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Intermediate 2 PhysicsIn addition to set homework you will be expected tofinish off class notes and regularly review work
againstthe learning outcomes.
You will be expected to take responsibility for your own
learning and for seeking help when you need it. At the
end of each section, you must ensure all notes arecompleted and examples attempted.
In unit 1 we will learn aboutthe physics of motion.
We will focus on the language,principles and laws whichdescribe and explain themotion of an object. Kinematicsis the science of describing themotion of objects using words,diagrams, numbers, graphsand equations.
The goal is to develop mental modelswhich describe and explain the motion ofreal-world objects.
Key words: vectors, scalars, distance,displacement, speed, velocity.
By the end of this lesson you will be able to:
Describe what is meant by vector and scalar quantities
State the difference between distance anddisplacementState the difference between speed and velocityState that force is a vector quantityUse a scale diagram to find the magnitude and
directionof the resultant of two forces acting at right angles toeach other.
Scalars and Vectors
Imagine a boatmaking a distresscall to thecoastguard.
The boat tells thecoastguard he is 60 kmfrom Aberdeen.
Scalars and Vectors
Is this enoughinformation for thecoastguard to findthe boat?
Scalars and Vectors
Scalars and Vectors
The coastguard needs both
distance (size)and
direction
to find the boat.
Scalars and Vectors - Definition
A scalar is a quantity which has onlymagnitude (size). It is defined by anumber and a unit.
A vector is a quantity which hasmagnitude (size) and direction. It isdefined by a number, a unit and adirection.
Distance and DisplacementA pupil walks from her house to her school.
Her brother makes the same journey, but via a shop.
How far has the girl walked?
How far has her brother walked?
50 m30 m
40 m
Distance and DisplacementThe girl has walked 50 m.Her brother has walked 70 m.
50 m30 m
40 m
Distance is a scalar quantity – it can be defined simply by a number and unit.
Distance and DisplacementDistance is simply a measure of how much ground an object has covered.
50 m30 m
40 m
Distance and DisplacementBut how far out of place is the girl? And her brother?
Displacement is a vector which requires number, unit and direction.
50 m30 m
40 m
Distance and DisplacementThe girl has a displacement of 50 m at a bearing of 117° East of North.
50 m
30 m
40 m
Distance and DisplacementWhat is her brother’s displacement?
50 m
30 m
40 m
Distance and DisplacementHer brother has a displacement of 50 m at a bearing of 117° (117° East of North).
50 m
30 m
40 m
Distance and DisplacementTheir displacement (how far out of place they each are) is the same.
50 m
30 m
40 m
Speed and Velocity
Speed is a scalar quantity requiring only magnitude (number and unit).
Velocity is a vector, requiring magnitude and direction.
Speed and Velocity
Speed tells us how fast an object is moving.
Velocity tells us the rate at which an object changes position.
Speed and Velocity
Imagine a person stepping one stepforward, then one step back at a speed of0.5 ms-1.
What is the person’s velocity? Remembervelocity keeps track of direction. Thedirection of the velocity is the same asthe direction of displacement.
Speed and Velocity
time
positionin change velocityAverage
time
distancespeed Average
and
Key words: vectors, scalars, distance,displacement, speed, velocity.
By the end of this lesson you will be able to:Describe what is meant by vector and scalar
quantitiesState the difference between distance anddisplacementState the difference between speed and velocityState that force is a vector quantityUse a scale diagram to find the magnitude and
directionof the resultant of two forces acting at right angles
toeach other.
Distance and Displacement
Virtual Int 2 Physics – Scalars and Vectors – Distance and Displacement
Speed and Velocity
Virtual Int 2 Physics – Scalars and Vectors – Speed and Velocity
A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the average speed and the average velocity.
The physics teacher walked a distance of 12 meters in 24seconds; thus, her average speed was 0.50 m/s.
However, since her displacement is 0 meters, her averagevelocity is 0 m/s. Remember that the displacement refers tothe change in position and the velocity is based upon thisposition change. In this case of the teacher's motion, there isa position change of 0 meters and thus an average velocity of0 m/s.
Scalar or
Vector?Virtual Int 2 Physics – Scalars & Vectors - Introduction
Key words: vectors, scalars, resultant, scale diagram
By the end of this lesson you will be able to:
Describe what is meant by vector and scalar quantities
State the difference between distance anddisplacementState the difference between speed and velocityState that force is a vector quantityUse a scale diagram to find the magnitude and
directionof the resultant of two forces acting at right angles toeach other.
Vectors
Vectors can be represented by a linedrawn in a particular direction.
The length of the line represents themagnitude of the vector.
The direction of the line represents thedirection of the vector.
Addition of Vectors
When two or more scalars are addedtogether, the result is simply a numericalsum.
For example a mass of 3kg and a mass of
5 kg, when added, make a mass of 8kg.
Addition of Vectors
When two or more vectors are addedtogether, providing they act in the
samedirection, the addition is
straightforward.5 N 3 N
8 N
Addition of Vectors
If they are acting in opposite directions
5 N 3 N
2 N
Addition of Vectors
The resultant of two or more vectors
which act at angle to each other can be
found either using a scale diagram, or by
Pythagoras and trigonometry.
To find the resultant of a set of vectors using a scale diagram
1. Decide on a suitable scale and write thisdown at the start
2 Take the direction to the top of the page asNorth. Draw a small compass to show this.
3 Draw the first vector ensuring it is thecorrect length to represent the magnitudeof the vector, and it is the correctdirection.
To find the resultant of a set of vectors using a scale diagram
4. Draw an arrow to represent the secondvector starting at the head of the first.Vectors are always added head to tail.
5 The resultant vector can now be determinedby drawing it on the diagram from the tailof the first to the head of the last vector.The magnitude and direction of this vectoris the required answer.
6 The final answer must have magnitude and direction – either a bearing from North or an angle marked clearly on the diagram
Scale Diagrams
1. Scale: remember if the question is in ms-1 then your scale should be a conversion from cm to ms-1.
2. Direction: draw compass on page
3. 1st vector: length and direction
4. 2nd vector: tail of 2nd starts at tip of first
5. Resultant vector: tail of 1st to tip of last
6. Answer must include magnitude (including units) and direction
Scale Diagrams
Direction should be given as a threefigure bearing from North
e.g. 045° or 175° or 035°
If you give any other angle, you mustclearly mark it on the scale diagram.
A car travels 100 km South, then 140 kmEast. The time taken for the wholejourney is 3 hours.
Using a scale diagram (and the six stepprocess) find(a) the car’s total distance travelled(b) its average speed(c) its overall displacement(d) its average velocity
Scale Diagrams
Scale diagrams are used to find themagnitude and direction of the
resultantof a number of a set of vectors.
Key words: vectors, scalars, resultant, scale diagram
By the end of this lesson you will be able to:
Describe what is meant by vector and scalar quantities
State the difference between distance anddisplacementState the difference between speed and velocityState that force is a vector quantityUse a scale diagram to find the magnitude and
directionof the resultant of two forces acting at right angles toeach other.
So you think you know your vectors and scalars?
Mass
Vector definition?
How do you write an answer which is a vector?
Velocity
DistanceKinetic energy
ForceVelocity=
Scale diagram – 6 steps?
Key words: vectors, resultantBy the end of this lesson you will be
ableto:
Use Pythagoras and Trigonometry to find
the magnitude and direction of theresultant of two forces acting at rightangles to each other.
The tropical island of
Sohcahtoa
hypopp
sin
The tropical island of
Sohcahtoa
hypadj
cos
The tropical island of
Sohcahtoa
adjopp
tan
The tropical island of
Sohcahtoa
adjopp
tanhypopp
sinhypadj
cos
hyp
adjcos
hypopp
sin
θ°
adjopp
tan
adj
hyp
opp
The Old Arab Carried A Heavy Sack Of Hay
Tan = Opp/Adj; Cos= Adj/Hyp; Sin=Opp/Hyp
222 oppadjhyp
TheoremPythagoras
'
θ°
adj
hyp
opp
The squaw on the hippopotamus is equal
to the sum of the squaws on the other
two hides
= +
N
E4 km East
+ 3 km North
Remember: The vectors above are not tip to tail. You must join them tip to tail
N
E4 km East
+ 3 km North
R = ?R = ?kmR 534 22
09.364
3tan
1
= Bearing of 053.10
6N North, 8N East - what is the resultant force R ?
6N
8NWe ADD vectors HEAD to TAIL [tip to toe]
RNR 1068 22
333.16
8tan
01.53
6N
Key words: average speed
By the end of this lesson you will be able to:
Describe how to measure an average speed
Carry out calculations involving distance, time
and average speed.
Which of these are units of speed?
miles per hour
gallons
Newtons
seconds
metres
amperesmiles
minutes
metres per second
kilometres per second
wattsmiles per minute
Speeds in….
In Physics we normally use units
m/s for velocity.
Average speed (m/s)
Light speed
Earth in orbit
7500 m/s
High speed train
648 m/s
833 m/s
Falcon
31 m/s
747 jumbo jet
Sound
13.4 m/s
Air molecule
Walking speed
Olympic sprinter
Snail
300000000 m/s
29790 m/s
Earth satellite
60 m/s
Concorde
Fast jet
97 m/s
UK motorway
270 m/s
340 m/s
UK town
500 m/s
1.7 m/s
10.3 m/s
0.006 m/s
Average speed ( m/s )Light speed 300000000 m/s
Earth in orbit 29790 m/s
Earth satellite 7500 m/s
High speed train 60 m/s
Concorde648 m/s
Fast jet833 m/s
Falcon 97 m/s
UK motorway31 m/s
747 jumbo jet270 m/s
Sound 340 m/s
UK town 13.4 m/s
Air molecule500 m/s
Walking speed 1.7 m/s
Olympic sprinter10.3 m/s
Snail 0.006 m/s
What is speed?
When we talk about speed we mean…
the distance covered by an object in agiven time.
What is speed?
If Hamish (the dog) runs 10 metres in 2
seconds, what is his speed?
What is speed?
His speed is 5 metres per second.
So speed is
timedistance
What is speed?
If you forget the formula think of cars travelling at 30 kilometres per hour
timedistancekm
Per
Hour=
Key words: average speed
By the end of this lesson you will be able to:
Describe how to measure an average speed
Carry out calculations involving distance, time
and average speed.
distance
speed time
Speed Calculations
A cyclist travels 100 m in
12 s. What is her speed?
Step 1: write down what you know.
d = 100 m
t = 12 s
s = ?
Step 2: write down your formula. You can use the triangle to help you but remember you get no marks for this!
d = 100 m
t = 12 s
s = ?d = s x t
Step 3: substitute in your values.
d = 100 m
t = 12 s
s = ?
d = s x t
100 = s x 12
Step 4: rearrange
d = 200 m
t = 40 s
v = ?
d = s x t
100 = s x 12
s = 100
12
Step 5: calculate
d = 100 m
t = 12 s
v = ?
d = s x t
100 = s x 12
s = = 8.33100
12
Step 6: units!!!!
d = 100 m
t = 12 s
s = ?
d = s x t
100 = s x 12
s = = 8.33 m/s100
12
Key words: average speed, instantaneousspeed
By the end of this lesson you will be able to:
Describe how to measure instantaneous speed.
Identify situations where average speed andinstantaneous speed are different.
Instantaneous and average speed
Are instantaneous and average speed the same?
Instantaneous or average?
A car’s speed between Arbroath andDundee
Average
Instantaneous or average?
The speed read from a car’s speedometer
Instantaneous
Instantaneous or average?
A tennis ball’s speed as it crosses the net
Instantaneous
Instantaneous or average?
A racing car’s speed over a lap of the track
Average
Instantaneous or average?
A parachutist’s speed as he/she lands
Instantaneous
Key words: acceleration, velocity
By the end of this lesson you will be able to:
Explain the term “acceleration”
State that acceleration is the change invelocity per unit time
Carry out calculations involving the relationshipbetween initial velocity, final velocity, time anduniform acceleration.
Measuring Acceleration Activity 3
Position of light gate from bottom of slope
Acceleration (m/s2)
1st attempt
2nd attempt
3rd attempt
Position 1
m
Position 2 m
Position 3 m
Position 4 m
Average acceleration (m/s2)
What do you expect to happen to the value of acceleration as the light gate is moved further up the slope?
What is acceleration?
Acceleration is the change in velocity of an object per second (in one second).
Is acceleration a vector or scalar quantity?
Acceleration
What is the definition of acceleration?
Is it a vector or a scalar?
Acceleration is the rate of change of velocity per unit time OR change in velocity per unit time.
Vector – since velocity is a vector.
What is acceleration?
The rocket starts off at 0 m/s and 1second later is travelling at 10 m/s. What is its acceleration?
10 metres per second per second 10 m/s2
change in speed in one second
Calculating acceleration
We need to know…the change in velocity so…initial velocity (u)
final velocity (v)and…
time (t)
timevelocity in change
onaccelerati
time(u) velocity initial - (v) velocity final
onaccelerati
tu-v
a
tuv
a
change in velocity
in one second
Acceleration
a = acceleration measured in m/s2
u = initial velocity measured in m/sv = final velocity measured in m/st = time measured in s
Units of acceleration
a = final velocity – initial velocity
time
acceleration is measured in m/s2
If the speed is measured in kilometres per hour, acceleration can be measured in kilometres per hour per second.
Acceleration p4
An object accelerates at a rate of 4 m/s2.
What does this mean?
The object goes 4 m/s faster eachsecond.
Acceleration p4
The object goes 4 m/s faster eachsecond.If the object is initially at rest, whatis its velocity after:1s? 4 m/s2s? 8 m/s3s? 12 m/s4s? 16 m/s
Acceleration
What does it mean if an object has a negative
value of acceleration?
It means that it is slowing down.
For example: an object which has anacceleration of -2 m/s2 is becoming 2 m/sslower each second.
Acceleration Calculations
A car, starting from rest, reaches avelocity of 18 m/s in 4 seconds. Find theacceleration of the car.
What do I know?Initial velocity u = 0 m/sFinal velocity v = 18 m/stime t = 4 s
Acceleration Calculations
What do I know?Initial velocity u = 0 m/sFinal velocity v = 18 m/stime t = 4 s
Formula?
2/5.44
018sm
t
uva
Acceleration Calculations
A cheetah starting from rest acceleratesuniformly and can reach a velocity of 24m/s in 3 seconds. What is theacceleration?
Use technique and show all working!Units!!
Acceleration Calculations
A student on a scooter is travelling at 6 m/s. 4 seconds later, she is travelling at2 m/s. Calculate her acceleration.
Use technique and show all working!Units!!What do you notice about her change invelocity?
Rearranging the acceleration equation
v-u
a t
Rearranging the acceleration equation
v-u
a t a
uvt
atuv
atuv
Key words: acceleration, velocity
By the end of this lesson you will be able to:
Explain the term “acceleration”
State that acceleration is the change invelocity per unit time
Carry out calculations involving the relationshipbetween initial velocity, final velocity, time anduniform acceleration.
Graph results
Acceleration using two light gates
http://www.crocodile-clips.com/absorb/AP5/sample/media/010102AccnApp.swf
The length of the mask is 5 cm. Calculatethe acceleration.
Remember calculate u (initial velocity) andv (final velocity) and use
tu-v
a
Acceleration using a double mask
http://www.crocodile-clips.com/absorb/AP5/sample/media/010102AccnApp2.swf
The length of each section mask is 4 cm. The gap is also 4 cm. Calculate the acceleration.
Remember calculate u (initial velocity) andv (final velocity) and use
tu-v
a
Key words: acceleration, velocity, displacement
By the end of this lesson you will be able to:
Draw velocity-time graphs of more than oneconstant motion.
Describe the motions represented by avelocity-time graph.
Calculate displacement and acceleration, fromvelocity-time graphs, for more than one constantacceleration.
Graphing Motion
Information about the motion of anobject can be obtained from velocity-
timegraphs.
Similarly, we can graph motion based on
descriptions of the motion of an object.
Velocity-time graph
The motion of a moving object can berepresented on a velocity – time graph.
Virtual Int 2 Physics – Mechanics and Heat – Velocity and Acceleration – Velocity Time Graphs
Vectors and Direction
When dealing with vector quantities we
must have both magnitude and
direction.
When dealing with one-dimensionalkinematics (motion in straight lines) weuse + and – to indicate travel in oppositedirections. We use + to indicate accelerationand – to indicate deceleration.
Velocity-Time Graphs
)/( smv
)( st
Constant velocity – does not change with time
00
Describe the motion of this object.
Velocity-Time Graphs
)/( smv
)( st
Increasing with time – constant acceleration
00
Describe the motion of this object.
Velocity-Time Graphs
)/( smv
)( st
Decreases with time – constant deceleration
00
Describe the motion of this object.
Velocity-Time Graphs
)/( smv
)( st0
0
Describe the motion of this object.
Speed-Time Graphs
)/( smspeed
2
00
Calculate the distance covered by the object in the first 10 s of its journey.
10 )( st
The area under the graph tells us the distancetravelled.
Speed-Time Graphs
)/( smspeed
2
00
Calculate the distance covered by the object in the first 10 s of its journey.
10 )( st
The area under the graph tells us the distancetravelled.
Key words: forces, newton balance, weight, mass, gravitational field strength.
By the end of this lesson you will be able to:
Describe the effects of forces in terms of their ability tochange the shape, speed and direction of travel of an object.
Describe the use of a newton balance to measure force.
State that weight is a force and is the Earth’s pull on anobject.
Distinguish between mass and weight.
State that weight per unit mass is called the gravitationalfield strength.
Carry out calculations involving the relationship between weight, mass and
gravitational field strength including situations where g is not equal to 10
N/kg.
What effect can a force have?
Force is simply a push or a pull.
Some forces (e.g. magnetic repulsion, or
attraction of electrically chargedobjects) act at a distance.
What is force?
A force can
change the shape of an objectchange the velocity of an objectchange the direction of travel of an object
Virtual Int 2 Physics – Mechanics & Heat – Forces - Introduction
Units of Force?
Force (F) ismeasured innewtons (N).
Measuring Forces
A Newton (orspring) balance
canbe used to
measureforces.
Mass and Weight
We often use the words mass and weight
as though they mean the same…
but do they?
Mass and Weight
An object’s mass is a measure of how much “stuff” makes
upthat object – how much matter, or howmany particles are in it.
Mass is measured in
grams or kilograms.
Mass and Weight
An object’s weight is the force exerted by gravity on a
mass.
Since it is a force, weight must bemeasured in
newtons.
Investigating the relationship between mass and weight
How can we find the relationship between
mass and weight?
A newton balance can be used to find the
weight of known masses.
Results
Mass Weight in N
100g
200g
300g
400g
500g
1kg
2kg
5kg
Relationship between mass and weight
From this we can see a relationshipbetween mass and weight
100g = 0.1 kg -> 1 N1kg -> 10 N
To convert kg -> N multiply by 10To convert N -> kg divide by 10
Gravitational Field Strength (g)
Gravitational field strength on Earth is
10 N / kg
What is gravitational field strength?
This is the pull of gravity on eachkilogram of mass.
So on Earth, the pull of gravity on a 1kg
mass is 10 N
What is gravitational field strength?
and the pull of gravity on a 2 kg mass is
20 N
Definition
A planet’s gravitationalfield strength is thepull of gravity ona 1 kg mass.
Gravity in the universe
Is gravitational field strength always the
same?
No! It varies on different planets.
http://www.exploratorium.edu/ronh/weight/index.html
Your weight on different planets
Use the website to find your weight ondifferent planets for a mass of 60 kg (aweight of 600 N on Earth).
From this calculate the gravitational field
strength for each planet.
Mass on Earth = 60 kgWeight on Earth = 600 NGravitational field strength =
Weight on Mercury = 226.8 N g = Weight on Venus = 544.2 N g = Weight on the Moon = 99.6 N g = Weight on Mars = 226.2 N g = Weight on Jupiter = 1418.4 N g = Weight on Saturn = 549.6 N g =
1060
600
78.360
8.226
07.960
2.544
77.360
2.226
66.160
6.99
64.2360
4.1418
91.960
6.549
Units for g
We found g by dividing weight in newtons
by mass in kilograms.
What are the units for g?
10 N / kg
Which of the planets has the greatestgravitational field strength?
Why do you think this is the case?
Weight, mass and gravity
We have seen that there is a link between
weight, mass and gravity.
On Earth
1 kg acted on by 10 N / kg weighs 10 N
mass Gravitational field strength g weight
m x g = W
W = mg
Weight, mass and gravity
Weight measured in newtons
Mass measured in kg
Gravitational field strength measured in N / kg
Why is weight measured in newtons?
Key words: friction, forceBy the end of this lesson you will be
ableto:State that the force of friction can opposethe motion of an object.
Describe and explain situations in whichattempts are made to increase or
decreasethe force of friction.
Frictional Forces
Moving vehicles such as cars can slowdown due to forces acting on them.
These forces can be due to…road surface and the tyresthe brakesair resistance.
Virtual Int 2 Physics – Mechanics & Heat – Forces – Friction
Frictional Forces
The force which tries to oppose motion is
called the force of friction.
A frictional force always acts to slow an
object down.
Increasing Friction
In some cases, we want to increasefriction. Some examples of this are:
• Car brakes – we need friction betweenthe brake shoes and the drum to slowthe car down
• Bicycle tyres – we need friction to give• “grip” on the surface
Increasing Friction
On the approach to traffic lights androundabouts, different road surfaces
areused to increase friction compared
withnormal roads.
Decreasing Friction
In some cases, we want to decreasefriction. Some examples of this are:
• Ice skating• Skiing• Aircraft design
Reducing Friction
Friction can be reduced by:
Lubricating the surfaces – this generallymeans using oil between two metalsurfaces. This is done in car engines toreduce wear on the engine – metal partsaren’t in contact because of a thin layerof oil between them.
Reducing Friction
Friction can be reduced by:
Separating surfaces with air (e.g. ahovercraft).
Making surfaces roll (e.g. by using ballbearings).
Reducing Friction
Friction can be reduced by:
Streamlining. Modern cars are designed
to offer as little resistance (or drag) tothe air as possible, reducing friction onthe car.
Streamlining
Cars are streamlined (that is, have their
drag coefficient reduced) by
Reducing the front area of the carHaving a smooth round body shapeUsing aerials built into the car windows
Virtual Int 2 Physics – Mechanics & Heat - Forces – Friction Effects
Key words: force, vector, balancedforces By the end of this lesson you will be ableto:State that force is a vector quantity.State that forces which are equal in size butact in opposite directions on an object arecalled balanced forces and are equivalent tono force at all.Explain the movement of objects in terms ofNewton’s first law.
Force
Force is a vector quantity. What do wemean by this?
To describe it fully we must have size
and direction.
Balanced Forces
Balanced forces are EQUAL FORCES which act in OPPOSITE DIRECTIONS. They CANCEL EACH OTHER OUT.
FF
If balanced forces act on a STATIONARY OBJECT, it REMAINS STATIONARY.
FF
If balanced forces act on a MOVING OBJECT, it continues moving in the same direction with CONSTANT VELOCITY.
F
This is summarised by NEWTON’S FIRST LAW which states:
An object remains at rest, or moves in a straight line with constant velocity unless an UNBALANCED FORCE acts on it.
Virtual Int 2 Physics – Mechanics & Heat – Forces - Newton’s First Law
To understand NEWTON’S FIRST LAW remember:
An object tends to want to keep doing what it is doing (so if it is sitting still it wants to stay that way, and if it is moving with constant velocity it wants to keep going).
This reluctance to change motion is known as inertia.
The greater the mass, the greater the reluctance.
Think! Is it easier to stop a tennis ball travelling towards you at 10 m/s or to stop a car travelling towards you at 10 m/s?
Forces and Supported Bodies
A stationary mass mhangs from a rope.
What is the weight of
the mass? In whatdirection doesthis act?
W = mg downwards
m
Forces and Supported Bodies
The mass is stationary.Newton’s law tells usthat the forces mustbe
balanced forces.The weight iscounterbalanced by aforce of the same sizeacting upwards due tothe tension in thestring.
m
Forces and Supported Bodies
A book of mass mrests on a shelf.
What is the weight of
the book? In whatdirection doesthis act?
W = mg downwards
m
Forces and Supported Bodies
The mass is stationary.Newton’s law tells usthat the forces must
be
balanced forces.
The weight iscounterbalanced by aforce of the same sizeacting upwards due tothe shelf.
m
What forces are acting on this stationary hovering helicopter?
W = mg
lift =W = mg
Newton’s First Law
Newton’s first law tells us that when theforces on an object are balanced, astationary object will remain stationary.
But it also says that if when forces arebalanced, an object moving at constantvelocity will continue in the same
directionwith the same velocity.Virtual Int 2 Physics – Mechanics & Heat – Forces - Newton’s First Law
A moving carIf a car moves with constant velocity, then what forces are acting on it?
The ENGINE FORCE and the FRICTION FORCE must be equal.
Engine force
Friction force
Newton’s Law & Car Seat BeltsIf a car stops suddenly, someone inside the car appears to be “thrown forwards”.
In fact, they simply carry on moving with the car’s previous speed.
A seat belt prevents this happening by applying an unbalanced force to the person, in the direction opposite to motion. This causes rapid deceleration.
No seatbelt – what’s going to happen when the car hits the wall?
Explain this in terms of Newton’s 1st law.
What’s going to happen when the motorbike hits the wall?
Explain this in terms of Newton’s 1st law.
Air bagsAir bags produce a similar effect to seatbelts. They apply a force which opposes the motion, causing rapid deceleration.
The large surface area also spreads the force of impact, reducing the pressure and reducing injury.
Terminal velocity
Any free-falling object in a fluid (liquid or gas) reaches a top speed, called ‘terminal velocity’.
Forces in a Fluid
Terminal velocity
The air resistance acting on a moving object increases as it gets faster.
Terminal velocity is reached when the air-resistance (acting upwards) has increased to the same size as the person’s weight (acting downwards)
W = weight
Friction Ff(air resistance) = 0 N
time = 0s, velocity = 0 m/s, friction = 0 N
a = -10 m/s2
W = weight
Ff
a < -10 m/s2
v
W = weight
Ff
a = 0 m/s2
v
Equal & opposite forcesAcceleration zeroTerminal velocity
Velocity – Time Graph
velocity(m/s)
00
time (s)
Terminal velocity
Virtual Int 2 Physics – Mechanics & Heat – Forces - Terminal Velocity
weight
air resistance
Terminal velocity is reached when the air resistance balances the weight.
Terminal Velocity
What effect does opening a parachutehave on the terminal velocity?
When the parachute is opened, air resistanceincreases a lot. There is now an unbalanced forceupwards, which causes deceleration. The velocitydecreases, and the air resistance decreases untilthe forces are balanced again. The parachutistfalls to the ground with a lower terminal velocity.
Virtual Int 2 Physics – Mechanics & Heat – Forces - Terminal Velocity
Key words: Newton’s second law,unbalanced forces, mass, force,accelerationBy the end of this lesson you will be
ableto:Describe the qualitative effects of the change ofmass or of force on the acceleration of an objectDefine the newtonCarry out calculations using the relationshipbetween a, F and m and involving more thanone force but in one dimension only
The example of the parachutist accelerating until the forces are balanced helps us to understand NEWTON’S SECOND LAW which states:
When an object is acted on by a constant UNBALANCED FORCE the body moves with constant acceleration in the direction of the unbalanced force.
Virtual Int 2 Physics – Mechanics & Heat – Forces - Newton’s First Law
Force, mass and acceleration
F = maForce (N)mass (kg)
Acceleration (m/s2)
Virtual Int 2 Physics – Mechanics & Heat – Forces - Force, mass and acceleration
Force, mass and acceleration
One newton (1N) is the force required to
accelerate 1 kg at 1 m/s2
F = ma
Find the unbalanced force required to accelerate a 4 kg mass at 5 m/s2
What do I know?m = 4kga = 5m/s2
F = maF= 4 x 5F = 20 N
Key words: free body diagrams, resultantforceBy the end of this lesson you will be ableto:Use free body diagrams to analyse the forceson an objectState what is meant by the resultant of anumber of forcesUse a scale diagram, or otherwise, to find themagnitude and direction of the resultant oftwo forces acting at right angles to eachother.
Newton’s First Law
A body remains at rest, or continues atconstant velocity, unless acted upon by
anexternal unbalanced force.
(that is objects have a tendency to keepdoing what they are doing)
Newton’s Second Law
Newton’s Second Law is about thebehaviour of objects when forces are notbalanced.
The acceleration produced in a body isdirectly proportional to the unbalancedforce applied and inversely proportional
tothe mass of the body.
Newton’s Second Law
In practice this means that
the acceleration produced increases asthe unbalanced force increases
the acceleration decreases as the mass of
the body increases
Which forces?
An object may be acted upon by a numberof forces but
only an overall unbalanced forcewill lead to acceleration in the directionof that force.
Forces are measured in…?
Newton’s Second Law can be written as
or more commonly
mF
a
maF
Forces are measured in…?
which gives us the definition of the Newton:
1N is the resultant (or unbalanced) force which causes a mass of 1kg toaccelerate at 1m/ s2
maF
2/11 skgmN
Quick Quiz
Unbalanced force (N)
Mass (kg) Acceleration(m/ s2)
10 2
20 2
20 4
2 5
10 10
5
10
5
10
1
Direction of force
Consider the oil drop trail left by the carin motion.
In which direction is the acceleration?
In which direction is the unbalancedforce?
To the right
To the right
Direction of force
Consider the oil drop trail left by the car
in motion.
In which direction is the unbalancedforce?
To the left – the car is moving to the right and slowing down.
Newton’s First and Second Laws
Remember
Forces do not cause motion
Forces cause acceleration
Free-Body DiagramsA free body diagram is a specialexample of a vector diagram.
They show the relative magnitudeand direction of all forces actingon an object.
They are used to help you identifythe magnitude and direction of anunbalanced Force acting on anobject.
Using Newton’s Second Law
In the simplest case
mFun
mF
a UN
Using Newton’s Second Law
mF1
mFF
a 21
F2
Direction of acceleration?Direction of unbalanced force?Formula for calculating acceleration?
Solving Problems
• Always draw a diagram showing all knownquantities (forces – magnitude anddirection, resultant acceleration anddirection, mass of object(s) )
• Remember that Fun=ma can be applied tothe whole system
• When working in the vertical directionalways include the weight
Key words: acceleration, gravitationalfield strength, projectilesBy the end of this lesson you will be ableto:Explain the equivalence of acceleration due togravity and gravitational field strengthExplain the curved path of a projectile interms of the force of gravityExplain how projectile motion can be treatedas two separate motionsSolve numerical problems using the above
methodfor an object projected horizontally.
Acceleration due to GravityDefinition:
A planet’s gravitational field strength equals the force of gravity PER UNIT MASS.
Units? N/kg
To calculate an object’s weight, use this equation -
mgW Virtual Int 2 Physics – Projectiles – Acceleration due to gravity and gravitational field strength
Near a planet’s surface all objects experience the same gravitational acceleration.
This acceleration is numerically equal to the planet’s gravitational field strength.
ga
Acceleration due to Gravity
For example, on Earth –
g = 10 N/kg
A free-falling object will experience acceleration of a = -10 m/ s2
What does the –ve sign tell you?
Acceleration due to Gravity
Gravitational field strength
Is the gravitational field strength the same on eachplanet?
How does distance affect gravitational field strength?
It decreases the further away you are from the planet’ssurface.
What will happen to the weight of an object as it getsfurther from the surface? Explain your answer.
It will decrease.
The force of gravity nearthe Earth’s surface givesall objects the sameacceleration.
So why doesn’t thefeather reach the
groundat the same time as theelephant?
Why are the gapsbetween the ballsincreasing?
An object is released from rest close to the Earth’ssurface. Which formula can be used to find its velocityat a given time?
v = u + atwhere v = ? , u = 0 , a = , t =
What is its velocity:At the time of release?After 1 second?After 2 seconds?After 3 seconds?After 4 seconds?
Projectiles
Virtual Int 2 Physics – Projectiles –Projectile Motion
Forces acting on projectiles
What would happen to a ball kicked off a
cliff, in the absence of gravity?
Forces acting on projectilesThere would be no vertical motiontherefore the ball would continue atconstant speed in a straightline (remember Newton’s first law)
What is the initial vertical speed of aprojectile fired horizontally?
How will the horizontal speed vary during
the object’s flight?
0 m/s
It will remain the same as the initial horizontal speed.
Objects projected horizontallyThink about…
Describe the vertical motion of an object
projected horizontally:It will accelerate downwards due to gravity.
Objects projected horizontallyThink about…
Projectiles
Virtual Int 2 Physics – Projectiles –Comparing Projectile Motion with Vertical Motion
Virtual Int 2 Physics – Projectiles – Graphs of Projectile Motion
What formula can be used to find thehorizontal displacement of an objectfired horizontally if horizontal velocityand time of flight are known?
sh = vht
Objects projected horizontallyThink about…
horizontal displacement (m)
horizontal velocity (m/s)
time of flight (s)
http://www.fearofphysics.com/XYIndep/xyindep_correct.html
Which ball will hit the ground first?
SummaryHorizontal motion
Vertical motion
ForcesAre there forcespresent? If so, inwhat direction arethey acting?
No Yes
The force of gravityacts downward
AccelerationIs there acceleration?If so, in whatdirection? What isthe value of theacceleration?
No Yes
Acceleration = "g" downwardat 10 m/s2
VelocityConstant or changing?
Constant Changing
by 10 m/s each second
Solving Numerical Problems
• Always write down what you know – many questions have a lot of text surrounding the Physics so pick out the information from the question
• Write down other relevant information you have e.g. acceleration due to gravity
• Select formula – this isn’t a test of memory so while you should learn your formulae, don’t be afraid to check against the data book or text book
• Substitute values and rearrange formula• Write answer clearly remembering magnitude
and direction, and units.
Example
A flare is fired horizontally out to sea from acliff top, at a horizontal speed of 40 m/s. Theflare takes 4 s to reach the sea.
(a) What is the horizontal speed of the flare after 4 s?
There are no forces acting in the horizontal. The
horizontal speed remains the same = 40 m/s.
Example
(b) Calculate the vertical speed of the flare after 4s
final speed v = ?initial vertical speed u = 0 m/s Initial vertical speed is always 0 m/s!
acceleration a = 10 m/s2
time t = 4 s
v = u + atv = 0 + 10 x 4v = 40 m/s
Example
(c) Draw a graph to show how vertical speed varies with time.
Initial vertical speed = 0 m/sFinal vertical speed = 40 m/s
Variation of vertical speed with time
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4 5
Time (s)
Ve
rtic
al s
pe
ed
(m
/s)
Example
(d) Use this graph to calculate the height of the cliff.
Variation of vertical speed with time
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4 5
Time (s)
Ve
rtic
al s
pe
ed
(m
/s)
Displacement = area under velocity-time graph
½ bh = ½ x 4 x 40= 80 m
Height of cliff = 80 m
Projectiles
Virtual Int 2 Physics – Projectiles Example Problem
Virtual Int 2 Physics – Projectiles –Newton’s Thought Experiment
Key words: Newton’s third law, newtonpairsBy the end of this lesson you will be ableto:State Newton’s third lawIdentify “Newton pairs” in situations involvingseveral forcesState that momentum is the product of massand velocity.State that momentum is a vector quantity.
Forces acting between objects
Newton realised that
When a body is acted upon by a force there must be another body which also has a force acting on it. The forces are equal in size but act in opposite directions.
Newton’s Third Law
If object A exerts a force on object B, then B exerts an
equal and opposite force on A
Forces always occur in equal and opposite pairs
For every action there is an equal and opposite reaction
Force of GUN on BULLET
Firing a gun
Force of BULLET on GUN
Force of RUNNER on
BLOCKS
Starting a sprint
Force of BLOCKS on
RUNNER
Force of EARTH on
APPLE
A falling apple
Force of APPLE on
EARTH
A Rocket
Force of ROCKET on
GAS
Force of GAS on ROCKET
Key words: momentum, law ofconservation of momentumBy the end of this lesson you will be ableto:State that momentum is the product of massand velocity.State that momentum is a vector quantity.State that the law of conservation of linearmomentum can be applied to the interactionof two objects moving in one direction, in theabsence of net external forces.Carry out calculations concerned withcollisions in which all the objects move in thesame direction and with one object initially atrest.
Collisions
When two objects collide, they applyforces to each other.
What does the size of the force dependon?
Virtual Int 2 Physics – Mechanics and Heat – Momentum – Momentum defined
Momentum
The momentum of an object is the
mass x velocity
It is a vector quantity.
It has units of kg m/s
Momentum & CollisionsVirtual Int 2 Physics – Mechanics and Heat – Momentum – Collisions
We will consider two types of collision:
1.Vehicles bounce apart after collision
2.Vehicles stick togetherafter collision
A 2kg trolley travelling at 3 m/s hits astationary 1kg trolley.
After the collision the 2kg trolleycontinues to travel in the same directionat 1 m/s. The 1 kg trolley moves offSeparately. Calculate the velocity of the 1kgtrolley after the collision.
Collisions Examples
How can we find the answer?
Using the Law of Conservation of Momentum!
total momentum before collision =
total momentum after collision
providing no external forces are acting.
A 2kg trolley travelling at 3 m/s hits astationary 1kg trolley.
After the collision the 2kg trolleycontinues to travel in the same directionat 1 m/s. The 1 kg trolley moves offseparately. Calculate the velocity of the 1kgtrolley after the collision.
Collisions Examples
Collisions where vehicles bounce apart
Before After
2 kg
3 m/s
1 kg
0 m/s
2 kg
1 m/s
1 kg
? m/s
m/skg 6
0) x 1 ( 3) x (2
umum before momentum total
2211
momentum = mass x velocity
m/skg 6
) x v1 ( 1) x (2
vmvm after momentum total
2
2211
momentum = mass x velocity
Conservation of momentum tells us momentum before = momentum after
Collisions where vehicles bounce apart
2 kg
1 m/s
1 kg
? m/s
positive) (sinceright the to travelofDirection
/4v
2-6 2-v2
6 v 2
m/skg 6 ) x v1 ( 1) x (2
vmvm after momentum total
2
2
2
2
2211
sm
momentum = mass x velocity
Collisions where vehicles bounce apart
m/skg 6
0) x 1 ( 3) x (2
umum before momentum total
2211
2 kg
1 m/s
1 kg
? m/s
Check does this work?
Conservation of momentum tells us momentum before = momentum after
m/skg 6
4) x 1 ( 1) x (2
vmvm after momentum total
2211
A 1kg trolley travelling at 2 m/s hits astationary 1kg trolley.
After the collision the trolleys stick togetherand continue to travel in the same direction.Calculate the velocity of the combined
vehicleafter the collision.
Collisions Examples
Collisions where vehicles stick together
Before After
1 kg
2 m/s
1 kg
0 m/s
1 kg
? m/s
1 kg
m/skg 2
0) x 1 ( 2) x (1
umum before momentum total
2211
momentum = mass x velocity
m/skg 2
2v
v v
x v)1 ( ) x v(1
v vther,stuck toge are vehiclesSince
) x v1 ( ) x v(1
vmvm after momentum total
21
21
2211
momentum = mass x velocity
Conservation of momentum tells us momentum before = momentum after
Collisions where vehicles stick together
1 kg
? m/s
1 kg
positive sinceright the to travelofDirection
m/s 1v
2 2v
m/skg 2
2v
v v
x v)1 ( ) x v(1
v vther,stuck toge are vehiclesSince
) x v1 ( ) x v(1
vmvm after momentum total
21
21
2211
momentum = mass x velocity
Check does this work?
Conservation of momentum tells us momentum before = momentum after
Collisions where vehicles stick together
1 kg
1 m/s
1 kg
momentum = mass x velocity
m/skg 2
0) x 1 ( 2) x (1
umum before momentum total
2211
m/s2kg
11
1) x 1 ( 1) x (1
/1 v vther,stuck toge are vehiclesSince
) x v1 ( ) x v(1
vmvm after momentum total
21
21
2211
sm
Key words: work done, energy, force,distance, power, timeBy the end of this lesson you will be ableto:State that work done is a measure of theenergy transferred.Carry out calculations involving therelationship between work done, force anddistance.Carry out calculations involving therelationship between work done, power andtime.
Work done?
What is meant by work done in Physics?
When a force acts upon an object tocause a displacement of the object, it
issaid that work was done upon the
object.
Work done?
There are three key ingredients to work –force, displacement, and cause.
In order for a force to qualify as having donework on an object, there must be adisplacement and the force must cause thedisplacement.
Work done?Formula linking work done, force and displacement?
Examples of work done?a horse pulling a plow through the fielda shopper pushing a grocery cart down the aisle of a supermarketa pupil lifting a backpack full of books upon her shouldera weightlifter lifting a barbell above his headan Olympian launching the shot-put, etc.
In each case described here there is a force exerted upon anobject to cause that object to be displaced.
FdEw
Work done
A dog pulls a 4 kg sledge for a distance on
15 m using a force of 30 N. How muchwork does he do?
What do I know?F = 30Nd = 15m
Work doneWhat do I know?F = 30Nd = 15m
Formula?
JE
xE
FdE
w
w
w
450
1530
Virtual Int 2 Physics – Mechanics & Heat – Work Done – Example Problem
Power
Power is the rate of doing work i.e. ifwork is done then the work done persecond is the power.
tE
P Power in watts (joules per seconds)
Energy in joules
time in seconds
Power
A dog pulls a 4 kg sledge for a distance on
15 m using a force of 30 N in 20 s.Calculate the power of the dog.
What do I know?F = 30Nd = 15mt = 20s
PowerWhat do I know?F = 30Nd = 15mt = 20s
Formula?
JE
xE
FdE
w
w
w
450
1530
PowerWhat do I know?F = 30Nd = 15mt = 20sEw = 450J
Formula?
WP
P
tE
P W
52220
450
.
Key words: gravitational potential energy,mass, gravitational field strength, kineticenergy
By the end of this lesson you will be ableto:Carry out calculations involving the relationshipbetween change in gravitational potential
energy,mass, gravitational field strength and change inheight.Carry out calculations involving the relationshipbetween kinetic energy, mass and velocity.
Gravitational Potential Energy
…is the potential energygained by an object whenwe do work to lift itvertically in a gravitationalfield.
Gravitational Potential Energy
The work done in lifting anobject vertically
FdEw What force is required?
Gravitational Potential Energy
FdEw
To lift the object we must overcome the weight W=mg
Gravitational Potential Energy
mgdE
Vertical distance – we call this height h
Gravitational Potential Energy
Virtual Int 2 Physics – Mechanics & Heat – Potential Energy – Example Problem
mghEP
Kinetic Energy
…is the energy associated with a moving object.
Kinetic Energy
depends on…
The mass of the object
depends on…
The velocity of the object
Kinetic Energy
Kinetic Energy
2
2
1mvEK
Virtual Int 2 Physics – Mechanics & Heat – Kinetic Energy – Example Problem
Virtual Int 2 Physics – Mechanics & Heat – Power – Example Problem
Speed and Stopping Distance
The distance required to stop a moving vehicle is a combination of two things:
Thinking distanceBraking distance
Speed and Stopping Distance
Each driver has a reaction time.
The thinkingdistance is thedistance you travelbetween realising youneed to stop andreacting.Thinking distance = speed x reaction time
Speed and Stopping Distance
Braking distance This is the distance you travel between pressing your brakes and the car coming to a stop.
To stop a vehicle, brakes do work to transform Ek into heat. This work = braking force x braking distance.
Speed and Stopping Distance
To stop a vehicle, brakes do work to transform Ek intoheat. This work = braking force x braking distanceEk = Ew = Fd
The kinetic energy depends on the mass and the squareof velocity of the object so as speed increases kineticenergy increases and therefore braking distanceincreases.
Speed and Stopping Distance
Thinking distance = speed x reaction timeBraking distance = speed x braking time
Total stopping distance = thinking distance +braking distance
Look at the graph of velocity against timefrom the moment the driver first sees ahazard until the moment the car comes torest.
velocity(m/s)
00
time (s)0.6 3
16
velocity(m/s)
00
time (s)0.6 3
16
Here, the driver has noticed the hazard but has not yet reacted. The distance travelled is reaction time x speed.
The reaction time is 0.6 s
Why is the graph in two distinct sections?
velocity(m/s)
00
time (s)0.6 3
16
Here, the driver is braking to astop. The braking distance is thedistance travelled while applyingthe brakes.
Why is the graph in two distinct sections?
Use the graph to
- calculate the thinking distance - calculate the car’s braking distance- calculate the car’s overall stopping
distance.
How is stopping distance affected by speed?
Stopping distances
050
100150200250300350400450500
0 50 100 150 200 250
Speed in km per hour
Dis
tanc
e in
met
res
Stoppingdistance
Brakingdistance
Thinkingdistance
Stopping distances
050
100150200250300350400450500
0 50 100 150 200 250
Speed in km per hour
Dis
tanc
e in
met
res
Stoppingdistance
Brakingdistance
Thinkingdistance
Kinetic energy is linked to the square of the velocity
Key words: gravitational potential energy,mass, gravitational field strength, kineticenergy, mass, velocity, input and outputenergy and power, efficiency
By the end of this lesson you will be able
to:Carry out calculations involving therelationship between efficiency and outputpower, output energy and input power,
inputenergy.
Energy Transformations & Efficiency
There are many occasions where energy is
transformed from one form to another.
For example: an electric motortransforms electrical energy in kineticenergy; a light bulb transforms electricalenergy into light energy.
Energy Transformations & Efficiency
However, in these examples, not all theelectrical energy is converted into theuseful form we want!
Some energy may be transformed intoheat, due to friction, and sound. Energy is notlost (the law of conservation of energy) howeverit has been “wasted” because it is not in a usefulform.
Energy Transformations & Efficiency
The efficiency of a machine (or energyconverter) is measured byexpressing the useful energy output as
apercentage of total energyinput.
Energy Transformations & Efficiency
1
100x
input energy totaloutput energy useful
efficiency %
Power & Efficiency
1
100x
input poweroutput power
efficiency %
Virtual Int 2 Physics – Mechanics & Heat – Work, Energy & Power - Efficiency – Example Problem
Conservation of Energy
Energy can neither be created nordestroyed – simply transformed from
oneform into another.
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