Understanding Kinematics in Mechanics: Speed, Velocity, and Acceleration

1. Review

2. http://astro.temple.edu/~elenab/

3. Describing Motion:Kinematics in one dimension Kinematicsis a part of mechanics, which is the description of how objects move.

4. Speed Speed is a measure of how fast object moves, measured by a unit of distance divided by a unit of time.

5. Instantaneous Speed Average speed doesn’t indicate the different speeds that may have taken place during shorter time intervals.

6. Average Speed average speed = total distance traveled/ time elapsed Total distance traveled = average speed X time

7. What is the average speed of a cheetah that sprints 100 m in 4 s? How about if it sprints 50 m in 2 s? • If a car moves with an average speed of 60 km/h for an hour, it will travel a distance of 60 km. • (a) how far would it travel if it moved at this rate for 4 h? • (b) for 10 h? • 3. In addition to speedometer on the dashboard of every car is an odometer, which records the distance traveled. If the initial reading is set at zero at the beginning of a trip and the reading is 40 km one half hour later, what has been your average speed? • 4. Would it be possible to attain the average speed in previous example and never go faster than 80 km/h?

8. Velocity When we describe speed and the direction of motion, we are specifying velocity

9. With what two physical values is the race-car driver concerned? Speed or velocity? • The speedometer of a car moving to the east reads 100 km/h. It passes another car that moves to the west at 100 km/h. Do both cars have the same speed? Do they have the same velocity? • During certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed or a constant velocity?

10. How might you estimate your speed if the speedometer in your car is broken? • 2. Which of the following can be used to measure an average speed: stopwatch, odometer, or speedometer? An instantaneous speed?

11. Acceleration

12. We can change the velocity of something by changing its speed; by changing its direction or by changing its speed and its direction.

13. Motion at Constant Acceleration Acceleration is a rate of change , or change per second of velocity. v= at

14. Which has the greater acceleration, an airplane that goes from 1000 km/h to 1005 km/h in 10 s, or a skateboard that goes from 0 to 5 km/h in 1 sec? • What is the acceleration of a race car that whizzes past you at a constant velocity 400 km/h?

15. Acceleration on Galileo Inclined Planes Galileo found greater accelerations for steeper inclines. The ball attains max acceleration when the incline is tipped vertically.

16. a ball rolling down an inclined plane is moving with constant acceleration • greater accelerations for steeper planes, max acceleration when incline is tipped vertically • regardless of weight and size, when air resistance is small enough to be neglected, all objects fall with the same unchanging acceleration.

17. We call this acceleration the acceleration due to gravity on the Earth, and we give it the symbol g. g = 9.80 m/ s2 ~ 10 m/ s2

18. How Far? With his inclined planes Galileo found that the distance a uniformly accelerating object travels is proportional to the square of the time Distance = acceleration x time x time /2.

19. At a given location on the Earth and in the absence of air resistance, all objects fall with the same constant acceleration

20. Which of the following (if any) could not be considered an “accelerator” in an automobile: gas pedal, brake pedal, steering wheel? • A sports car accelerates from 65 mph to 75 mph in 2 seconds while a minivan accelerates from 20 mph to 35 mph in 2 seconds. Which one has the larger acceleration? • You are standing on a high cliff above the ocean. You drop a pebble, and it strikes the water 4 seconds later. Ignoring the effects of air resistance, how fast was the pebble traveling just before striking the water? What is the height of the cliff?

21. Explaining Motion

22. Galileo’s inclined planes revisited Slope upward – speed decreases Slope downward – speed increases No slope. Does speed change?

23. Initial Final position Where is the final position?

24. Newton’s first law of motion The first law incorporates Galileo’s idea of inertia and introduces a new concept, force.

25. Every object continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change the state by forces impressed upon it.

26. Examples • Assume that you are pushing car across a level parking lot. When you are stop pushing, the car comes to stop. Does this violate Newton’s first law? Why? • Why does a tassel hanging from the rearview mirror appear to swing forward as you apply the brakes?

27. If you were traveling toward a distant star and you ran out of fuel, would your spaceship slow down and stop? Explain.

28. Addition of Vectors – Graphical Methods

29. Examples • In everyday use, inertia means that something is hard to get moving. Is this the only meaning it has in physics? If not, what other meaning does it have? • How would you determine that two objects have the same inertia? • When a number of different forces act on an object, is the net force necessarily in the same direction as one of the individual forces? Why? • Modern cars are required to have headrests to protect your neck during collisions. For what type of collision are these headrests most effective?

30. Newton’s Second Law The net force on an object is equal to its mass times its acceleration and points in the direction of acceleration Fnet = ma

31. Examples • Forces of 4 N and 6 N act on the object. What is the minimum value for the sum of these two forces? • Two ropes are being used to pull a car out of a ditch. Each rope exerts a force of 700 N on the car. Is it possible for the sum of these two forces to have a magnitude of 1000N? Explain your reasoning. • If the net force on a boat is directed due east, what is the direction of the acceleration of the boat? Would your answer change if the boat had a velocity due north but the net force still acted to the east?

32. Examples • Describe the force(s) that allow you to walk across the room. • You are analyzing a problem in which two forces act on an object. A 200 N force pulls to the right, and a 40 N force pulls to the left. Your classmate asserts that the net force is 200 N because that is the dominant force that is acting. What is wrong with that assertion?

33. Net Force The combination of forces that act on the object is the net force

34. Units of Force 1 newton (N) = 1 Kg *m/s2

35. You push on a crate that sits on a smooth floor and it accelerates. If you apply four times the pushing force, how much greater will be the acceleration? • Same for a rough surface.

36. Friction If you apply a force to an object, a force of friction usually reduces the net force and resulting acceleration. The direction of friction force is always in the direction opposing motion. The force of dry friction between solid surfaces doesn’t depend on speed or area of contact.

37. Question • A jumbo jet cruises at constant velocity of 1000 km/h when the thrusting force of its engines is constant 100000 N. • What is the acceleration of the jet? • What is the force resistance on the jet?

38. Mass and Force of Gravity Mass: The quantity of matter in an object. It is also the measure of the inertia or sluggishness, that an object exhibits in response to any effort made to start it, stop it, or change its state of motion in any way. Force of Gravity= mg

39. Newton’s Second Law The net force on an object is equal to its mass times its acceleration and points in the direction of acceleration Fnet = ma

40. Important: acceleration of a body is always in the direction of net force!!!!

41. Free-body diagrams

42. Free fall revisited

43. When Acceleration is Less Than g – Nonfree Fall

44. Examples • Forces of 4 N and 6 N act on the object. What is the minimum value for the sum of these two forces? • Two ropes are being used to pull a car out of a ditch. Each rope exerts a force of 700 N on the car. Is it possible for the sum of these two forces to have a magnitude of 1000N? Explain your reasoning. • If the net force on a boat is directed due east, what is the direction of the acceleration of the boat? Would your answer change if the boat had a velocity due north but the net force still acted to the east?

45. Newton’s Third Law of MotionForces and Interactions

46. In a broader sense, a force is not a thing in itself but makes up an interaction between one thing and another.

47. Newton’s Third Law of Motion Whenever one object exerts a force on a second object, the second exerts equal and opposite force on the first. “On every action there is equal and opposite reaction”…

48. Which force we call action and which we call reaction doesn’t matter. The point is that neither exists without the other.

49. Action and Reaction on Different Masses

50. A car accelerates along a road. Identify the force that moves the car. • A high speed bus and an innocent bug have a head-on collision. The force of impact splatters the poor bug over the windshield. Is the corresponding force that bug exerts against the windshield greater, less or the same? Is the resulting acceleration of the bus greater than, less than or the same as that of the bug?