National 4/5 Physics In addition to set homework you will be expected to finish off class notes and regularly review work against the 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 are completed and examples attempted.

In unit 1 we will learn about the physics of motion. We will focus on the language, principles and laws which describe and explain the motion of an object. Kinematics, also known as Mechanics is the science of describing the motion of objects using words, diagrams, numbers, graphs and equations. Print for lab books The goal is to develop mental models which describe and explain the motion of real-world objects.

Key words: vectors, scalars, distance, displacement, speed, velocity. By the end of this section you will be able to: Describe what is meant by vector and scalar quantities State the difference between distance and displacement State the difference between speed and velocity State that force is a vector quantity Use a scale diagram to find the magnitude and direction of the resultant of two forces acting at right angles to each other. Tuesday 28th August Initial lesson only 25 minutes with class moves etc

Key words: average speed By the end of this section 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? metres gallons miles per hour seconds minutes amperes miles kilometres per second miles per minute watts metres per second Newtons

Speeds in…. In Physics we normally use units m/s for velocity.

Average speed (m/s) High speed train Snail Sound 270 m/s 13.4 m/s UK town Fast jet 747 jumbo jet 10.3 m/s 29790 m/s 97 m/s Air molecule Earth in orbit Falcon 60 m/s 648 m/s 7500 m/s Olympic sprinter UK motorway Earth satellite 500 m/s Can you match the correct speeds 300000000 m/s 340 m/s Walking speed Light speed Concorde 1.7 m/s 31 m/s 833 m/s

Average speed ( m/s ) Light speed 300000000 m/s Earth in orbit Earth satellite 7500 m/s Fast jet 833 m/s Concorde 648 m/s Air molecule 500 m/s Sound 340 m/s 747 jumbo jet 270 m/s Falcon 97 m/s High speed train 60 m/s UK motorway 31 m/s UK town 13.4 m/s Familiarisation with realistic speeds in m/s to aid calculations. Olympic sprinter 10.3 m/s Walking speed 1.7 m/s Snail 0.006 m/s

What is speed? When we talk about speed we mean… the distance covered by an object in a given 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

What is speed? If you forget the formula think of cars travelling at 30 kilometres per hour km Per Hour =

Key words: average speed By the end of this section 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 speed = ?

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 speed = ? d = speed x t

d = speed x t Step 3: substitute in your values. d = 100 m t = 12 s

d = speed x t 100 = speed x 12 Step 4: rearrange d = 100 m t = 12 s

d = speed x t 100 = speed x 12 speed = = 8.33 100 12 Step 5: calculate d = 100 m t = 12 s speed = ? 100 12

d = speed x t 100 = speed x 12 Speed = = 8.33 m/s 100 12 Step 6: units!!!! d = speed x t 100 = speed x 12 Speed = = 8.33 m/s d = 100 m t = 12 s speed = ? 100 12

Key words: average speed, instantaneous By the end of this section you will be able to: Describe how to measure instantaneous speed. Identify situations where average speed and instantaneous speed are different.

Instantaneous and average speed Are instantaneous and average speed the same?

Instantaneous or average? A car’s speed between North Berwick and Edinburgh 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

Scalars and Vectors Imagine a boat making a distress call to the coastguard. The boat tells the coastguard he is 60 km from Aberdeen.

Scalars and Vectors Is this enough information for the coastguard to find the boat?

Scalars and Vectors

distance (size) direction 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 only magnitude (size). It is defined by a number and a unit. A vector is a quantity which has magnitude (size) and direction. It is defined by a number, a unit and a direction. Print for lab books

Distance and Displacement A 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? 500 m 300 m 400 m

Distance and Displacement The girl has walked 500 m. Her brother has walked 700 m. Distance is a scalar quantity – it can be defined simply by a number and unit. 500 m 300 m 400 m

Distance and Displacement Distance is simply a measure of how much ground an object has covered. 500 m 300 m 400 m

Distance and Displacement But how far out of place is the girl? And her brother? Displacement is a vector which requires number, unit and direction. 500 m 300 m 400 m

Distance and Displacement The girl has a displacement of 500 m at a bearing of 117° East of North. 500 m 300 m 400 m

Distance and Displacement What is her brother’s displacement? 500 m 300 m 400 m

Distance and Displacement Her brother has a displacement of 500 m at a bearing of 117° (117° East of North). 500 m 300 m 400 m

Distance and Displacement Their displacement (how far out of place they each are) is the same. 500 m 300 m 400 m

Speed and Velocity Speed is a scalar quantity requiring only magnitude (number and unit). Velocity is a vector, requiring magnitude and direction. Print for lab books

Speed and Velocity Speed tells us how fast an object is moving. Velocity tells us the rate at which an object changes position. Print for lab books http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/1DKin/U1L1d.html Physics animations?

Speed and Velocity Imagine a person stepping one step forward, then one step back at a speed of 0.5 ms-1. What is the person’s velocity? Remember velocity keeps track of direction. The direction of the velocity is the same as the direction of displacement.

Speed and Velocity Print for lab books

Key words: vectors, scalars, distance, displacement, speed, velocity. By the end of this section you will be able to: Describe what is meant by vector and scalar quantities State the difference between distance and displacement State the difference between speed and velocity State that force is a vector quantity Use a scale diagram to find the magnitude and direction of the resultant of two forces acting at right angles to each other. Wednesday 29th August

Distance and Displacement

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 24                                                           The physics teacher walked a distance of 12 meters in 24 seconds; thus, her average speed was 0.50 m/s. However, since her displacement is 0 meters, her average velocity is 0 m/s. Remember that the displacement refers to the change in position and the velocity is based upon this position change. In this case of the teacher's motion, there is a position change of 0 meters and thus an average velocity of 0 m/s.

Scalar or Vector?

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 and displacement State the difference between speed and velocity State that force is a vector quantity Use a scale diagram to find the magnitude and direction of the resultant of two forces acting at right angles to each other. Thursday 30th August.

Vectors Vectors can be represented by a line drawn in a particular direction. The length of the line represents the magnitude of the vector. The direction of the line represents the direction of the vector.

Addition of Vectors When two or more scalars are added together, the result is simply a numerical sum. For example a mass of 3kg and a mass of 5 kg, when added, make a mass of 8kg.

Addition of Vectors 8 N When two or more vectors are added together, providing they act in the same direction, the addition is straightforward. 5 N 3 N 8 N

Addition of Vectors 2 N If they are acting in opposite directions 5 N

Key words: vectors, resultant By the end of this section you will be able to: Use Pythagoras and Trigonometry to find the magnitude and direction of the resultant of two forces acting at right angles to each other. Thursday 30th August

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 this down at the start 2 Take the direction to the top of the page as North. Draw a small compass to show this. 3 Draw the first vector ensuring it is the correct length to represent the magnitude of the vector, and it is the correct direction.

To find the resultant of a set of vectors using a scale diagram Draw an arrow to represent the second vector starting at the head of the first. Vectors are always added head to tail. 5 The resultant vector can now be determined by drawing it on the diagram from the tail of the first to the head of the last vector. The magnitude and direction of this vector is 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 Scale: remember if the question is in ms-1 then your scale should be a conversion from cm to ms-1. Direction: draw compass on page 1st vector: length and direction 2nd vector: tail of 2nd starts at tip of first Resultant vector: tail of 1st to tip of last Answer must include magnitude (including units) and direction Print for lab books

Scale Diagrams Direction should be given as a three figure bearing from North e.g. 045° or 175° or 035° If you give any other angle, you must clearly mark it on the scale diagram. Print for lab books

A car travels 100 km South, then 140 km East. The time taken for the whole journey is 3 hours. Using a scale diagram (and the six step process) find the car’s total distance travelled its average speed its overall displacement its average velocity Review on board – pupils to come up and draw / write

Scale Diagrams Scale diagrams are used to find the magnitude and direction of the resultant of a number of a set of vectors.

The tropical island of Sohcahtoa

The tropical island of Sohcahtoa

The tropical island of Sohcahtoa

The tropical island of Sohcahtoa Print for lab books

hyp opp θ° adj Print for lab books

Tan = Opp/Adj; Cos= Adj/Hyp; The Old Arab Carried A Heavy Sack Of Hay Tan = Opp/Adj; Cos= Adj/Hyp; Sin=Opp/Hyp

hyp opp θ° adj

N + 3 km North E 4 km East Remember: The vectors above are not tip to tail. You must join them tip to tail

N R = ? + 3 km North  E 4 km East = Bearing of 053.10

We ADD vectors HEAD to TAIL [tip to toe] 6N 6N North, 8N East - what is the resultant force R ? We ADD vectors HEAD to TAIL [tip to toe] 8N 6N R  8N

Key words: acceleration, velocity By the end of this section you will be able to: Explain the term “acceleration” State that acceleration is the change in velocity per unit time Carry out calculations involving the relationship between initial velocity, final velocity, time and uniform acceleration.

Measuring Acceleration Activity What do you expect to happen to the value of acceleration as the light gate is moved further up the slope? Position of light gate from bottom of slope Acceleration (m/s2) 1st attempt 2nd attempt 3rd attempt Position 1 m Position 2 Position 3 Position 4 Average acceleration (m/s2) Print for lab books

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 1 second 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)

change in velocity in one second

Acceleration a = acceleration measured in m/s2 u = initial velocity measured in m/s v = final velocity measured in m/s t = time measured in s

Units of acceleration a = acceleration is measured in m/s2 final velocity – initial velocity a = 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 An object accelerates at a rate of 4 m/s2. What does this mean? The object goes 4 m/s faster each second.

Acceleration The object goes 4 m/s faster each second. If the object is initially at rest, what is its velocity after: 1s? 4 m/s 2s? 8 m/s 3s? 12 m/s 4s? 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 an acceleration of -2 m/s2 is becoming 2 m/s slower each second.

Acceleration Calculations A car, starting from rest, reaches a velocity of 18 m/s in 4 seconds. Find the acceleration of the car. What do I know? Initial velocity u = 0 m/s Final velocity v = 18 m/s time t = 4 s

Acceleration Calculations What do I know? Initial velocity u = 0 m/s Final velocity v = 18 m/s time t = 4 s Formula? Example on p5 to do themselves

Acceleration Calculations A cheetah starting from rest accelerates uniformly and can reach a velocity of 24 m/s in 3 seconds. What is the acceleration? 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 at 2 m/s. Calculate her acceleration. Use technique and show all working! Units!! What do you notice about her change in velocity?

Rearranging the acceleration equation v-u a t Pupils found rearranging the equation difficult!

Rearranging the acceleration equation v-u a t

Key words: acceleration, velocity By the end of this section you will be able to: Explain the term “acceleration” State that acceleration is the change in velocity per unit time Carry out calculations involving the relationship between initial velocity, final velocity, time and uniform acceleration. Graph results

Acceleration using two light gates The length of the mask is 5 cm. Calculate the acceleration. Remember calculate u (initial velocity) and v (final velocity) and use

Acceleration using a double mask The length of each section mask is 4 cm. The gap is also 4 cm. Calculate the acceleration. Remember calculate u (initial velocity) and v (final velocity) and use

Key words: acceleration, velocity, displacement By the end of this seection you will be able to: Draw velocity-time graphs of more than one constant motion. Describe the motions represented by a velocity-time graph. Calculate displacement and acceleration, from velocity-time graphs, for more than one constant acceleration. Tuesday 11th September

Graphing Motion Information about the motion of an object can be obtained from velocity-time graphs. Similarly, we can graph motion based on descriptions of the motion of an object.

Velocity-time graph The motion of a moving object can be represented on a velocity – time graph. Virtual Int 2 Physics – can pupils predict – remember area under speed time graph = distance, so area under velocity time graph = displacement.

Vectors and Direction direction. When dealing with vector quantities we must have both magnitude and direction. When dealing with one-dimensional kinematics (motion in straight lines) we use + and – to indicate travel in opposite directions. We use + to indicate acceleration and – to indicate deceleration.

Velocity-Time Graphs Describe the motion of this object. Constant velocity – does not change with time

Velocity-Time Graphs Describe the motion of this object. Increasing with time – constant acceleration

Velocity-Time Graphs Describe the motion of this object. Decreases with time – constant deceleration

Velocity-Time Graphs Describe the motion of this object.

Speed-Time Graphs Calculate the distance covered by the object in the first 10 s of its journey. The area under the graph tells us the distance travelled.

Speed-Time Graphs Calculate the distance covered by the object in the first 10 s of its journey. The area under the graph tells us the distance travelled.

Describe the effects of forces in terms of their ability to Key words: forces, newton balance, weight, mass, gravitational field strength. By the end of this section you will be able to: Describe the effects of forces in terms of their ability to change 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 an object. Distinguish between mass and weight. State that weight per unit mass is called the gravitational field 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 charged objects) act at a distance.

What is force? A force can change the shape of an object change the velocity of an object change the direction of travel of an object

Units of Force? Force (F) is measured in newtons (N).

Measuring Forces A Newton (or spring) balance can be used to measure Show newton balances – hang masses on and read off force.

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 up that object – how much matter, or how many 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 be measured 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 relationship between mass and weight 100g = 0.1 kg -> 1 N 1kg -> 10 N To convert kg -> N multiply by 10 To 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 each kilogram 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

A planet’s gravitational field strength is the pull of gravity on Definition A planet’s gravitational field strength is the pull of gravity on a 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 on different planets for a mass of 60 kg (a weight of 600 N on Earth). From this calculate the gravitational field strength for each planet.

Mass on Earth = 60 kg Weight on Earth = 600 N Gravitational 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 =

10 N / kg 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 greatest gravitational 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 m x g = W mass Gravitational field strength g weight

Weight, mass and gravity W = mg Why is weight measured in newtons? Gravitational field strength measured in N / kg Mass measured in kg Weight measured in newtons

Key words: friction, force By the end of this section you will be able to: State that the force of friction can oppose the motion of an object. Describe and explain situations in which attempts are made to increase or decrease the force of friction. 18th September 2007

Frictional Forces Moving vehicles such as cars can slow down due to forces acting on them. These forces can be due to… road surface and the tyres the brakes air resistance.

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 increase friction. Some examples of this are: Car brakes – we need friction between the brake shoes and the drum to slow the car down Bicycle tyres – we need friction to give “grip” on the surface

Increasing Friction On the approach to traffic lights and roundabouts, different road surfaces are used to increase friction compared with normal roads.

Decreasing Friction In some cases, we want to decrease friction. Some examples of this are: Ice skating Skiing Aircraft design

Reducing Friction Friction can be reduced by: Lubricating the surfaces – this generally means using oil between two metal surfaces. This is done in car engines to reduce wear on the engine – metal parts aren’t in contact because of a thin layer of oil between them.

Reducing Friction Friction can be reduced by: Separating surfaces with air (e.g. a hovercraft). Making surfaces roll (e.g. by using ball bearings).

Reducing Friction Friction can be reduced by: Streamlining. Modern cars are designed to offer as little resistance (or drag) to the air as possible, reducing friction on the car.

Streamlining Cars, aeroplanes and rockets are streamlined (that is, have their drag coefficient reduced) by: Reducing the front area Having a smooth body shape

Key words: force, vector, balanced forces By the end of this section you will be able to: State that force is a vector quantity. State that forces which are equal in size but act in opposite directions on an object are called balanced forces and are equivalent to no force at all. Explain the movement of objects in terms of Newton’s first law.

Force and direction. Force is a vector quantity. What do we mean by this? To describe it fully we must have size and direction.

Balanced Forces F F Balanced forces are EQUAL FORCES which act in OPPOSITE DIRECTIONS. They CANCEL EACH OTHER OUT.

If balanced forces act on a STATIONARY OBJECT, it REMAINS STATIONARY. 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.

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 m hangs from a rope. What is the weight of the mass? In what direction does this act? W = mg downwards m

Forces and Supported Bodies The mass is stationary. Newton’s law tells us that the forces must be balanced forces. The weight is counterbalanced by a force of the same size acting upwards due to the tension in the string. m

Forces and Supported Bodies A book of mass m rests on a shelf. What is the weight of the book? In what direction does this act? W = mg downwards m

Forces and Supported Bodies The mass is stationary. Newton’s law tells us that the forces must be balanced forces. The weight is counterbalanced by a force of the same size acting upwards due to the shelf. m

What forces are acting on this stationary hovering helicopter? lift = W = mg W = mg

Newton’s First Law Newton’s first law tells us that when the forces on an object are balanced, a stationary object will remain stationary. But it also says that if when forces are balanced, an object moving at constant velocity will continue in the same direction with the same velocity.

The ENGINE FORCE and the FRICTION FORCE must be equal. A moving car If 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 Belts If 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. http://www.thinkseatbelts.com/

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 bags Air 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.

Forces in a Fluid Terminal velocity Any free-falling object in a fluid (liquid or gas) reaches a top speed, called ‘terminal velocity’.

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)

a = -10 m/s2 time = 0s, velocity = 0 m/s, friction = 0 N Friction Ff(air resistance) = 0 N a = -10 m/s2 W = weight

Ff a < -10 m/s2 v W = weight

Equal & opposite forces Acceleration zero Terminal velocity Ff a = 0 m/s2 v W = weight

Velocity – Time Graph velocity (m/s) Terminal velocity time (s)

air resistance Terminal velocity is reached when the air resistance balances the weight. weight

Terminal Velocity What effect does opening a parachute have on the terminal velocity? When the parachute is opened, air resistance increases a lot. There is now an unbalanced force upwards, which causes deceleration. The velocity decreases, and the air resistance decreases until the forces are balanced again. The parachutist falls to the ground with a lower terminal velocity.

Key words: Newton’s second law, unbalanced forces, mass, force, acceleration By the end of this section you will be able to: Describe the qualitative effects of the change of mass or of force on the acceleration of an object Define the newton Carry out calculations using the relationship between a, F and m and involving more than one 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.

Force, mass and acceleration Acceleration (m/s2) F = ma Force (N) mass (kg)

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 = 4kg a = 5m/s2 F = ma F= 4 x 5 F = 20 N

Key words: free body diagrams, resultant force By the end of this section you will be able to: Use free body diagrams to analyse the forces on an object State what is meant by the resultant of a number of forces Use a scale diagram, or otherwise, to find the magnitude and direction of the resultant of two forces acting at right angles to each other.

Newton’s First Law A body remains at rest, or continues at constant velocity, unless acted upon by an external unbalanced force. (that is objects have a tendency to keep doing what they are doing)

Newton’s Second Law Newton’s Second Law is about the behaviour of objects when forces are not balanced. The acceleration produced in a body is directly proportional to the unbalanced force applied and inversely proportional to the mass of the body.

Newton’s Second Law In practice this means that the acceleration produced increases as the unbalanced force increases the acceleration decreases as the mass of the body increases

Which forces? An object may be acted upon by a number of forces but only an overall unbalanced force will lead to acceleration in the direction of that force.

Forces are measured in…? Newton’s Second Law can be written as or more commonly

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 to accelerate at 1m/ s2

Quick Quiz 5 10 5 10 1 Unbalanced force (N) Mass (kg) Acceleration (m/ s2) 10 2 20 4 5 5 10 5 10 1

Direction of force To the right To the right Consider the oil drop trail left by the car in motion. In which direction is the acceleration? In which direction is the unbalanced force? 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 unbalanced force? 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 Diagrams Free body diagrams are special examples of a vector diagram. They show the relative magnitude and direction of all forces acting on an object. They are used to help you identify the magnitude and direction of an unbalanced Force acting on an object. Weight

Using Newton’s Second Law In the simplest case m Fun

Using Newton’s Second Law Direction of acceleration? Direction of unbalanced force? Formula for calculating acceleration? m F1 F2 Fu

Solving Problems Always draw a diagram showing all known quantities (forces – magnitude and direction, resultant acceleration and direction, mass of object(s) ) Remember that Fun=ma can be applied to the whole system When working in the vertical direction always include the weight

Key words: acceleration, gravitational field strength, projectiles By the end of this section you will be able to: Explain the equivalence of acceleration due to gravity and gravitational field strength Explain the curved path of a projectile in terms of the force of gravity Explain how projectile motion can be treated as two separate motions Solve numerical problems using the above method for an object projected horizontally.

Acceleration due to Gravity Definition: 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 -

Acceleration due to Gravity Near a planet’s surface all objects experience the same gravitational acceleration. This acceleration is numerically equal to the planet’s gravitational field strength.

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?

Gravitational field strength Is the gravitational field strength the same on each planet? How does distance affect gravitational field strength? It decreases the further away you are from the planet’s surface. What will happen to the weight of an object as it gets further from the surface? Explain your answer. It will decrease.

The force of gravity near the Earth’s surface gives all objects the same acceleration. So why doesn’t the feather reach the ground at the same time as the elephant?

Why are the gaps between the balls increasing?

An object is released from rest close to the Earth’s surface. Which formula can be used to find its velocity at a given time? v = u + at where 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

Forces acting on projectiles What would happen to a ball kicked off a cliff, in the absence of gravity?

Forces acting on projectiles There would be no vertical motion therefore the ball would continue at constant speed in a straight line (remember Newton’s first law)

Objects projected horizontally Think about… What is the initial vertical speed of a projectile 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 horizontally Think about… Describe the vertical motion of an object projected horizontally: It will accelerate downwards due to gravity.

Objects projected horizontally Think about… What formula can be used to find the horizontal displacement of an object fired horizontally if horizontal velocity and time of flight are known? time of flight (s) horizontal displacement (m) sh = vht horizontal velocity (m/s)

Which ball will hit the ground first? http://www.fearofphysics.com/XYIndep/xyindep_correct.html

Summary Horizontal motion Vertical motion Forces Are there forces present? If so, in what direction are they acting? No Yes The force of gravity acts downward Acceleration Is there acceleration? If so, in what direction? What is the value of the acceleration? Acceleration = "g" downward at 10 m/s2 Velocity Constant 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 a cliff top, at a horizontal speed of 40 m/s. The flare takes 4 s to reach the sea. 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 + at v = 0 + 10 x 4 v = 40 m/s

Example (c) Draw a graph to show how vertical speed varies with time. Initial vertical speed = 0 m/s Final vertical speed = 40 m/s

Example (d) Use this graph to calculate the height of the cliff. Displacement = area under velocity-time graph ½ bh = ½ x 4 x 40 = 80 m Height of cliff = 80 m

Key words: Newton’s third law, newton pairs By the end of this section you will be able to: State Newton’s third law Identify “Newton pairs” in situations involving several forces State that momentum is the product of mass and 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

Firing a gun Force of GUN on BULLET Force of BULLET on GUN

Force of RUNNER on BLOCKS Starting a sprint Force of RUNNER on BLOCKS Force of BLOCKS on RUNNER

A falling apple Force of EARTH on APPLE Force of APPLE on EARTH

A Rocket Force of GAS on ROCKET Force of ROCKET on GAS

Key words: work done, energy, force, distance, power, time By the end of this section you will be able to: State that work done is a measure of the energy transferred. Carry out calculations involving the relationship between work done, force and distance. relationship between work done, power and time.

Work done? What is meant by work done in Physics? When a force acts upon an object to cause a displacement of the object, it is said 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 done work on an object, there must be a displacement and the force must cause the displacement. Note; at this level, we can use distance instead of displacement.

Work done? Formula linking work done, force and displacement? Examples of work done? a horse pulling a plough through the field a shopper pushing a grocery cart down the aisle of a supermarket a pupil lifting a backpack full of books upon her shoulder a weightlifter lifting a barbell above his head an Olympian launching the shot-put, etc. In each case described here there is a force exerted upon an object to cause that object to be displaced.

Work done A dog pulls a 4 kg sledge for a distance on 15 m using a force of 30 N. How much work does he do? What do I know? F = 30N d = 15m

Work done What do I know? F = 30N d = 15m Formula?

Power Power is the rate of doing work i.e. if work is done then the work done per second is the power. Energy in joules time in seconds Power in watts (joules per 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 = 30N d = 15m t = 20s

Power What do I know? F = 30N d = 15m t = 20s Formula?

Power What do I know? F = 30N d = 15m t = 20s Ew = 450J Formula?

By the end of this section you will be able to: Key words: gravitational potential energy, mass, gravitational field strength, kinetic energy By the end of this section you will be able to: Carry out calculations involving the relationship between change in gravitational potential energy, mass, gravitational field strength and change in height. between kinetic energy, mass and velocity.

Gravitational Potential Energy …is the potential energy gained by an object when we do work to lift it vertically in a gravitational field.

Gravitational Potential Energy The work done in lifting an object vertically What force is required?

Gravitational Potential Energy To lift the object we must overcome the weight W=mg

Gravitational Potential Energy Vertical distance – we call this height h

Gravitational Potential Energy

…is the energy associated with a moving object. Kinetic Energy …is the energy associated with a moving object.

Kinetic Energy depends on… The mass of the object

Kinetic Energy depends on… The velocity of the object

Kinetic Energy