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# 1 - Revision of Y11 Mechanics

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This file is a useful introduction to Y12 Mechanics. It provides theory notes and exercises which lay a foundation for the Mechanics Achievement Standard.

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### 1 - Revision of Y11 Mechanics

1. 1. FORCE AND MOTION REVISION 1. Define a force as a push or a pull and be able to describe loosely the effect on motion that a force has. 2. Know that there are two different types of forces and recall examples of these. 3. Use v=d/t to calculate speed, distance and time. (Rearranging simple equations) 4. Use a = ∆v/∆t to calculate acceleration, speed and time. 5. Describe the units of both speed and acceleration (ms-1) and (ms-2) 6. Perform basic unit conversions including the conversion from kmh-1 to ms-1 (Use of prefixes) 7. Make labelled diagrams showing all the forces acting on an object in motion or an object at rest. 8. Recognise that the change in the velocity of an object is a result of the action of an unbalanced force and be able to calculate the size of the unbalanced force in simple 1D situations. 9. Use F=ma to calculate force, mass and acceleration. (Rearranging simple equations)
2. 2. WHAT IS A FORCE? • A force is a push or a pull • You cannot see a force but you can sometimes see the effects of a force (what a force does). • Forces can be either contact or non-contact in nature. 1. Examples of contact forces: Tension (lifting a bucket of water using a rope) Thrust (pushing on a desk) Lift (Air pressure differences holding a plane up in the air) Support (standing on the ground instead of falling to the earth’s centre) Friction (a force that opposes motion) 2. Examples on non-contact forces: Gravity, Magnetism, Electrostatic forces A force can: 1. Cause movement in an object that is initially stationery 2. Change the speed of an object (speed it up or slow it down) 3. change the direction of an object. 4. change the shape of an object. 5. hold an object up (or lift an object)
3. 3. BALANCED AND UNBALANCED FORCES BALANCED FORCES Back Forward Support force Friction force Driving force speed stays the same v OR speed equals ZERO (STANDING STILL) Force due to gravity Draw diagrams showing all the forces acting in the following situations: 1.An aeroplane travels through the air in level flight at a constant speed. 2.A rock falls vertically with constant speed
4. 4. UNBALANCED FORCES Back Forward The object will be speed up or it will slow down or change direction Support force Friction force Driving force speed increases Force due to gravity Support force Friction force Driving force speed decreases Force due to gravity
5. 5. Changing direction Car B is on a “collision course” car A’s path after the crash with car A Car B Car A
6. 6. CALCULATING AVERAGE SPEED distance travelled Average speed = time taken This formula allows you to calculate the average speed when the distance and time are known. It can be written using symbols: v= d where v = average speed (in metres per second, ms-1) t d = distance travelled (in metres, m) t = time taken (in seconds, s) Use this formula to calculate time when distance and speed are known t= d v and this formula to calculate time when distance and speed are known d= v x t “Here’s an easy way of remembering the formulae” d Just put your ﬁnger over the quantity you want to calculate and the v t formula appears
7. 7. CALCULATING ACCELERATION change in velocity Acceleration = change in time This formula allows you to calculate the acceleration when the change in velocity and the change in time are known. It can be written using symbols: a = ∆v where a = acceleration (in metres per second per second, ms-2) ∆t ∆v = change in speed (in metres per second,ms-1) ∆t = change in time (in seconds, s) Use this formula to calculate time when change in speed and acceleration are known ∆t = ∆v a and this formula to calculate time when acceleration and change in speed are known ∆v = a x ∆t ∆v “Here’s an easy way of remembering the formulae” a ∆t Just put your ﬁnger over the quantity you want to calculate and the formula appears
8. 8. FORCE AND ACCELERATION When an object experiences an unbalanced force it will speed up (acceleration), slow down (negative accleration) or change direction (acceleration because the velocity is changing). SO AN UNBALANCED FORCE CAUSES ACCELERATION 20 N 1500 N Parachutist Parachutist falling slowly falling rapidly at at first the time that the parachute opens 1000 N 1000 N The unbalanced force on the The unbalanced force on the parachutist is 980 N acting parachutist is 500 N acting downwards upwards so he will speed up so he will slow down
9. 9. Summary FORCE, MASS & ACCELERATION When the forces acting on an object are unbalanced the object will accelerate: F = ma Where F = Force measured in Newtons, N m = mass measured in kilograms, kg a = acceleration measured in metres per second squared, ms-2 Use this formula to calculate acceleration when Force and mass are known a= F m Use this formula to calculate mass when Force and acceleration are known m= F a F Example m a A skyrocket of mass 0.1kg accelerates upwards at 10 ms-2. What is the unbalanced force acting on the rocket? F = ma = 0.1 x 10 = 1 N
10. 10. UNITS AND CONVERSIONS SI Units Standard units in Physics originate from Europe. These are called SI units (which stands for Systeme Internationale) In Mechanics these are: metres, m kilograms, kg ‘mks’ system of measurement seconds, s These units can be prefixed to show multiples of 10. A prefix shows what the standard unit is multiplied by. For example: kilo ‘k’ means ‘x 103’ (or x 1000) Other Prefixes 3 so 1 km = 1 x 10 m = 1000 m M mega 106 & 20.5 km = 20.5 x 103 m = 20500 m k kilo 103 m milli 10-3 centi ‘c’ means ‘x 10-2’ (or x 1 ) 100 µ micro 10-6 so 1 cm = 1 x 10-2 m = 0.01 m n nano 10-9 & 15.3 cm = 15.3 x 10-2 m = 0.153 m p pico 10-12
11. 11. QUICK TEN Rearrange the following equations: 1. y = 5x x= ? 2. R = V I=? I 3. P = VI2 V=? 4. P = VI2 I=? 5. Ek = 1 mv2 v=? 2 6. F = ! r t t=? 7. Express 5231 x 103 in standard form. 8. Express 0.0201 x 10-3 9. How many cm in 100m? 10. A car travels at a constant speed of 100 kmh-1 . What is this speed in ms-1?
12. 12. EX ERC IS ES
13. 13. PRETEST 1. What is the name of the force that drives objects in the forward direction 2. Name the force that always acts in the opposite direction to the object’s motion. 3. Name the force that slows down the motion of a parachute. 4. If an object is traveling at a steady speed, what can we say about the forces acting on that object 5. If an object is speeding up what can we say about the forces acting on that object 6. How does a force change the direction of an object? 7. Scientific word that means the same as 'speeding up" 8. What is a scientific word that means the same as "slowing down". 9. Sketch a distance time graph that shows an object traveling at a steady speed. 10. Sketch a distance time graph that shows an object stationery.
14. 14. SPEED CALCULATIONS Calculate the average speed in each case: 1. A cyclist travels 100m in 5s. 2. A snail travels 1m in 200s. 3. An old man walks 300 cm in 2s. Calculate the distance travelled in each case: 1. A car travels at 10ms-1 for 10s. 2. A Rocket in space travels 1500ms-1 for 60s. Calculate the time taken in each case: 1. A car travels 100 m at an average speed of 10ms-1 2. A Rocket in space travels 30000 m at an average speed of 1500ms-1.
15. 15. ACCELERATION CALCULATIONS
16. 16. FORCE CALCULATIONS 1. Complete the table below: Force (N) Mass (kg) Acceleration (ms-2) 1 1 10 1 8 3 17 1.7 4 0.2 5 0.4 2. The diagram shows the forces being applied to a 160 kg bicycle and rider (ignore the support force and gravity for the purposes of your calculation): (a) Name the forces drawn: A A = _________ B = _________ (b) What is the size and direction of 100 N the nett (unbalanced) Force acting B on the rider. (c) Calculate the acceleration of the bicycle and rider. Give the correct unit with your answer. 800 N (d) Why have you ignored the support and gravity forces
17. 17. 3. Study the diagram below. It shows Bart Simpson on a skateboard. Bart is slowing down. Bart and the skateboard have a combined mass of 35 kg and the force due to friction acting on him is 100N. (a) Draw the forces acting on Bart. Label those forces showing the size of each force and the symbol which represents the type of force that it is. ___________________________________________________________ (b) What is the size and direction of the unbalanced force that is acting on Bart? (Hint: Ask yourself if Bart is able to provide a thrust force) ___________________________________________________________ (c) Calculate Bart’s acceleration (taking care to note whether it is a positive or a negative value). Show all your working. ______________________________________________________________ ______________________________________________________________ (d) Suggest two things that Bart could do to help him to travel for further before he stops. ______________________________________________________________ ______________________________________________________________
18. 18. UNIT CALCULATIONS 1. Write the SI units for the following physical quantities: time ___ mass ___ height ____ radius _____ area _____ volume ______ energy _______ force _______ speed _______ 2. Convert these lengths to metres, m. 5.15 km __________ 1.25 km __________ 883 cm __________ 45.02 cm __________ 68 mm __________ 523 µm __________ 3. Convert these lengths to cm. 5.24 m __________ 1.4 m ____________ 0.013 km __________ 666 mm __________ 3.6 mm __________ 225 µm __________ 4. Convert these quantities to the indicated units. 5.261 m = _____mm 7054 mm = _____m 1.25 cm = ______mm 5.24 m = _____mm 735 cm = _______ m 2.4 kg = _______ g 803g = _______kg 9.1 s = ________ms 642 ms = ______ s 23.1 g = ______µg 1300 mL = ______L 0.087 s = _______ms