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Wallace Hall Academy
Physics Department
Dynamics
Pupil Notes
Name: _________
Learning intentions for this unit
✓?✘
Be able to state the difference between a scalar and a vector and state whether a
quantity is a scalar or a vector.
Be able to perform calculations using the d = vt formula.
Be able to state the difference between distance and displacement.
Be able to calculate a resultant vector.
Be able to measure instantaneous and average speed.
Be able to perform calculations using the s = vt formula.
Be able to define acceleration.
Be able to perform calculations using the a = (v-u)/t formula.
Be able to draw a velocity time graph and describe the motion of an object from its
velocity time graph.
Be able to calculate acceleration and displacement from a velocity time graph.
Be able to state the 3 effects a force can have on an object.
Be able to draw free body diagrams to indicate the forces acting on an object.
Be able to define mass, weight and gravitational field strength.
Be able to perform calculations using the W = mg formula.
Be able to describe the factors affecting the size of gravitational field strength.
Be able to describe different ways of increasing or reducing friction.
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Be able to state Newton’s three laws and describe their implications.
Be able to calculate the resultant force on an object when more than one force acts on
it.
Be able to what a terminal velocity is and explain why an object reaches a terminal
velocity.
Be able to perform calculations using the Fun = ma formula.
Be able to state the law of conservation of energy
Be able to perform calculations using the Ek = ½mv2 formula.
Be able to perform calculations using the Ep = mgh formula.
Be able to perform calculations using the Ew = Fd formula.
Be able to define power and perform calculations using the P = E/t formula.
Be able to perform calculations in situations where energy is transformed from one
type to another.
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S CALARS & V ECTORS
Vector and Scalar Quantities
Physical quantities can be divided into two groups:
•
•
Scalar quantities are completely described by stating their magnitude.
Vector quantities are completely described by stating their magnitude and direction.
In the table below make a list of scalar and vector quantities.
Scalar
Vector
Speed, distance and time
You will recall from the waves topic that the speed of an object can be calculated from the following
equation:
d=
v=
t=
Example
Susan runs a distance of 4 km in 20 minutes. Calculate her average speed.
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Distance and displacement
Distance is a scalar quantity and describes the length of the journey taken by an object.
Displacement is a vector quantity and describes the difference in position between the start
and finish point of a journey.
For example if Joanne walked a distance of 100 m East then turned around and walked 20 m West
her total distance walked would be 120 m. Her displacement, however, would be 80 m East as that
describes the difference in position from when she started until she finished. Displacement is a
vector so it is important to include the direction.
Example 1
John runs 200 m North then turns around and runs 40 m South.
a. Calculate his total distance travelled.
b. Calculate his final displacement.
Example 2
Leah walks 100 m North then 40 m East and then 100 m South.
a. Calculate her total distance travelled.
b. Calculate her final displacement.
Example 3
Michele runs two laps of a 400 m running track.
a. Calculate her total distance travelled.
b. Calculate her final displacement.
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Vector diagrams
In many areas of Physics (displacement, forces, velocity) it may be necessary to combine two
components in a vector diagram. These will take the form of a scale diagram which will be a right
angled triangle.
When drawing vector diagrams it is essential to pick a suitable scale so that your vector diagram is
not too big and not too small but is also easy to translate. For example if a pupil were to walk a
distance of 80 m East then a distance of 60 m North it would make sense to use a scale of 10 m = 1
cm. This means the scale diagram would have a horizontal 8 cm line followed by a vertical 6 cm line
as shown below.
•
On your diagram you should include an arrow in the middle of each vector to show which
direction it is.
•
On your diagram you should indicate the start and finish points with an s (start) and an f
(finish).
•
On your diagram you should draw a straight line from the start to the finish.
•
On your diagram the line from the start to the finish should have two arrows drawn on it from
the start to the finish.
•
Measure the length of the line from the start to the finish.
•
Convert the length from cm to m using the scale you have selected.
•
This length is the magnitude of the displacement.
•
Measure the two internal angles of the triangle and label them on the diagram.
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Practice problems
1.
Josh walks a distance of 600 m North then a distance of 700 m East.
a. Calculate the total distance Josh walked.
b. Calculate Josh’s final displacement from his starting point.
2. Joanne walks a distance of 900 m West then 400 m South.
a. Calculate the total distance Joanne walked.
b. Calculate Joanne’s final displacement from her starting point.
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Measuring Average Speed Experiment
The average speed is measured over an entire journey.
To calculate the average speed we need to make 2 measurements, the distance of the journey and
the time for the object to complete the journey.
Aim: To measure the average speed of a car rolling down a ramp.
Diagram:
Method:
Results:
Distance =
Time (s)
Exp. 1
Exp. 2
Exp. 3
Exp. 4
Calculation:
Conclusion:
Evaluation:
8
Exp. 5
Average (s)
Measuring Instantaneous Speed Experiment
The instantaneous speed is measured over a very short period of time.
To calculate the average speed we need to make 2 measurements, the length of the object in
motion and the time for the object to pass a light gate.
Aim: To measure the instantaneous speed of a car at the bottom of a ramp.
Diagram:
Method:
Results:
Distance =
Time (s)
Exp. 1
Exp. 2
Exp. 3
Exp. 4
Calculation:
Conclusion:
Evaluation:
9
Exp. 5
Average (s)
Practice Questions
1. In the laboratory, a vehicle travels down a ramp. The vehicle is 10cm long and takes 0.2s to
travel through a light gate. Calculate the instantaneous speed of the vehicle?
2. Given the following information from an experiment, calculate the instantaneous speed of a
vehicle.
Mass of vehicle, 0.5 kg
Length of card on vehicle, 4 cm
Time taken to pass through light gate, 14 ms.
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Velocity, displacement and time
The equation which links velocity, displacement and time is shown below.
s=
v=
t=
Example 1
John runs 200 m North then turns around and runs 40 m South in a time of 50 s.
a. Calculate his total distance travelled.
b. Calculate his average speed.
c. Calculate his final displacement.
d. Calculate his average velocity.
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Example 2
Michele runs three laps of a 400 m running track in a time of 8 minutes.
a. Calculate her total distance travelled.
b. Calculate her average speed.
c. Calculate her final displacement.
d. Calculate her average velocity.
Example 3
Sharon walks a distance of 400 m North then a distance of 300 m East in a time of 5 minutes.
a. Calculate her total distance travelled.
b. Calculate her average speed.
c. Calculate her final displacement.
d. Calculate her average velocity.
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A CCELERATION
Acceleration is how much an objects velocity changes per second.
If an object has an acceleration of 2.4 ms-2 then you would say, the objects velocity increases by
2.4 ms-1 every second.
A deceleration is calculated in the same way as an acceleration except the value will be negative as
it is getting slower.
The acceleration of an object is given by the change in velocity divided by the time taken.
=
a=
u=
v=
t=
Example 1
Bob starts from rest and accelerates to 8 ms-1 in 2 s. Calculate his acceleration.
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Example 2
Sean starts from 3 ms-1 up to a final velocity of 24 ms-1 in a time of 7 s. Calculate his acceleration.
Example 3
Cheryl starts from rest and accelerates at 4 ms-2 to a final speed of 20 ms-1. Calculate how long this
takes her.
Example 4
Luke starts at 4 ms-1 and accelerates at 2 ms-2 for a time of 8 s. Calculate his final velocity.
Example 5
Hannah accelerates at 3 ms-2 for a time of 5 s to a final speed of 20 ms-1. Calculate her initial
velocity.
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Measuring Acceleration Experiment
Aim: To measure the acceleration of a car down a ramp.
Diagram:
Method:
Results:
Time down ramp =
Distance =
Time (s)
Exp. 1
Exp. 2
Exp. 3
Exp. 4
Calculations:
Conclusion:
Evaluation:
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Exp. 5
Average (s)
V ELOCITY / T IME G RAPHS
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One of the best ways to get a ‘picture’ of how something is moving is to draw a graph of velocity
against time. The graph will display the instantaneous velocity at any time on the journey. The graph
will show when an15
object has constant acceleration, constant velocity or constant deceleration.
Velocity (ms-1)
10
5
0
0
10
20
30
Time (s)
40
50
60
The gradient of the line is equal to the acceleration.
The area underneath the line is equal to the displacement of the object.
In order to calculate the final displacement it is necessary to split the shape into triangles and
rectangles and calculate the area of each and add them together.
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Example 1
Simon goes on a short cycle. The velocity time graph of his journey is shown below.
Velocity (ms-1)
20
15
10
5
0
0
10
20
30
Time (s)
a. Calculate his acceleration during the first 20 s.
b. Calculate his acceleration during the final 10 s.
c. Calculate the final displacement after 50 s.
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40
50
60
Practice problem
Stacey goes on a short cycle. The velocity time graph of her journey is shown below.
Velocity (ms-1)
20
15
10
5
0
0
10
20
30
40
Time (s)
a. Calculate her acceleration during the first 20 s.
b. Calculate her acceleration during the final 10 s.
c. Calculate the final displacement after 60 s.
d. Calculate her average velocity for the journey.
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50
60
F ORCES
The application of a force can do 3 things to an object.
1.
2.
3.
Examples of forces
In the table below make a list of all the forces you can think of and an example of when they act.
Name of force
When it acts
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Free body diagrams
Air resistance
When discussing the different types of forces that can act
on an object it is often useful to draw free body diagram to
name the forces acting on an object and identify the
direction in which they act. For example the two vertical
forces acting on a falling apple are shown opposite.
Weight
For the examples shown below draw and label arrows representing any forces which are acting.
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Measuring forces
Forces are a vector meaning they have both magnitude and
direction. Forces can be measured using a Newton Balance. A
Newton balance is simply a calibrated spring. A spring is used
to measure forces because it increases its length when you
apply a force to it. The unit used to measure force is the
Newton (N) - after Sir Isaac Newton.
Gravity, weight and mass
Mass is a measure of the amount of matter an object contains. Mass is measured in kg.
Gravity is an invisible thing which attracts all masses towards each other. The strength of gravity is
called the gravitational field strength which described the Weight per unit Mass and is
measured in N kg-1.
Weight is the force we feel as gravity pulls us towards the Earth. Weight is measured in N.
In everyday life people often confuse mass and weight. People talk about having a weight measured
in stones, pounds or kg but what they are actually talking about is their mass.
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Experiment to measure the gravitational field strength
Aim: To measure the gravitational field strength on Earth.
Diagram:
Method:
Results:
Mass (kg)
Weight (N)
Conclusion:
Evaluation:
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Weight/Mass (N kg-1)
From the experiment we have shown the weight, mass and gravitational field strength can be linked
by the equation shown below.
W=
m=
g=
Example 1
A small dog has a mass of 6 kg. Calculate its weight on Earth.
Example 2
Jane has a weight of 620 N on Earth. Calculate her mass.
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Gravitational field strength when not on Earth
As we have measured the gravitational field
strength on the surface of the Earth is 9.8 N kg-1.
As we move away from the Earth the
gravitational field strength reduces. The table
opposite shows how it decreases for every 1000
km above the Earth’s surface. Plot this data on
the graph paper provided.
Height (km)
g (N kg-1)
0
9.8
1000
7.3
2000
5.7
3000
4.5
4000
3.7
5000
3.1
6000
2.6
7000
2.2
8000
1.9
9000
1.7
10000
1.5
Graph of gravitational field strength variation with height above the Earth’s surface.
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As well as varying depending on how far above the Earth’s surface you are gravitational field
strength also varies across different bodies (planets, moons and stars) in the solar system. The
value of gravitational field strength of some bodies in our solar system is shown below.
Body
g (N kg-1)
Body
g (N kg-1)
Body
g (N kg-1)
Mercury
3.7
Jupiter
23
The Sun
270
Venus
8.9
Saturn
9
Pluto
0.7
Earth
9.8
Uranus
8.7
Titan
1.4
Mars
3.7
Neptune
11
The moon
1.6
It is worth noting that although your weight varies as you move from planet to planet your mass
remains the same.
Example 1
An astronaut has a mass of 64 kg. Calculate her weight on the surface of the moon.
Example 2
A space rocket has a mass of 3400 kg. Calculate its weight at an altitude of 5600 km above the
surface of the Earth.
Example 3
An astronaut has a weight of 250 N on the surface of mars. Calculate her weight on the surface of
Neptune.
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Friction
Friction is a force which opposes movement and always acts in the opposite direction to which
the objects are moving. Friction can sometimes be helpful but can also be unhelpful. In the table
below give 3 examples of when friction is helpful and 3 examples of when friction is unhelpful.
Friction is helpful when ….
Friction is unhelpful when ….
There are two methods of reducing friction.
Streamlining reduces friction by reducing the frontal area of an object. In the box below
describe 2 examples where streamlining is used to reduce friction.
Streamlining reduces friction …
Lubrication reduces friction by placing an air, water or oil between 2 surfaces. In the box
below describe 2 examples where lubrication is used to reduce friction.
Lubrication reduces friction …
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Resultant Force
In most situations encountered in Physics, such as those you drew free body diagrams about, more
than 1 force will be acting on an object. To simplify these problems it is necessary to represent all of
the forces with a single force. A resultant force combines two or more forces into a single
force.
When forces act in the same direction they can be added.
When forces act in opposite directions they can be subtracted.
When forces act at right angles to each other they can be added by scale diagram.
Calculate the resultant force for the 4 examples below.
Example 1
9N
12 N
Example 2
100 N
80 N
70 N
11 N
Example 3
4N
10 N
10 N
8N
Example 4
8N
6N
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Newton’s first law – dealing with balanced forces
An object will remain at rest or continue moving at a constant velocity unless acted on by an
unbalanced force.
What this means is that if an object is stationary it will remain stationary unless a force is applied to
it. What is slightly more confusing is that an object which is already moving will continue to move at
the same velocity unless a force is applied to it.
Balanced forces means constant velocity.
Constant velocity means balanced forces.
Newton’s second law – dealing with unbalanced forces
An object will accelerate if an unbalanced force is applied to it. The size of the acceleration is
dependent on the size of the force and the mass of the object.
Newton’s second law can be summarized in the equation below.
Fun =
m=
a=
Example 1
A car has a mass of 1300 kg and an engine thrust of 2 kN. Calculate its acceleration.
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Example 2
A block of mass 12 kg is subjected to the forces shown below.
9N
14 N
a. Calculate the unbalanced force acting on the block.
b. Calculate the acceleration of the block.
Example 3
A rocket has a mass of 18 000 kg and an engine thrust of 250 kN.
a. Calculate the weight of the rocket.
b. Draw a free body diagram of the forces acting on the rocket.
c. Calculate the initial acceleration of the rocket.
d. Explain what would happen to the magnitude of the acceleration of the rocket as its speed
increases.
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Newton’s third law – dealing with pairs of forces
For every action there is an equal and opposite reaction.
Whenever a force is applied a force which is equal in size but opposite in direction also acts. In
static situations such as a pupil sitting on a char the force which is applied is the downward force of
weight. The equal and opposite force applied is the reaction force of the chair keeping you from
falling. In moving situations such as a rocket launch the rocket pushes the fuel downwards. The
equal and opposite force applied is from the fuel on the rocket which in turn propels the rocket
upwards.
Example 1
A rugby ball has a mass of 400g. When kicked, the ball accelerates briefly at 500ms-2.
a) Calculate the unbalanced force acting on the ball.
b) Calculate the magnitude of the force acting on the kickers boot.
c) Calculate the direction of the force on the kickers boot.
Parachuting experiment
In pairs your task is to build a parachute to allow an egg to safely fall through a
height of 5 m.
• Complete the free body diagram to show your understanding of the
vertical forces involved.
• Give your egg a name.
• Design your parachute.
• Build your parachute with the resources provided.
• Test your parachute.
Raft building experiment
In pairs your task is to build a raft capable of holding as much mass as possible.
• Complete the free body diagram to show your understanding of the
vertical forces involved.
• Design your raft.
• Build your raft with the resources provided.
• Test your raft.
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Energy
There are many types of energy that you will know about and will learn about in this course. In the
box below make a list of all of the types of energy you know about.
Types of energy ……
The law of conservation of energy states that energy can never be created or destroyed, only
transferred from one type to another.
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Kinetic energy
Kinetic energy is a type of energy to do with the movement of an object. It is dependent on mass
and velocity and is described by the equation below.
Ek =
m=
v=
Example 1
A car has a mass of 1250 kg and a velocity of 18 ms-1. Calculate its kinetic energy.
Example 2
John has a velocity of 4 ms-1 and a kinetic energy of 500 J. Calculate his mass.
Example 3
Sheila has a mass of 45 kg and a kinetic energy of 300 J. Calculate her velocity.
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Measuring kinetic energy experiment
Aim: To measure the kinetic energy of a car at the bottom of a ramp.
Diagram:
Method:
Results:
Mass =
Distance =
Time (s)
Exp. 1
Exp. 2
Exp. 3
Exp. 4
Calculation:
Conclusion:
Evaluation:
33
Exp. 5
Average (s)
Potential energy
Potential energy is a type of energy that an object gains as it moves away from the surface of the
Earth. It is also called gravitational potential energy. It is dependent on mass, gravitational field
strength and height as described by the equation below.
Ep =
m=
g=
h=
Example 1
A box has a mass of 40 kg and is lifted through a height of 80 cm on Earth. Calculate how much
potential energy it gains.
Example 2
John has a mass of 63 kg and he falls through a height of 50 cm on Earth. Calculate how much
potential energy he loses.
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Word done
Work done describes a form of energy that is usually energy which is lost due to friction. For
example when a car brakes its kinetic energy is lost due to friction. Word done is described by the
equation below.
Ew =
F=
d=
Example 1
A frictional force of 400 N is applied to a toy car with a kinetic energy of 120 J. Calculate the
distance it will take for the car to stop.
Example 2
A train has a mass of 150 000 kg and a velocity of 45 ms-1.
a. Calculate the kinetic energy of the train.
b. Calculate the force applied by the trains brakes if it comes to a stop in a distance of 800 m.
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Potential energy to kinetic energy transfer experiment
Aim: To measure the potential energy of a toy car at the top of a ramp. To measure the kinetic
energy of a toy car at the bottom of a ramp. To calculate the average frictional force acting against
the toy car as it travelled down the ramp.
Diagram:
Method:
Results:
Mass =
Distance =
Time (s)
Exp. 1
Exp. 2
Exp. 3
Exp. 4
Length of ramp =
Calculation:
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Exp. 5
Average (s)
Conclusion:
Evaluation:
Power
Power is a measure of energy transfer per unit time.
P=
E=
t=
Example 1
An electric motor with a power rating of 500 W lifts a 20 kg mass through a height of 60 cm.
Calculate how long this would take.
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Measuring pupil power experiment
Aim: To measure how powerful I am.
Diagram:
Method:
Results:
Mass =
Height =
Time =
Calculation:
Conclusion:
Evaluation:
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Practice Problems
1. A ball of mass 0.5kg is dropped from a tower which is 75m high.
a) Before the ball is dropped, calculate how much gravitational potential energy does it
have?
b) Assuming all energy is transferred to kinetic energy, calculate the speed of the ball just
before it reaches the ground.
2. A model rocket is fired straight up with an initial speed of 8 ms-1. The rocket has a mass of
0.2kg.
a) Calculate the initial kinetic energy of the rocket.
b) The mass of the rocket does not change. The rocket reaches its maximum height.
Calculate the gravitational potential energy gained by the rocket?
c) Use your answer from b to calculate the maximum height reached by the rocket.
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