Mechanics. Course Overview

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1 Mechanics Course Overview

2 Course Overview Mechanics Kinema3cs 8 lessons Introduc3on to Physics (2 lessons) Administra3ve Procedure Introduc3on to Physics SI Units Metric prefixes Vectors (1 lesson) Vector versus scalar quan33es Graphical representa3on of vectors basic introduc3on Magnitude of a vector Kinema3cs (4 lessons) Displacement/velocity/accelera3on Speed vs. Velocity/Distance versus Displacement Velocity Time Graphs/Displacement Time Graphs/Accelera3on Time Graphs Accelera3on due to gravity Possible ac3vity to determine g Forces 5 lessons Newton s laws of mo3on (2 lessons) Mass and weight (0.5 lessons) Equilibrium (1 lesson) Unbalanced forces (1.5 lessons) Trolley Lab (DEF) Work, Energy & Power 4 lessons Types of energy and energy transforma3ons (0.5 lessons) Work (0.5 lessons) Kine3c energy (0.5 lessons) Gravita3onal Poten3al Energy (0.5 lessons) Conserva3on of (Mechanical) Energy (0.5 lessons) Applica3on of conserva3on of energy to KE, GPE and work (0.5 lesson) Efficiency (0.5 lessons) Power (0.5 lessons) Lab 4 lessons Unit Test + Revision/Review 2 lessons

3 Kinema3cs Mechanics

4 Learning Objec3ves Understand what SI units are and why they are used Be able to use prefixes and scien3fic nota3on in calcula3ons correctly.

However, when you fill petrol into your car, you measure in litres, in the US you measure in gallons Tourists are

5 Why SI units? When you buy a beer in the UK, you buy a pint. When you tell someone how tall you are, you talk about feet. The distance between London and Birmingham is 117 miles! However, when you fill petrol into your car, you measure in litres, in the US you measure in gallons Tourists are constantly confused and calcula3ng as they don t have a feel for what the units mean! To avoid confusion at the most basic level in science we need to share units across the globe.

6 The SI system of fundamental and derived units SI units are those of the Système Interna3onal d Unités (interna3onal system of units) adopted in There are fundamental units and derived units. Fundamental units form the basic units. All derived units can be expressed from fundamental units.

7 The fundamentals or base units Length metre m Mass kilogram kg Time second s Electric current ampere A Temperature Kelvin K Amount of a subst. mole mol The first three units are also oken referred to as mks units. They are the ones we will use in the context of mechanics.

8 Derived units Speed is measured in ms - 1, which is a derived unit. Force is measured in N (newton). To express the derived unit newton in base units we use the formula F = ma. à 1N = 1kgms - 2 As you get to know more formulae you will become more able to show how units are derived.

9 Some derived units SI derived unit SI base unit Alterna1ve SI unit Newton (N) kgm Pascal (Pa) kgm - 1 s - 2 Nm - 2 Hertz (Hz) s Joule (J) kgm 2 s - 2 Nm Wap (W) kgm 2 s - 3 Js - 1 Volt (V) kgm 2 s - 3 A - 1 WA - 1

10 Conversions Express the following units in base units. The formulae will be given to you by your teacher. unit to another for the same quan3ty like J to kwh Years to seconds Pa to base units

11 KWh to J 1 kwh = 1kW x 1 h = 1000W x 60 x 60 s = 1000 Js - 1 x 3600 s = J = 3.6 x 10 6 J

12 Prefixes help to compare very large or very small numbers. The power of a power sta3on is stated in MW (mega waps) or GW, distances in the atomic nucleus in fm (femto metres). Prefixes

13 Prefixes Express the following numbers with a suitable prefix: 10,000,000, Express the numbers above in scien3fic nota3on.

14 Do the following sums Calculate the result and write it in Scien3fic nota3on and then also with a prefix a. 5 x 10 8 x 3 x 10-5 = b. 2.5 x 10 3 x 1.2 x 10 4 = c. 1.4 x 10-6 x 13 x 10 7 = d. 107 x x 11.8 x 10-4 = e. 4.5 x x 11.8 x 10 5 =

15 Vectors and Scalars Dis3nguish between vector and scalar quan33es, and give examples of each. Determine the sum or difference of two vectors by a graphical method.

16 Scalars and vectors what s the fuss? In Physics we deal with many quan33es. When we measure them we represent them with a magnitude and when appropriate a unit. Some of the quan33es like force or velocity have a direc3on in the three dimensions, others like mass or temperature don t. A vector is a quan3ty with magnitude and direc3on, a scalar has a magnitude only.

17 Presenta3on of vectors and scalars To dis3nguish vectors from scalars the vectors are printed in bold, italisized lepers, e.g. force F.* As vectors have a direc3on they are oken represented through arrows. The length of the arrow represents the magnitude (size) of the vector. *While this is the standard at university the IB does not fully follow through with this and you do not need to write your vectors any differently in your exercises. However, you should know about this.

18 Examples of vectors and scalars Scalars Vectors List as many scalars and vectors as you can think of.

19 Free- Body Force Diagrams Draw all the exis3ng forces on this bicycle with the length of the arrows represen3ng the magnitude of the force. What would the diagram look like if the bike was accelera3ng, slowing down or moving at steady speed?

20 Addi3on and subtrac3on of vectors If two vectors point in the same direc3on they can simply be added by adding their numbers. The graphical method would of course lead to the same result. For opposite direc3ons you would subtract the vectors. Note: in the case of forces the overall vector a2er addi4on/subtrac4on is called the resultant force.

21 Addi3on and subtrac3on of vectors A cyclist is accelera3ng, which means that the forward force (130N) is larger than the total backward force (70N: air resistance & fric3on). Draw a force diagram (to scale) for the horizontal forces. What is the resultant or net force ac3ng on the cyclist and bicycle?

22 Kinema3cs Kinema3cs (4 lessons) Displacement/velocity/accelera3on Speed vs. Velocity/Distance versus Displacement Velocity Time Graphs/Displacement Time Graphs/Accelera3on Time Graphs Accelera3on due to gravity Possible ac3vity to determine g

23 Kinematic Concepts Displacement and Distance Displacement is the distance from a fixed point in a given direction (vector quantity) IB def Distance is the length of the actual path taken (scalar quantitiy). Example: Eva s and Alan s displacements are the same, but their distances are very different. Symbol used for both in calculations: s SI base unit: m

24 Distance- 3me graph What can you tell about the mo3on of the object shown on the graph?

25 Distance- 3me graph and displacement- 3me graph Draw the graph of an object that is moving across the room and back at a constant speed. as a distance- 3me graph as a displacement- 3me graph

26 How would you know from a distance- 3me graph how fast an object was moving? On the graph draw a line for an object moving faster and another line for an object moving more slowly!

27 The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Kinematic Concepts Velocity and Speed Speed is the rate of change of distance or distance covered per unit time (scalar quantity). Velocity is the rate of change of displacement or the speed in a given direction (vector quantity). Symbol for both: v. SI base unit: ms -1 The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.

28 Speed and velocity Use the formula to find the speed of a car travelling 2.7 km in 20s. Give the answer in the SI unit ms - 1. Look at the distance- 3me graph a few slides back and calculate the speed in the first 10h. Give your answer in kmh - 1.

29 Velocity- 3me graphs The graph on the right shows how the velocity of a bicycle changes over 3me. The area under the graph gives the distance covered. 1. Find the distance covered during the period of constant velocity. 2. Find the distance covered during the first 4s (red line).

30 Speed- 3me graph velocity- 3me graphs Draw both a speed- 3me and velocity- 3me graph of a ball being thrown up in the air and falling ver3cally down again to where it started from.

31 Kinematic Concepts Acceleration is defined as the rate of change of velocity (vector quantity) or the change in velocity per unit time. u: initial velocity, v: final velocity Symbol: a, SI base unit: ms -2 a = Δv t = v u t

32 Accelera3on This Porsche 911 Turbo PDK accelerates from 0 to 100kmh - 1 in 2.72s. Calculate its accelera3on, given that 100 km - 1 are 27.8ms - 1.

33 Accelera3on and v- t graphs 1. Look at the last graph and calculate all three accelera3ons. Note: decelera3on is nega3ve accelera3on! 2. Which of the three sec3ons has the greatest magnitude of accelera3on? How would you know without calcula3ons? 3. Draw an accelera3on- 3me graph for this velocity- 3me graph.

34 Accelera3on- 3me graphs Challenge: draw a possible v- t graph for the following accelera3on- 3me graph.

35 Summary Mo3on graphs The gradient of the s- t graph is the velocity. The gradient of the v- t graph is the accelera3on. The area under the v- t graph is the displacement. The area under the a- t graph is the change in velocity. Example: Note: to find the gradient always draw the biggest possible triangle (here 0-100, 0-100), then divide Δx by Δt. From: hpp:// latest&h=952&w=1298&sz=50&tbnid=fr3mu6vdhncu5m:&tbnh=88&tbnw=120&zoom=1&usg= Az6EGJiEyc8w24GT3T6hNTELOg=&docid=H6fifNFxVS80M&sa=X&ei=Ck8DUtXxD8bcswbyhIDwBA&ved=0CDgQ9QEwAQ&d ur=632

36 Check for yourself Look at the example above and calculate the gradient of both s- t and v- t graph. Find out whether the velocity and the accelera3on are correctly calculated. Find out whether the area under the v- t graph does indeed give you the total displacement.

37 Mo3on graphs Further example: Same source as previous example

38 Average velocity Average velocity is the mean velocity over the en3re 3me considered, i.e. total displacement divided by the total 3me taken. v avg = s tot t tot v avg = u + v 2 Note: this formula only applies for constant accelera3on! Find the average velocity in the very first distance- 3me graph. Challenge: give the result also in ms - 1.

39 Further exercise 1. Calculate the average velocity during the first 3s.

40 Mo3on graphs Draw all three mo3on graphs for an object that is Sta3onary Moving at constant velocity Moving at constant accelera3on star3ng from velocity and displacement 0. Moving at constant accelera3on, but accelera3ng from a given velocity. Try this without looking at the next slide.

41 Constant velocity Mo3on graphs From: hpp:// collec3on%3dcol11305/ latest&h=952&w=1298&sz=50&tbnid=fr3mu6vdhncu5m:&tbnh=88&tbnw=120&zoom=1&usg= Az6EGJiEyc8w24GT3T6hNTELOg=&docid=H6fifNFxVS80M&s a=x&ei=ck8dutxxd8bcswbyhidwba&ved=0cdgq9qewaq&dur=632

42 Phet simula3on Mo3on Graphs

43 Exercises on Mo3on Graphs 3. Draw a distance- and displacement- 3me graph for the same scenario. 4. Draw the a- t graph for the same scenario. Note: define first which direc4on should be posi4ve and which nega4ve! Apply this s, v and a!

44 Exercises on Mo3on Graphs 6. The posi3on vs. 3me graph for the mo3on of a car is given on the right. Draw the corresponding a. velocity vs. 3me and b. accelera3on vs. 3me graphs, c. and then describe the mo3on of the car. From: hpp:// latest&h=952&w=1298&sz=50&tbnid=fr3mu6vdhncu5m:&tbnh=88&tbnw=120&zoom=1&usg= Az6EGJiEyc8w24GT3T6hNTELOg=&docid=H6fifNFxVS80M&sa=X&ei=Ck8DUtXxD8bcswbyhI DwBA&ved=0CDgQ9QEwAQ&dur=632

45 Exercises on Mo3on Graphs 7. The velocity vs. 3me graph of a truck is ploped below. Calculate the distance and displacement of the truck aker 15 seconds. From: hpp:// latest&h=952&w=1298&sz=50&tbnid=fr3mu6vdhncu5m:&tbnh=88&tbnw=120&zoom=1&usg= Az6EGJiEyc8w24GT3T6hNTELOg=&docid=H6fifNFxVS80M&sa=X&ei=Ck8DUtXxD8bcswbyhIDwBA&ved=0CDgQ9QEwAQ&dur=632

46 Exercises on Mo3on Graphs 8. The posi3on vs. 3me graph below describes the mo3on of an athlete. a. What is the velocity of the athlete during the first 4 seconds? b. What is the velocity of the athlete from t=4 s to t=7 s? From: hpp:// latest&h=952&w=1298&sz=50&tbnid=fr3mu6vdhncu5m:&tbnh=88&tbnw=120&zoom=1&usg= Az6EGJiEyc8w24GT3T6hNTELOg=&docid=H6fifNFxVS80M&sa=X&ei=Ck8DUtXxD8bcswbyhI DwBA&ved=0CDgQ9QEwAQ&dur=632

47 Exercises on Mo3on Graphs 9. The accelera3on vs. 3me graph for a car star3ng from rest, is given below. Calculate the velocity of the car at various points and draw the velocity vs. 3me graph. From: hpp:// latest&h=952&w=1298&sz=50&tbnid=fr3mu6vdhncu5m:&tbnh=88&tbnw=120&zoom=1&usg= Az6EGJiEyc8w24GT3T6hNTELOg=&docid=H6fifNFxVS80M&sa=X&ei=Ck8DUtXxD8bcswbyhI DwBA&ved=0CDgQ9QEwAQ&dur=632

48 Accelera3on due to gravity If we neglect air resistance, the accelera3on of a body in free- fall remains constant close to the surface of the Earth: approximately 10 ms - 2 (9.81 ms - 2 ). The image shows a photo- graph taken with a stro- boscope flashing at regular intervals.

49 Finding g experimentally Accelera3on due to gravity can be found with the formula a = 2st 2 with g = a. Drop a steel ball or marble from a known height and 3me the drop. Take several repeats and calculate an average to get a more reliable answer.

Course overview. Forces 5 lessons

Course overview. Forces 5 lessons Forces Mechanics Course overview Forces 5 lessons Newton s laws of mo9on (2 lessons) Mass and weight (0.5 lessons) Equilibrium (1 lesson) Unbalanced forces (1.5 lessons) Trolley Lab (DEF) Newton s first