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Forces
AQA 2016 Physics topic 5
W Richards
Education Using
PowerPoint
5.1 – Forces and their Interactions
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Vector vs. scalar
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Scalar quantities have size (“magnitude”) only and no direction.
Vector quantities have both size and direction.
Scalar or vector???
Scalar
8. Power
2. Distance
1. Mass
6. Energy
7. Time
3. Acceleration
4. Speed
9. Force
5. Velocity
Vector
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Vectors
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:
10km
The same can be applied to
velocity vectors:
10km
100ms-1
14.1km
5ms-1
100.1ms-1
Introduction to Forces
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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 “noncontact 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
25/07/2024
Weight vs. Mass
Earth’s Gravitational Field Strength is 10N/kg. In other
words, a 1kg mass is pulled downwards by a force of 10N.
W
Weight = Mass x Gravitational Field Strength
(in N)
(in kg)
(in N/kg)
You need to learn this equation!!
M
g
1) What is the weight on Earth of a book with mass 2kg?
20N
2) What is the weight on Earth of an apple with mass 100g?
1N
3) Charles weighs 700N on the Earth. What is his mass?
70kg
4) On the moon the gravitational field strength is 1.6N/kg.
What will Charles weigh if he stands on the moon?
112N
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More information about Weight
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
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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?
Resultant Force
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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
50N
700N
700N
200N
800N
800N
100N
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Higher Tier – Resultant Force
1. Draw the resultant force for these people and describe
where the person will go:
50N
500N
100N
700N
600N
200N
2. If you were going to describe these resultant forces as the
resultant of two other forces, what forces would you draw?
700N
800N
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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?
We can represent these forces
as a “vector diagram”
200N
500N
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Higher Tier - Vector Diagrams
200N
500N
You can now use a ruler and protractor to measure
the size and angle of this resultant force
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Higher Tier – Example Questions
Use squared or graph paper to find the resultant vector for
these forces:
4N
300N
8N
800N
Magnitude = 8.9N
Angle to vertical = 63O
Magnitude = 854N
Angle to (upwards)
vertical = 159O
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
You need to learn this equation!!
W
in m
F
s
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?
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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?
60kg
2) Chris pushes Gabriel with a force of 20N. If Gabriel
moves 2m how much work did Chris do on him?
40J
3) Matt weighs 120N on the moon, where g=1.6N/Kg. What
is his mass and what would he weigh on the Earth?
75kg,
750N
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?
20m
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?
1J =
1Nm
5.3 – Forces and Elasticity
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Force and Extension
Consider a mass on a spring:
What happens when a mass is
added?
When a force is applied to
this spring it will change
shape and extend.
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Investigating Force and Extension
Task: Find an expression that
relates extension to the
amount of weight added.
Weight added
(N)
Extension (cm)
1
2
3
4
5
6
Force = Spring constant x extension
F = ke
You need to learn this equation!!
Q. What is the
spring constant for
your spring?
Questions on Hooke’s Law
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Force = Spring constant x extension
F = ke
1) A spring has a spring constant of 20N/m. If it
extends by 3m how much force was applied?
2) The force on this spring is now doubled. What
is its new extension?
3) Another spring of spring constant 2N/cm is
extended by 5cm. How much force was
applied?
4) Another spring has 10N applied to it and it
extends by 50cm. What is its spring constant
in N/m?
5) How much will a spring extend if it has a spring
constant of 10N/m and 4N is applied to it?
60N
6m
10N
20N/m
0.4m
Force-Extension Graph for a spring
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Force/N
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.
Extension/mm
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Elastic and Inelastic Deformation
Force/N
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”.
Extension/mm
Force and compression
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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
Elastic Potential Energy
Consider a mass on a spring:
What happens when a mass is
added?
When a force is applied to
this spring it will change
shape and extend. The
spring will have “stored
elastic potential energy”
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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)
1
2
3
4
5
6
Extension
(m)
Stored
EPE (J)
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5.4 – Moments, levers and gears
(PHYSICS ONLY)
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Balanced or unbalanced?
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Turning Moments
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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)
You need to learn this equation!!
Calculate the following turning moments:
5 metres
100 Newtons
2 metres
200 Newtons
Turning Moments
2 metres
200 Newtons
Total ANTI-CLOCKWISE
turning moment = 200x2 =
400Nm
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2 metres
100 Newtons
Total CLOCKWISE turning
moment = 100x2 = 200Nm
The anti-clockwise moment is bigger so the seesaw will
turn anti-clockwise
An example question
5 metres
2000 Newtons
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? metres
800 Newtons
Calculate the missing quantity
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The following are all balanced:
??N
2N
4m
2m
5N
3N
2m
5N
??m
5N
4m
15N
??m
2m
A hard question…
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Consider a man walking along a plank of wood on a cliff.
How far can he walk over the cliff before the plank tips over?
Aaarrgghh
Man’s weight =
800N
1m
3m
Plank’s weight =
200N
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A recap question
Calculate the mass of man in the example given below:
30kg
0.4m
1.2m
How do Levers work?
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Consider a simple lever – the nutcracker:
Pivot
Effort
Load
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?
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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).
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)
F
Area (in m2)
OR in cm2 and N/cm2
You need to learn this equation!!
P
A
Some pressure questions
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1) Calculate the pressure exerted by a 1000N
elephant when standing on the floor if his feet
have a total area of 2m2.
500 Pa
2) A brick is rested on a surface. The brick has
an area of 20cm2. Its weight is 10N. Calculate
the pressure.
0.5 N/cm2
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?
5cm2
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?
Around
1kg per
cm2!
Pressure in Fluids
Consider a column of fluid:
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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Area A
Density ρ
h
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?
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4000Pa
1500Pa
4.87m
Pressure vs. Depth
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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
Why do objects float?
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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
Floating in more detail
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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
Atmospheric Pressure
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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
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Why does atmospheric pressure decrease when you go up a
mountain?
There are less air
molecules up here
… than down here
Less air molecules = fewer collisions =
less pressure!
5.6 - Forces and Motion
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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
= =
Which one is a scalar quantity and which one is a vector
quantity?
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Some questions on Displacement
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
Distance, Speed
and Time
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s
Speed = distance (in metres)
time (in seconds)
You need to learn this equation!!
v
t
1) Arthur walks 200 metres in 40 seconds. What is his
speed?
5m/s
2) Josh covers 2km in 1,000 seconds. What is his speed?
2m/s
3) How long would it take Charlotte to run 100 metres if
she runs at 10m/s?
10s
4) Alfie runs to the shop to buy the new FarCrygame and
travels at 50m/s for 20s. How far does he go?
1000m
5) Cody drives her car at 85mph (about 40m/s). How long
does it take her to drive 20km?
500s
Speed
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Speed is a scalar quantity. What does this mean?
What are the typical speeds for when you walk, run and ride a
bike?
Walking ≈ 1.5m/s
Running ≈ 3m/s
Cycling ≈ 6m/s
What about cars? Aeroplanes?
Speed of sound
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The speed of sound in air is around 330m/s. Notice that the
speed can vary as well:
Speed of
sound
(in m/s)
5000
4000
3000
2000
1000
0
Air
Water
Brick
Iron
Material
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 (higher)
D
Speed = distance (in metres)
time (in seconds)
S
T
1) Matilda walks 2000m in 50 minutes. What is her speed in
m/s?
0.67m/s
2) James tries to walk the same distance at a speed of 5m/s.
How long does he take?
400s
3) Greg drives at 60mph (about 100km/h) for 3 hours. How
far has he gone?
300km
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!)
495m
Speed vs. Velocity
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Speed (a SCALAR quantity) is simply how fast you are
travelling…
This car is travelling at a
speed of 20m/s
Velocity (a VECTOR quantity) is “speed in a given direction”…
This car is travelling at a
velocity of 20m/s east
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Speed vs Velocity (HT only)
1) Is this car travelling at constant speed?
2) Is this car travelling at constant velocity?
Distance-time graphs
2) Horizontal line =
40
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4) Diagonal line
downwards =
30
Distance
(metres)
20
10
0
Time/s
20
1) Diagonal line =
40
60
80
100
3) Steeper diagonal line =
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40
Distance
(metres)
30
20
10
0
Time/s
20
40
60
80
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
Distance-Time graphs
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Task: Produce a distance-time graph for the following
journey:
1) Annie 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.
40
Distance
(metres)
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G
30
B
N
20
10
0
Time/s
Y
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?
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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Understanding Velocity (Higher tier)
40
30
Displacement
(metres)
20
10
0
Time/s
20
40
60
80
100
1) What’s the average velocity?
0.4m/s
2) What’s the velocity at 60s?
0.5m/s
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Acceleration
∆V
Acceleration = change in speed (in m/s)
(in m/s2)
time taken (in s)
You need to learn this equation!!
A
T
1) A cyclist accelerates from 0 to 10m/s in 5 seconds.
What is her acceleration?
2m/s2
2) A ball is dropped and accelerates downwards at a rate of
10m/s2 for 5 seconds. How fast will it be going?
50m/s
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?
10s
2500m/s2
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Acceleration (harder)
∆V
Acceleration = change in velocity (in m/s)
(in m/s2)
time taken (in s)
A
T
1) A cyclist slows down from 10 to 0m/s in 5 seconds.
What is her acceleration?
-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
change 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 (harder)
∆V
Acceleration = change in velocity (in m/s)
(in m/s2)
time taken (in s)
A
T
1) Mikey accelerates from standstill to 50m/s in 25 seconds.
What is his acceleration?
2m/s2
2) Jack accelerates at 5m/s2 for 5 seconds. He started at
10m/s. What is his new speed?
35m/s
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?
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
4) Downward line =
60
Velocity
m/s
40
20
0
10
2) Horizontal line =
20
30
40
50
3) Upwards line =
T/s
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80
60
Velocity
m/s
40
20
0
T/s
10
20
30
40
50
1) How fast was the object going after 10 seconds?
40m/s
2) What is the acceleration from 20 to 30 seconds?
2m/s2
3) What was the deceleration from 30 to 50s?
3m/s2
4) How far did the object travel altogether?
1700m
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80
60
Velocity
m/s
40
20
0
T/s
10
20
30
40
50
1) How fast was the object going after 10 seconds?
10m/s
2) What is the acceleration from 20 to 30 seconds?
4m/s2
3) What was the deceleration from 40 to 50s?
6m/s2
4) How far did the object travel altogether?
1500m
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80
60
Velocity
m/s
40
20
0
T/s
10
20
30
40
50
This velocity-time graph shows Mai’s journey to school.
How far away does she live?
2500m
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80
60
Velocity
m/s
40
20
0
T/s
10
20
30
40
50
This velocity-time graph shows Kier’s journey to school.
How far away does he live?
2200m
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Another equation of motion
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) Angus 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!) Alisha decelerates from 30 to 10m/s
over a distance of 5m. What is her
acceleration?
80m/s
64m/s
-80m/s2
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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 10m/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 = 10m/s2
3) Therefore s = 80m
Terminal Velocity
Consider a ball falling through a liquid:
Some questions to consider:
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
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Velocity-time graph for terminal velocity
(Physics only)
Parachute opens –
diver slows down
Velocity
Speed
increases…
Terminal
velocity
reached…
Time
New, lower terminal
velocity reached
Diver hits the ground
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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
25/07/2024
Balanced and unbalanced forces
Reaction
What would happen if we took the
road away?
The camel is acted on by an
“unbalanced force”, which
causes it to accelerate. This is
called Newton’s 1st law of
motion.
Weight
25/07/2024
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.
…and an unbalanced
Newton 1642-1727
backwards force will make
me slow down…
An unbalanced forwards
force will make me
accelerate…
Without an unbalanced force,
Newton would carry on doing what he
was doing. This is called “Inertia”.
Balanced and unbalanced forces
25/07/2024
Q. What will these cars do and why?
25/07/2024
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 of Newton’s 1st law
25/07/2024
Complete these sentences…
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
25/07/2024
Newton’s 2nd Law of Motion
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.
Newton 1642-1727
In other words…
force = mass x acceleration
F
You need to learn this equation!!
M
A
25/07/2024
Force, mass and acceleration
1) A force of 1000N is applied to push
a mass of 500kg. How quickly does
it accelerate?
2) A force of 3000N acts on a car to
make it accelerate by 1.5m/s2. How
heavy is the car?
3) A car accelerates at a rate of
5m/s2. If it weighs 500kg how
much driving force is the engine
applying?
4) A force of 10N is applied by a boy
while lifting a 20kg mass. How
much does it accelerate by?
F
M
A
2m/s2
2000kg
2500N
0.5m/s2
25/07/2024
Inertial Mass (higher only)
Inertial mass is a measure of how difficult it is
to change the velocity of an object:
Inertial mass = force / acceleration
Newton 1642-1727
Determine the inertial mass of the following:
1) A car that needs a force of 2000N to
accelerate it by 1m/s2.
2000kg
2) A bus that accelerates at a rate of 0.5m/s 2
when 5 people push it, each with a force of
750N.
7500kg
25/07/2024
Approximate Values (higher only)
Which approximate values of speed, acceleration and force
would you put with these moving objects?
Speed = 1.5m/s
Acceleration = 1.5m/s
Force = 70N
Speed = 30m/s
Acceleration = 2m/s
Force = 3000N
Speed = 300m/s
Acceleration = 3m/s
Force = 600,000N
25/07/2024
Newton’s 3rd Law of Motion
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.
Newton 1642-1727
25/07/2024
Newton’s 3rd Law of Motion
What will happen if I push
this satellite away from me?
Stopping a car…
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What two things must the driver of the car do in order to stop
in time?
Stopping a car…
Thinking
distance
(reaction time)
Braking
distance
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Tiredness
Too many
drugs
Stopping a car…
Thinking
distance
(reaction time)
Too much
alcohol
Poor
visibility
Wet roads
Icy roads
Tyres/brakes
worn out
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Braking
distance
Driving too
fast
Total Stopping Distance = Thinking Distance + Braking Distance
Stopping a car…
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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!
Estimating Forces and Deceleration
(higher only)
25/07/2024
Estimate rough values for the forces involved in decelerating these
objects:
A skydiver when he
opens his parachute
A car slowing down
at traffic lights
A formula 1 car
about to take a
sharp turn
Taking u = 50m/s, v
= 10m/s, t = 0.1s
and m = 70kg we
get…
28000N
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…
60000N
8000N
Q. What happens to the human body when these forces get TOO big?
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5.7 – Momentum (higher only)
25/07/2024
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
You need to learn this equation!!
What is the momentum of the following?
1) A 1kg football travelling at 10m/s
10kgm/s
2) A 1000kg car travelling at 30m/s
30,000kgm/s
3) A 0.02kg pen thrown across the room at 5m/s
0.1kgm/s
4) A 70kg bungi-jumper falling at 40m/s
2800kgm/s
25/07/2024
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?
Speed = 50m/s
Mass = 1000kg
Speed = 20m/s
Mass = 800kg
Mass = 1800kg
Speed = ??m/s
Momentum before = momentum after…
…so 1000 x 50 + 800 x 20 = 1800 x V…
…V = 36.7m/s
25/07/2024
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
Another example
25/07/2024
Consider the nuclear decay of Americium-241:
237
93
Np
241
95
Am
If the new neptunium atom moves away at
a speed of 5x105 m/s what was the speed
of the alpha particle?
2.96x107 m/s
4
2
α
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?
25/07/2024
5.6m/s
70m/s
3m/s
400m/s
25/07/2024
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.
12.9m/s
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.
3.3m/s
25/07/2024
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…
Force = Change in momentum (in kgm/s)
(in N)
mv
Time (in s)
You DON’T need to learn this
equation!!
F
T
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
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.
25/07/2024
16kgm/s,
80m/s
4.5kgm/s,
18m/s
40N
0.2s