Understanding Speed and Velocity Concepts

Speed vs. Velocity 04/01/2020 1) Is this car travelling at constant speed? 2) Is this car travelling at constant velocity?

Vector vs. scalar Scalar quantities have size (“magnitude”) only and no direction. Vector quantities have both size and direction. Scalar or vector??? Scalar Vector 2. Distance 10. Acceleration 1. Mass 6. Energy 7. Time 3. Displacement 4. Speed 9. Force 8. Current 5. Velocity

Distance, Speed and Time 04/01/2020 Speed = distance (in metres) time (in seconds) D S T • Freddie walks 200 metres in 40 seconds. What is his speed? • Hayley covers 2km in 1,000 seconds. What is her speed? • How long would it take Lauren to run 100 metres if she runs at 10m/s? • Jake travels at 50m/s for 20s. How far does he go? • Izzy drives her car at 85mph (about 40m/s). How long does it take her to drive 20km? 5m/s 2m/s 10s 1000m 500s

Distance, Speed and Time 04/01/2020 Speed = distance (in metres) time (in seconds) D S T • Sarah walks 2000m in 50 minutes. What is her speed in m/s? • Jack tries to walk the same distance at a speed of 5m/s. How long does he take? • James drives at 60mph (about 100km/h) for 3 hours. How far has he gone? • The speed of sound in air is 330m/s. Molly shouts at a mountain and hears the echo 3 seconds later. How far away is the mountain? (Careful!) 0.67m/s 400s 300km 495m

Distance-time graphs 04/01/2020 • 2) Horizontal line = • 4) Diagonal line downwards = • Diagonal line = • 3) Steeper diagonal line = 40 30 20 10 0 Distance (metres) Time/s 20 40 60 80 100

40 30 20 10 0 04/01/2020 Distance (metres) Time/s 20 40 60 80 100 0.5m/s • What is the speed during the first 20 seconds? • How far is the object from the start after 60 seconds? • What is the speed during the last 40 seconds? • When was the object travelling the fastest? 40m 1m/s 40-60s

Acceleration 04/01/2020 V-U Acceleration = change in velocity (in m/s) (in m/s2) time taken (in s) A T • A cyclist accelerates from 0 to 10m/s in 5 seconds. What is her acceleration? • A ball is dropped and accelerates downwards at a rate of 10m/s2 for 12 seconds. How much will the ball’s velocity increase by? • A car accelerates from 10 to 20m/s with an acceleration of 2m/s2. How long did this take? • A rocket accelerates from 1,000m/s to 5,000m/s in 2 seconds. What is its acceleration? 2m/s2 120m/s 5s 2000m/s2

Acceleration V-U Acceleration = change in velocity (in m/s) (in m/s2) time taken (in s) A T 04/01/2020 • Will accelerates from standstill to 50m/s in 25 seconds. What is his acceleration? • Pierre accelerates at 5m/s2 for 5 seconds. He started at 10m/s. What is his new speed? • Elliott is in trouble with the police. He is driving up the A29 and sees a police car and brakes from 50m/s to a standstill. His deceleration was 10m/s2. How long did he brake for? • Another boy racer brakes at the same deceleration but only for 3 seconds. What speed did he slow down to? 2m/s2 35m/s 5s 20m/s

Velocity-time graphs 04/01/2020 • 1) Upwards line = • 4) Downward line = • 2) Horizontal line = • 3) Upwards line = 80 60 40 20 0 Velocity m/s T/s 10 20 30 40 50

80 60 40 20 0 04/01/2020 Velocity m/s T/s 10 20 30 40 50 • How fast was the object going after 10 seconds? • What is the acceleration from 20 to 30 seconds? • What was the deceleration from 30 to 50s? • How far did the object travel altogether? 40m/s 2m/s2 3m/s2 1700m

80 60 40 20 0 04/01/2020 Velocity m/s T/s 10 20 30 40 50 • How fast was the object going after 10 seconds? • What is the acceleration from 20 to 30 seconds? • What was the deceleration from 40 to 50s? • How far did the object travel altogether? 10m/s 4m/s2 6m/s2 1500m

80 60 40 20 0 04/01/2020 Velocity m/s T/s 10 20 30 40 50 This velocity-time graph shows Coryn’s journey to school. How far away does she live? 2500m

Introduction to Forces A force is a “push” or a “pull”. Some common examples: Air resistance/drag – a contact force that acts against anything moving through air or liquid Weight (mg) – pulls things towards the centre of the Earth Friction – a contact force that acts against anything moving Upthrust – keeps things afloat

Free body force diagrams direction on what what type size The Earth pulls Newton down with a gravitational force of 700N. Newton pulls the Earth up with a gravitational force of 700N. Action and reaction are equal and opposite!!

Balanced and unbalanced forces 04/01/2020 Reaction Consider a camel standing on a road. What forces are acting on it? These two forces would be equal – we say that they are BALANCED. The camel doesn’t move anywhere. Weight

Balanced and unbalanced forces 04/01/2020 Reaction What would happen if we took the road away? Weight

Air Resistance 04/01/2020 Air resistance is a force that opposes motion through air. The quicker you travel, the bigger the air resistance: The same applies to a body falling through a liquid (called “drag” or “upthrust”).

Balanced and unbalanced forces 04/01/2020

Balanced and unbalanced forces 04/01/2020 1) This animal is either ________ or moving with _______ _____… 2) This animal is getting ________… 3) This animal is getting _______…. 4) This animal is also either _______ or moving with ________ ______.. Words - Stationary, faster, slower or constant speed?

Summary 04/01/2020 Complete these sentences… If an object is stationary and has NO resultant force on it the object will… If an object is stationary and a resultant force acts on it the object will… If an object is already moving and NO resultant force acts on it the object will… If an object is already moving and a resultant force acts on it the object will… …accelerate in the direction of the resultant force …continue to move at the same speed and the same direction …continue to stay stationary …accelerate in the direction of the resultant force

Resultant Force 04/01/2020 Calculate the resultant force of the following: 500N 100N 700N 600N 50N 700N 700N 800N 800N 200N 100N

Force and acceleration 04/01/2020 F M A If the forces acting on an object are unbalanced then the object will accelerate, like these wrestlers: Force (in N) = Mass (in kg) x Acceleration (in m/s2)

Force, mass and acceleration 04/01/2020 F M A • A force of 1000N is applied to push a mass of 500kg. How quickly does it accelerate? • A force of 3000N acts on a car to make it accelerate by 1.5m/s2. How heavy is the car? • A car accelerates at a rate of 5m/s2. If it weighs 500kg how much driving force is the engine applying? • A force of 10N is applied by a boy while lifting a 20kg mass. How much does it accelerate by? 2m/s2 2000kg 2500N 0.5m/s2

Weight vs. Mass 04/01/2020 W M g Earth’s Gravitational Field Strength is 10N/kg. In other words, a 1kg mass is pulled downwards by a force of 10N. Weight = Mass x Gravitational Field Strength (in N) (in kg) (in N/kg) 20N • What is the weight on Earth of a book with mass 2kg? • What is the weight on Earth of an apple with mass 100g? • James weighs 700N on the Earth. What is his mass? • On the moon the gravitational field strength is 1.6N/kg. What will James weigh if he stands on the moon? 1N 70kg 112N

Terminal Velocity 04/01/2020 Consider a skydiver: • At the start of his jump the air resistance is _______ so he _______ downwards. 2) As his speed increases his air resistance will _______ 3) Eventually the air resistance will be big enough to _______ the skydiver’s weight. At this point the forces are balanced so his speed becomes ________ - this is called TERMINAL VELOCITY Words – increase, small, constant, balance, accelerates

Terminal Velocity 04/01/2020 Consider a skydiver: • 4) When he opens his parachute the air resistance suddenly ________, causing him to start _____ ____. 5) Because he is slowing down his air resistance will _______ again until it balances his _________. The skydiver has now reached a new, lower ________ _______. Words – slowing down, decrease, increases, terminal velocity, weight

Velocity-time graph for terminal velocity… 04/01/2020 Parachute opens – diver slows down Speed increases… Terminal velocity reached… On the Moon New, lower terminal velocity reached Diver hits the ground Velocity Time

Topic 4 – Momentum, Energy, Work and Power 04/01/2020

Stopping a car… 04/01/2020 What two things must the driver of the car do in order to stop in time?

Stopping a car… 04/01/2020 Thinking distance (reaction time) Braking distance Tiredness Too much alcohol Too many drugs Poor visibility Wet/icy roads Heavy vehicle Tyres/brakes worn out Driving too fast Total Stopping Distance = Thinking Distance + Braking Distance

Momentum 04/01/2020 Momentum = Mass x Velocity P (in kgm/s)(in kg)(in m/s) M V Any object that has both mass and velocity has MOMENTUM. Momentum (symbol “p”) is simply given by the formula: • What is the momentum of the following? • A 1kg football travelling at 10m/s • A 1000kg Ford Capri travelling at 30m/s • A 20g pen being thrown across the room at 5m/s • A 70kg bungi-jumper falling at 40m/s 10kgm/s 30,000kgm/s 0.1kgm/s 2800kgm/s

Conservation of Momentum 04/01/2020 Speed = 50m/s Speed = 20m/s Speed = ??m/s In any collision or explosion momentum is conserved (provided that there are no external forces have an effect). Example question: Two cars are racing around the M25. Car A collides with the back of car B and the cars stick together. What speed do they move at after the collision? Mass = 1000kg Mass = 800kg Mass = 1800kg Momentum before = momentum after… …so 1000 x 50 + 800 x 20 = 1800 x V… …V = 36.7m/s

Momentum in different directions 04/01/2020 Speed = 20m/s Mass = 1000kg Mass = 800kg Speed = 50m/s What happens if the bodies are moving in opposite directions? Momentum is a VECTOR quantity, so the momentum of the second car is negative… Total momentum = 1000 x 50 – 800 x 20 = 34000 kgm/s Speed after collision = 34000 kgm/s / 1800 = 18.9m/s

Another example 04/01/2020 α 241 237 Am Np 4 95 93 2 Consider the nuclear decay of Americium-241: If the new neptunium atom moves away at a speed of 5x105 m/s what was the speed of the alpha particle? 2.96x107 m/s

More questions… 04/01/2020 • A car of mass 1000kg heading up the M1 at 50m/s collides with a stationary truck of mass 8000kg and sticks to it. What velocity does the wreckage move forward at? • A defender running away from a goalkeeper at 5m/s is hit in the back of his head by the goal kick. The ball stops dead and the player’s speed increases to 5.5m/s. If the ball had a mass of 500g and the player had a mass of 70kg how fast was the ball moving? • A white snooker ball moving at 5m/s strikes a red ball and pots it. Both balls have a mass of 1kg. If the white ball continued in the same direction at 2m/s what was the velocity of the red ball? • A gun has a recoil speed of 2m/s when firing. If the gun has a mass of 2kg and the bullet has a mass of 10g what speed does the bullet come out at? 5.6m/s 70m/s 3m/s 400m/s

Recap question on momentum 04/01/2020 • Matt and Dan are racing against each other over 400m at Sports Day. Matt is running at 8m/s and catches up with Dan who is running at 6m/s. After the collision Matt stops and Dan moves slightly faster. If Matt’s mass is 60kg and Dan’s is 70kg calculate how fast Dan moves after the collision. • Bobbie is driving her 5kg toy car around. It is travelling at 10m/s when it hits the back of Heather’s (stationary) leg and sticks to it. Assuming Heather’s leg can move freely and has a mass of 10kg calculate how fast it will move after the collision. 12.9m/s 3.3m/s

Safety features 04/01/2020 How do air bags and crumple zones work? • Basically: • The change in momentum is the same with or without an airbag • But having an airbag increases the time of the collision and therefore reduces the “rate of change of momentum” • Therefore the force is reduced

Force and momentum Force = Change in momentum mv-mu (in kgm/s) (in N) Time (in s) F T Also called “impulse” Newton’s second law of motion says that the force acting on an object is that object’s rate of change of momentum. In other words… • For example, Ronaldo takes a free kick by kicking a stationary football with a force of 40N. If the ball has a mass of 0.5kg and his foot is in contact with the ball for 0.1s calculate: • The change in momentum of the ball (its impulse), • The speed the ball moves away with

Example questions • Paddy likes playing golf. He strikes a golf ball with a force of 80N. If the ball has a mass of 200g and the club is in contact with it for 0.2s calculate a) the change in momentum of the golf ball, b) its speed. • Courtney thinks it’s funny to hit tennis balls at Kit. She strikes a serve with a force of 30N. If the ball has a mass of 250g and the racket is in contact with it for 0.15s calculate the ball’s change in momentum and its speed. • Tom takes a dropkick by kicking a 0.4kg rugby ball away at 10m/s. If his foot was in contact with the ball for 0.1 seconds calculate the force he applied to the ball. • Jenny strikes a 200g golf ball away at 50m/s. If she applied a force of 50N calculate how long her club was in contact with the ball for. 16Kgm/s, 80m/s 4.5Kgm/s, 18m/s 40N 0.2s

Work done 04/01/2020 E F D When any object is moved around work will need to be done on it to get it to move (obviously). We can work out the amount of work done in moving an object using the formula: Work done=Forcexdistance moved in J in N in m

Example questions 04/01/2020 • Hannah pushes a book 5m along the table with a force of 5N. She gets tired and decides to call it a day. How much work did he do? • Courtney lifts a laptop 2m into the air with a force of 10N. How much work does she do? What type of energy did the book gain? • Tom does 200J of work by pushing a wheelbarrow with a force of 50N. How far did he push it? What type of energy did the wheelbarrow gain? • Dan cuddles his cat and lifts it 1.5m in the air. If he did 75J of work how much force did he use? • Simon drives his car 1000m. If the engine was producing a driving force of 2000N how much work did the car do? 25J 20J, GPE 4m, KE 50N 2MJ

Stopping a car… 04/01/2020 Recall our earlier situation regarding stopping distances…

Energy and Power E P T The POWER RATING of an appliance is simply how much energy it uses every second. In other words, 1 Watt = 1 Joule per second E = Energy (in joules) P = Power (in watts) T = Time (in seconds)

Some example questions • What is the power rating of a light bulb that transfers 120 joules of energy in 2 seconds? • What is the power of an electric fire that transfers 10,000J of energy in 5 seconds? • Rob runs up the stairs in 5 seconds. If he transfers 1,000,000J of energy in this time what is his power rating? • How much energy does a 150W light bulb transfer in a) one second, b) one minute? • Jonny’s brain needs energy supplied to it at a rate of 40W. How much energy does it need during a 50 minute physics lesson? • Lloyd’s brain, being more intelligent, only needs energy at a rate of about 20W. How much energy would his brain use in a normal day? 60W 2KW 0.2MW 150J, 9KJ 120KJ 1.73MJ

Gravitational Potential Energy GPE mg H To work out how much gravitational potential energy (GPE) an object gains when it is lifted up we would use the simple equation… GPE = Weight x Change in height (Joules) (newtons)(metres) (Remember - W=mg)

Some example questions… • How much gravitational potential energy have the following objects gained?: • A brick that weighs 10N lifted to the top of a house (10m), • A 1,000kg car lifted by a ramp up to a height of 2m, • A 70kg person lifted up 50cm by a friend. • How much GPE have the following objects lost?: • A 2N football dropping out of the air after being kicked up 30m, • A 0.5N egg falling 10m out of a bird nest, • A 1,000kg car falling off its 200cm ramp. 100J 20KJ 350J 60J 5J 20KJ

Kinetic energy 04/01/2020 Any object that moves will have kinetic energy. The amount of kinetic energy an object has can be found using the formula: Kinetic energy = ½ x mass x velocity squared in J in kg in m/s KE = ½ mv2

Example questions 04/01/2020 • Bex drives her car at a speed of 30m/s. If the combined mass of her and the car is 1000kg what is her kinetic energy? • Emma rides her bike at a speed of 10m/s. If the combined mass of Emma and her bike is 80kg what is her kinetic energy? • Rob is running and has a kinetic energy of 750J. If his mass is 60kg how fast is he running? • Josh is walking to town. If he has a kinetic energy of 150J and he’s walking at a pace of 2m/s what is his mass? 450,000J 4000J 5m/s 75kg

Stopping a car… 04/01/2020 What happens inside the car when it stops? In order to stop this car the brakes must “do work”. This work is used to reduce the kinetic energy of the vehicle and the brakes will warm up.

Understanding Speed and Velocity Concepts