Forces and Motion

1. Kinematics Forces and Motion

2. Physics • Physics – a study of matter and energy with an emphasis on energy • Mechanics – a branch of physics that deals with a study of motion, there are 2 types

3. Motion

4. Types of Motion • Kinematics – a study of how objects move • Types of motion are: • Uniform • Accelerated • Free-fall • Projectile • Circular • Harmonic • Dynamics – a study of why objects move • Quantitative studies of why objects move began with Newton • Motion is broken up into 2 different types • Uniform Motion – movement at a constant speed in a straight line • Nonuniform Motion – movement that involves a change in speed, direction, or both

5. Significant Digits • When we do calculations, we must look at the accuracy and precision of the results. • To do this, we have some simple rules to follow that are called Significant Digits or Significant figures • These are very important and if done incorrectly will cost you marks on assignments, quizzes, and tests

6. Sig Digs, Sig Figs…etc. • Sig Figs tell us how many digits we can have in our answers. • The numbers 1 through 9 are significant all the time, but 0 is a special case. • 1234 - has 4 sig figs • 1.92 – has 3 sig figs • 1.201 x 104 has 4 sig figs • 0.00124 has 3 sig figs • If a 0 comes before a decimal or directly after, it is not significant

7. Sig Figs – Addition/Subtraction • What about calculations then?? • Addition/subtraction • Take the number with the least number of decimal places to make the final answer 1.2043 + 31.2 +0.000023 =32.404323 Sig figs – 32.4

8. Sig Figs – Multiplication/Division • In multiplication and division, you take the smallest number of significant digits • 3.14 * 2.2 • = 6.908 • Sig figs = 6.9

9. Base Units for this course • Time – the base units are seconds (s) • Length – the base units are metres (m) • Mass – the base units are kilograms (kg) • All other measurements are typically taken in these units or some variation of them and are called Derived Units

10. Scientific Notation • When your values get too large, which will happen a lot, you need to be able to display them in a compact form, Scientific Notation • 123000000 – 1.23x108 • 0.00479 – 4.79x10-3 • When you have large or very small numbers, it is expected you use Scientific Notation

11. How to give direction • X-axis Method • This is measured from the positive x axis counter-clockwise • Navigator Method • This is measured from the North, clockwise

12. Examples • X-axis Method • 34.2 m/s [34° above the horizontal] • 1.24x103 N [283°] • Navigator Method • 34.2 m/s [34° N of E] • 34.2 m/s [56° E of N] • 1.24x103 N [13° N of W] • 1.24x103 N [77° W of N]

13. Quantities • There are 2 types of quantities that you are going to look at for the rest of your physics career. • Scalars • Vectors

14. Scalar Quantities • Scalar quantities are things like speedometer, speed limits, a measurement on a ruler, etc. • Each of these is a measurement, but they are only have units and do not give you a direction • Any number that is not given a direction but has units is a Scalar Quantity

15. Speed • Instantaneous • This is the speed calculated at a particular point. • Ex: at some point on a road you car may be travelling 100 km/h • You get these measurements by directly looking at your speedometer • Average • This takes into account the total distance travelled and the total time travelled • Ex: on a road trip, you travel for 2.5 hours and cover a distance of 328 km. You have an average speed of 131.2 km/h • It is calculated using vav =d/t

16. Vector Quantities • If a measurement is given a direction, then it is a vector quantity. • Does the direction really matter? • Yes, it allows you to determine if something is positive or negative

17. Vectors • Vector Quantity – tells you “how much” (magnitude) and direction • Must be denoted with a vector arrow • Must also be given a sign, either positive or negative according to the following grid

18. Multiple Vectors • What happens if you have to add multiple vectors together? • You can draw out each vector, and place them together (as arrows), with the tip of the first touching the tail of the second, and so on.

19. Multiple Vectors Cont’d • Once you have placed all the vectors together, the resultant vector is the displacement of the object. • The resultant is found by placing a line from the starting point to the tip of the last arrow, and then use Trig to help you out.

20. Distance and Displacement • Distance “d” • Indicates how far something is from a starting point or a reference point • Distance travelled “Δd” • Indicates how far or the total distance an object has travelled from a starting point • Δd = Δd1 + Δd2 • Position “d” • Indicates how far something is from a starting point or a reference point and in what direction • Displacement “Δd” • Indicates the change in position or how far an object has travelled from a stating point and in what direction • Δd = Δd1 + Δd2

21. Which “d” is it?

22. Time, Velocity, and Speed

23. 1 Dimensional Uniform Motion – traveling in 1 direction

24. 1 Dimensional Uniform Motion – traveling in 2 directions

25. Resultant Displacement • How do you deal with the following? • A person travels 1.7 km [E] then turns and travels 2.1 km [S]. What is the person’s displacement? • First draw a diagram to help Dd1 =1.7 km [E] Dd2 =2.1 km [S] DdR =2.7 km [51° S of E]

26. Graphing • Graphing is one method of representing the motion of an object. • There are 2 different types of graph that we will look at • Position – time • Velocity – time

27. Position – Time Graphs • If a car was traveling East at +10 m/s, the car undergoes constant velocity giving a positive slope to the upper right • If the same car was traveling at a changing velocity to the right, the graph would still be positive

28. Is Slope Important? • You bet it is. The slope of the p-t graph gives important information about the problem. • Constant slope (straight line) – constant velocity • Changing slope (curved line) – acceleration • Steep slope – fast velocity • Shallow slope – slow velocity

29. Curved Slopes • A curved line is a sign of accelerated motion • The first image shows an object with a small, negative velocity and finishes with a large negative velocity • The second image shows a large negative slope that changes to a small velocity at the end.

30. Slope Continued • What happens if a line is horizontal? • In this case, the object is stationary • In the example below, at the 5 second mark, the object comes to a complete stop for 5 seconds

31. How do you find the slope? • We find the slope of a p-t graph the same way we would find the slope in a mathematical graph

32. Velocity – Time Graphs • If a car was traveling East at +10 m/s, the car undergoes constant velocity, a v-t graph would look like this • If the same car was traveling at a changing velocity to the right, the v-t graph would look like the following

33. Slopes and V-T Graphs • Slopes are very important when looking at V-T graphs • There are 2 types of motion • Constant velocity • Accelerated velocity

34. Slopes • Constant Velocity • These are always horizontal lines at the velocity • If it is above 0, it is positive, below 0 it is negative • Acceleration • Positive • All accelerations are positive if the line is on the positive side • All accelerations are negative if they are on the negative side

35. Slopes • In an v-t graph, we also need to know if an object is speeding up or slowing down. • How can we determine this?

36. What else can we get from VT? • We can get other information other than acceleration from a v-t graph. • We can also get the displacement of the object • This is done by calculating the area under the curve

37. The Other Method • There will be more times in Physics, where you will not have a graph to help you out. • When this happens, we have some equations to help us out.

38. Kinematic Equations • See p.44 for more information

39. Kinematic Equations • The previous equations were given for scalar calculations • You can have the same equations for vector quantities • These are shown with the variables having a line above each one

40. Forces

41. No Push – No Go • If there is nothing pushing on an object, it will not move. • If there is nothing pushing on an object, it will not stop. • The List: • No Push – No Go • No Push – No Stop • No Push – No Speed Up • No Push – No Slow Down • No Push – No Turn

42. In Short: No Push – No Accelerate

43. Who Discovered this? The first person to realize the relationship was Sir Isaac Newton

44. Newton’s First Law • An object in motion at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and direction unless acted upon by an unbalanced force

45. NFL • Think about it this way: • If you are in a car at a stop light, and the driver speeds up really fast, where do you tend to go? • If you are driving and come to a quick stop, which way do you tend to go? • If you spin a bucket on a rope, in what direction will the bucket go if the line is cut?

46. Some Clarification • What is a force? • This is the push or pull on an object that either gets the object moving, makes it stop, or makes it turn. • It is measured in the units of Newtons (N) • What does unbalanced mean? • This means that, if you add all the pushes and pulls together, there is a overall push/pull in one direction

47. Balanced Forces A) 10 N • When we look at forces, we will break them into forces working in the same plane. • This means all vertical forces can be added and all horizontal forces can be added • Which forces can be added together in the diagram? D) 10 N B) 10 N C) 10 N

48. Unbalanced Forces A) 10 N • What happens if the forces do not add to 0? • These are unbalanced forces, and this creates an acceleration in the object. • What is the size of the unbalanced force? D) 10 N B) 40 N C) 10 N

49. REMEMBER!!!!!!!! Forces are vectors and need a direction!!!

50. Free Body Diagrams • When you are performing calculations, you should always look at a drawing of the situation. • We do this using an FBD or Free body diagram • An FBD uses arrows to describe the forces acting on the body and in which direction.