was this person travelling the fastest?
4) What was the average speed for the first 40 seconds?
Distance
(metres)
Time/s
1.5m/s
0.5m/s
80-100s
1m/s
21/11/2017
Understanding Velocity (Higher tier)
40
30
20
10
0 20 40 60 80 100
Displacement
(metres)
Time/s
1) What’s the average velocity?
2) What’s the velocity at 60s?
0.4m/s
0.5m/s
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Acceleration ∆V
T A
Acceleration = change in speed (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 5 seconds. How fast will it be going?
3) A car accelerates from 0 to 20m/s with an acceleration of 2m/s2. How long did this take?
4) A rocket accelerates from 0m/s to 5,000m/s in 2 seconds. What is its acceleration?
2m/s2
50m/s
10s
2500m/s2
You need to learn this equation!!
21/11/2017 21/11/2017
Acceleration (harder) ∆ V
T A
Acceleration = change in velocity (in m/s)
(in m/s2) time taken (in s)
1) A cyclist slows down from 10 to 0m/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 change 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?
-2m/s2
120m/s
5s
2000m/s2
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Acceleration (harder) ∆ V
T A
Acceleration = change in velocity (in m/s)
(in m/s2) time taken (in s)
1) Mikey accelerates from standstill to 50m/s in 25 seconds. What is his acceleration?
2) Jack accelerates at 5m/s2 for 5 seconds. He started at 10m/s. What is his new speed?
3) Rob 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?
4) Another boy racer brakes at the same deceleration but only for 3 seconds. What speed did he slow down to?
2m/s2
35m/s
5s
20m/s
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Velocity-time graphs
80
60
40
20
0 10 20 30 40 50
Velocity
m/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
Velocity
m/s
T/s
40m/s
2m/s2
3m/s2
1700m
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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 40 to 50s?
4) How far did the object travel altogether?
10 20 30 40 50
Velocity
m/s
T/s
10m/s
4m/s2
6m/s2
1500m
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80
60
40
20
0 10 20 30 40 50
Velocity
m/s
T/s
This velocity-time graph shows Mai’s journey to school. How far away does she live?
2500m
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80
60
40
20
0 10 20 30 40 50
Velocity
m/s
T/s
This velocity-time graph shows Kier’s journey to school. How far away does he live?
2200m
Another equation of motion 21/11/2017
For a constantly-accelerating body, we can also use this equation:
v2 = u2 + 2as You DON’T need to learn this equation!!
1) An object starts from rest and accelerates at a rate of 2m/s2 over a distance of 20m. What is its final velocity?
2) Steve drives up the M1 and covers 30km. He started at 2m/s and constantly accelerated during the whole journey at a rate of 0.001m/s2. What was his final speed?
3) (Harder!) Sarah decelerates from 30 to 10m/s over a distance of 5m. What is her acceleration?
80m/s
64m/s
-80m/s2
21/11/2017
Acceleration due to Gravity
If I throw this ball upwards with a speed of 40m/s why does it come back down again?
The ball is acted on by a force called gravity, which accelerates the ball downwards at a rate of 9.8m/s2 near the Earth’s surface.
Extension question – how far up would the ball go?
1) Take u = 40m/s and v = 0m/s (at the top of the throw)
2) Take a = 9.8m/s2
3) Therefore s = 81.6m
21/11/2017
Terminal Velocity
Some questions to consider:
Consider a ball falling through a liquid:
1) What forces are acting on the ball?
2) How do those forces change when the ball gets faster?
3) Will the ball keep getting faster? Explain your answer in terms of forces
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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
21/11/2017 21/11/2017 Velocity-time graph for terminal velocity (Physics only)
Velocity
Time
Speed increases…
Terminal velocity reached…
Parachute opens – diver slows down
New, lower terminal velocity reached
Diver hits the ground
21/11/2017 21/11/2017
Balanced 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 forces
What would happen if we took the road away?
Weight
Reaction
The camel is acted on by an “unbalanced force”, which causes it to accelerate. This is called Newton’s 1st law of motion.
21/11/2017
Newton 1642-1727
Newton’s 1st Law of Motion Basically, 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…
Without an unbalanced force, Newton would carry on doing what he was doing. This is called “Inertia”.
21/11/2017 21/11/2017 Balanced and unbalanced forces Q. What will these cars do and why?
21/11/2017 21/11/2017
Balanced and unbalanced forces
1) This animal is either ________ or moving with _______ _____…
4) This animal is also either _______ or moving with ________ ______..
2) This animal is getting ________…
3) This animal is getting _______….
Words - Stationary, faster, slower or constant speed?
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Summary of Newton’s 1st law
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…
Complete these sentences…
…continue to stay stationary
…accelerate in the direction of the resultant force
…continue to move at the same speed and the same direction
…accelerate in the direction of the resultant force
21/11/2017
Newton’s 2nd 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. It is inversely
proportional to the mass of the object.
In other words…
force = mass x acceleration F
A M
You need to learn this equation!!
21/11/2017 21/11/2017
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
A M
2m/s2
2000kg
2500N
0.5m/s2
Inertial Mass (higher only) 21/11/2017
Newton 1642-1727
Inertial mass is a measure of how difficult it is to change the velocity of an object:
Inertial mass = force / acceleration
Determine the initial mass of the following: 1) A car that needs a force of 2000N to
accelerate it by 1m/s2.
2) A bus that accelerates at a rate of 0.5m/s2 when 5 people push it, each with a force of 750N.
2000kg
7500kg
Approximate Values 21/11/2017
Which approximate values of speed, acceleration and force would you put with these moving objects?
Speed = 30m/s
Speed = 1.5m/s
Speed = 300m/s
Acceleration = 1.5m/s
Acceleration = 2m/s
Acceleration = 3m/s
Force = 70N
Force = 3000N
Force = 600,000N
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Testing Newton’s 2nd Law
For 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.
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Newton’s 3rd 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 3rd Law of Motion
What will happen if I push this satellite away from me?
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Stopping a car…
What two things must the driver of the car do in order to stop in time?
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Stopping a car…
Braking distance
Thinking distance
(reaction time)
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Stopping a car…
Braking distance
Too much alcohol Thinking
distance
(reaction time)
Tiredness
Too many drugs
Wet roads
Driving too fast
Tyres/brakes worn out
Icy roads
Poor visibility
Total Stopping Distance = Thinking Distance + Braking Distance
Representing Stopping Distance Graphically (Physics only)
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Measuring Reaction Times
For the experiment:
1) Describe your method (i.e. how will you measure reaction time?)
2) Describe what you are varying (your “independent variable”)
3) Describe what equipment you used to get the results and how you analysed them.
Typical reaction times are around 0.4 to 0.9s. How did you compare?
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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.
Greater speed = greater force needed to stop in a given distance = hotter brake pads!
21/11/2017 21/11/2017 Estimating Forces and Deceleration (higher only)
Estimate rough values for the forces involved in decelerating these objects:
A skydiver when he opens his parachute
A formula 1 car about to take a sharp turn
A car slowing down at traffic lights
Taking u = 50m/s, v = 10m/s, t = 0.1s and m = 70kg we get…
Taking u = 20m/s, v = 0m/s, t = 2 s and m = 800kg we get…
Taking u = 100m/s, v = 20m/s, t = 2 s and m = 1500kg we get… 28000N 8000N 60000N
Q. What happens to the human body when these forces get TOO big?
5.7 – Momentum (higher only) 21/11/2017
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Momentum Any object that has both mass and velocity has MOMENTUM. Momentum (symbol “p”) is simply given by the formula:
Momentum = Mass x Velocity (in kgm/s) (in kg) (in m/s)
P
V M
What is the momentum of the following?
1) A 1kg football travelling at 10m/s
2) A 1000kg car travelling at 30m/s
3) A 0.02kg pen 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
You need to learn this equation!!
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Conservation of Momentum In 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 = 50m/s Speed = 20m/s
Momentum before = momentum after…
…so 1000 x 50 + 800 x 20 = 1800 x V…
…V = 36.7m/s
Mass = 1800kg Speed = ??m/s
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Momentum in different directions
What happens if the bodies are moving in opposite directions?
Speed = 50m/s
Mass = 1000kg
Speed = 20m/s
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 kgm/s
Speed after collision = 34000 kgm/s / 1800 = 18.9m/s
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Another example
Consider the nuclear decay of Americium-241:
Am 241 95
α 4 2
If the new neptunium atom moves away at a speed of 5x105 m/s what was the speed
of the alpha particle?
Np 237 93
2.96x107 m/s
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More questions…
1. 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?
2. 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?
3. 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?
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?
5.6m/s
70m/s
400m/s
3m/s
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Recap question on momentum
1. Bradley and Jack are racing against each other over 400m at Sports Day. Brad is running at 8m/s and catches up with Jack who is running at 6m/s. After the collision Brad stops and Jack moves slightly faster. If Brad’s mass is 60kg and Jack’s is 70kg calculate how fast Jack moves after the collision.
2. Coryn is driving her 5kg toy car around. It is travelling at 10m/s when it hits the back of Shannon’s (stationary) leg and sticks to it. Assuming Shannon’s leg can move freely and has a mass of 10kg calculate how fast it will move after the collision.
12.9m/s
3.3m/s
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Change in Momentum and Force
Instead of F=ma Newton actually said that the force acting on an object is that object’s rate of change of momentum. In other words…
mv
T F
Force = Change in momentum
Time (in N)
(in kgm/s)
(in s)
For example, Rob Stocker scores from 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
You DON’T need to learn this equation!!
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Example questions 1) Jack 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) Chad thinks it’s funny to hit tennis balls at Illy. 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) Oli 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) Paddy 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.
16kgm/s,
80m/s
4.5kgm/s,
18m/s
0.2s
40N