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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.

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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. The goal is to develop mental models which describe and explain the motion of real-world objects.

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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.

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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.

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Which of these are units of speed? miles per hour gallons Newtons seconds metres amperes miles minutes metres per second kilometres per second watts miles per minute

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

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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 m/s 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 m/s

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

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

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What is speed? If Hamish (the dog) runs 10 metres in 2 seconds, what is his speed?

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What is speed? His speed is 5 metres per second. So speed is

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

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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.

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distance speed time

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Speed Calculations A cyclist travels 100 m in 12 s. What is her speed?

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Step 1: write down what you know. d = 100 m t = 12 s speed = ?

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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

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

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

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

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

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Key words: average speed, instantaneous speed 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.

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

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Instantaneous or average? A cars speed between North Berwick and Edinburgh Average

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Instantaneous or average? The speed read from a cars speedometer Instantaneous

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Instantaneous or average? A tennis balls speed as it crosses the net Instantaneous

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Instantaneous or average? A racing cars speed over a lap of the track Average

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Instantaneous or average? A parachutists speed as he/she lands Instantaneous

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

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

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Scalars and Vectors

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The coastguard needs both distance (size) and direction to find the boat.

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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.

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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

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

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

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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

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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

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Distance and Displacement What is her brothers displacement? 500 m 300 m 400 m

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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

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

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

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Speed and Velocity Speed tells us how fast an object is moving. Velocity tells us the rate at which an object changes position.

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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 persons velocity? Remember velocity keeps track of direction. The direction of the velocity is the same as the direction of displacement.

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Speed and Velocity

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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.

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Distance and Displacement

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Speed and Velocity

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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.

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The physics teacher walked a distance of 12 meters in 24distance 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 todisplacement 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.

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Scalar or Vector?

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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.

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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.

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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.

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Addition of Vectors When two or more vectors are added together, providing they act in the same direction, the addition is straightforward. 5 N3 N 8 N

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Addition of Vectors If they are acting in opposite directions 5 N3 N 2 N

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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.

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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.

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

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To find the resultant of a set of vectors using a scale diagram 4.Draw an arrow to represent the second vector starting at the head of the first. Vectors are always added head to tail. 5The 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. 6The final answer must have magnitude and direction – either a bearing from North or an angle marked clearly on the diagram

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Scale Diagrams 1.Scale: remember if the question is in ms -1 then your scale should be a conversion from cm to ms Direction: draw compass on page 3.1 st vector: length and direction 4.2 nd vector: tail of 2 nd starts at tip of first 5.Resultant vector: tail of 1 st to tip of last 6.Answer must include magnitude (including units) and direction

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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.

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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 (a)the cars total distance travelled (b)its average speed (c)its overall displacement (d)its average velocity

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

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The tropical island of Sohcahtoa

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The tropical island of Sohcahtoa

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The tropical island of Sohcahtoa

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The tropical island of Sohcahtoa

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θ°θ° adj hyp opp

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

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θ°θ° adj hyp opp

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

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

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

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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.

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

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What is acceleration? Acceleration is the change in velocity of an object per second (in one second). Is acceleration a vector or scalar quantity?

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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.

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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/s 2 change in speed in one second

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Calculating acceleration We need to know… the change in velocity so… initial velocity (u) final velocity (v) and… time (t)

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change in velocity in one second

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Acceleration a = acceleration measured in m/s 2 u = initial velocity measured in m/s v = final velocity measured in m/s t = time measured in s

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Units of acceleration a = final velocity – initial velocity time acceleration is measured in m/s 2 If the speed is measured in kilometres per hour, acceleration can be measured in kilometres per hour per second.

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Acceleration An object accelerates at a rate of 4 m/s 2. What does this mean? The object goes 4 m/s faster each second.

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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

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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/s 2 is becoming 2 m/s slower each second.

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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

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

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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!!

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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?

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Rearranging the acceleration equation v-u a t

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Rearranging the acceleration equation v-u a t

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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

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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

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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

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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.

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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.

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Velocity-time graph The motion of a moving object can be represented on a velocity – time graph.

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Vectors and 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.

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Velocity-Time Graphs Constant velocity – does not change with time 0 0 Describe the motion of this object.

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Velocity-Time Graphs Increasing with time – constant acceleration 0 0 Describe the motion of this object.

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Velocity-Time Graphs Decreases with time – constant deceleration 0 0 Describe the motion of this object.

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Velocity-Time Graphs 0 0 Describe the motion of this object.

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Speed-Time Graphs 0 0 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.

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Speed-Time Graphs 0 0 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.

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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 Earths 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.

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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.

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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

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

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Measuring Forces A Newton (or spring) balance can be used to measure forces.

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Mass and Weight We often use the words mass and weight as though they mean the same… but do they?

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Mass and Weight An objects 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.

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Mass and Weight An objects weight is the force exerted by gravity on a mass. Since it is a force, weight must be measured in newtons.

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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.

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Results Mass Weight in N 100g 200g 300g 400g 500g 1kg 2kg 5kg

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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

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Gravitational Field Strength (g) Gravitational field strength on Earth is 10 N / kg

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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

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What is gravitational field strength? and the pull of gravity on a 2 kg mass is 20 N

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Definition A planets gravitational field strength is the pull of gravity on a 1 kg mass.

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Gravity in the universe Is gravitational field strength always the same? No! It varies on different planets.

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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.

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Mass on Earth = 60 kg Weight on Earth = 600 N Gravitational field strength = Weight on Mercury = Ng = Weight on Venus = Ng = Weight on the Moon = 99.6 Ng = Weight on Mars = Ng = Weight on Jupiter = Ng = Weight on Saturn = Ng =

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Units for g We found g by dividing weight in newtons by mass in kilograms. What are the units for g? 10 N / kg

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Which of the planets has the greatest gravitational field strength? Why do you think this is the case?

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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 massGravitational field strength gweight m x g = W

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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?

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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.

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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.

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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.

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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

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

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

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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 arent in contact because of a thin layer of oil between them.

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

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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.

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

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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 Newtons first law.

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

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

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If balanced forces act on a STATIONARY OBJECT, it REMAINS STATIONARY. F F If balanced forces act on a MOVING OBJECT, it continues moving in the same direction with CONSTANT VELOCITY. F F

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This is summarised by NEWTONS 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.

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To understand NEWTONS 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).

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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?

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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

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Forces and Supported Bodies The mass is stationary. Newtons 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

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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

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Forces and Supported Bodies The mass is stationary. Newtons 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

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

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Newtons First Law Newtons 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.

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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 forceFriction force

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Newtons 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 cars 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.

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No seatbelt – whats going to happen when the car hits the wall? Explain this in terms of Newtons 1 st law.

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Whats going to happen when the motorbike hits the wall? Explain this in terms of Newtons 1 st law.

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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.

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

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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 persons weight (acting downwards)

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W = weight Friction F f (air resistance) = 0 N time = 0s, velocity = 0 m/s, friction = 0 N a = -10 m/s 2

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W = weight FfFf a < -10 m/s 2 v

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W = weight FfFf a = 0 m/s 2 v Equal & opposite forces Acceleration zero Terminal velocity

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Velocity – Time Graph velocity (m/s) 0 0 time (s) Terminal velocity

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

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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.

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Key words: Newtons 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

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The example of the parachutist accelerating until the forces are balanced helps us to understand NEWTONS 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.

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Force, mass and acceleration F = ma Force (N) mass (kg) Acceleration (m/s 2 )

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Force, mass and acceleration One newton (1N) is the force required to accelerate 1 kg at 1 m/s 2

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F = ma Find the unbalanced force required to accelerate a 4 kg mass at 5 m/s 2 What do I know? m = 4kg a = 5m/s 2 F = ma F= 4 x 5 F = 20 N

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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.

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Newtons 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)

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Newtons Second Law Newtons 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.

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Newtons 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

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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.

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Forces are measured in…? Newtons Second Law can be written as or more commonly

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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/ s 2

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Quick Quiz Unbalanced force (N) Mass (kg)Acceleration (m/ s 2 )

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Direction of force 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

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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.

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Newtons First and Second Laws Remember Forces do not cause motion Forces cause acceleration

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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

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Using Newtons Second Law In the simplest case m F un

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Using Newtons Second Law m F1F1 F2F2 Direction of acceleration? Direction of unbalanced force? Formula for calculating acceleration? FuFu

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

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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.

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Acceleration due to Gravity Definition: A planets gravitational field strength equals the force of gravity PER UNIT MASS. Units? N/kg To calculate an objects weight, use this equation -

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

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For example, on Earth – g = 10 N/kg A free-falling object will experience acceleration of a = -10 m/ s 2 What does the –ve sign tell you?

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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 planets surface. What will happen to the weight of an object as it gets further from the surface? Explain your answer. It will decrease.

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The force of gravity near the Earths surface gives all objects the same acceleration. So why doesnt the feather reach the ground at the same time as the elephant?

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Why are the gaps between the balls increasing?

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An object is released from rest close to the Earths 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?

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Projectiles

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

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

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What is the initial vertical speed of a projectile fired horizontally? How will the horizontal speed vary during the objects flight? 0 m/s It will remain the same as the initial horizontal speed. Objects projected horizontally Think about…

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Describe the vertical motion of an object projected horizontally: It will accelerate downwards due to gravity. Objects projected horizontally Think about…

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

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Which ball will hit the ground first?

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Summary Horizontal motion Vertical motion Forces Are there forces present? If so, in what direction are they acting? NoYes The force of gravity acts downward Acceleration Is there acceleration? If so, in what direction? What is the value of the acceleration? NoYes Acceleration = "g" downward at 10 m/s 2 Velocity Constant or changing? ConstantChanging by 10 m/s each second

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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 isnt a test of memory so while you should learn your formulae, dont 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.

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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. (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.

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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/s 2 timet = 4 s v = u + at v = x 4 v = 40 m/s

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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

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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

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Key words: Newtons third law, newton pairs By the end of this section you will be able to: State Newtons 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.

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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.

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Newtons 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

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

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

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

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

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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. Carry out calculations involving the relationship between work done, power and time.

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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.

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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.

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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.

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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

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

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Power Power is the rate of doing work i.e. if work is done then the work done per second is the power. Power in watts (joules per seconds) Energy in joules time in seconds

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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

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

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

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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. Carry out calculations involving the relationship between kinetic energy, mass and velocity.

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

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

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

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Gravitational Potential Energy Vertical distance – we call this height h

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Gravitational Potential Energy

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

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Kinetic Energy depends on… The mass of the object

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depends on… The velocity of the object Kinetic Energy

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