2. Motion I Kinematics and Newton’s Laws

3. Basic Quantities to Describe Motion Motion is about Space (position) and Time (duration) and how we change position as a function of time Motion is about Space (position) and Time (duration) and how we change position as a function of time

4. A Brief Review Vectors Scalars Size Size only Size Size only Direction Direction

5. A Brief Review Vectors Scalars Displacement Distance Displacement Distance Velocity Speed Velocity Speed Acceleration Acceleration Time Time

6. A Brief Review Speed: Rate of change of distance Speed: Rate of change of distance v = distance traveled/time for travel v = distance traveled/time for travel v = x/t v = x/t

7. Example Suppose that we have a car that covers 20 miles in 30 minutes. What was its average speed? Suppose that we have a car that covers 20 miles in 30 minutes. What was its average speed? Speed = (20 mi)/(30 min) = 0.67 mi/min OR Speed = (20 mi)/(0.5 hr) = 40 mi/hr Note: Units of speed are distance divided by time.

8. A Brief Review Given the speed, we can also calculate the distance traveled in a given time. Given the speed, we can also calculate the distance traveled in a given time. distance = (speed)×(time) x = v×t Example: If speed = 35m/s, how far do we travel in 1 hour.

9. Distance traveled in 1 hour A. 35 m B. 103 m C. 2100 m D. 126,000 m

10. Velocity Velocity: Rate of change of Displacement Velocity: Rate of change of Displacement v = displacement/time of movement v = displacement/time of movement Velocity is a vector that tells us how fast and in what direction Velocity is a vector that tells us how fast and in what direction v = x/t v = x/t

11. Example: Plane Flight to Chicago Displacement: 133 mi northeast Displacement: 133 mi northeast Time = ½ hr Time = ½ hr v = 133 mi northeast/½ hr v = 133 mi northeast/½ hr v= 266 mi/hr northeast v= 266 mi/hr northeast

12. EXAMPLE: Daytona 500 Average speed is approximately 200 mi/hr, but what is average velocity? Average speed is approximately 200 mi/hr, but what is average velocity? Daytona is run around a loop Daytona is run around a loop Start and stop at the same location Start and stop at the same location

13. Track is 4000 m (2.5 mi)

14. Is the Daytona 500 race a spped race or a velocity race? A. Speed B. Velocity

15. What is the displacement for the race (200 laps)? A. 0 m B. 4000 m C. 400,000 m D. 800,000 m

16. What is the velocity for the race (200 laps)? A. 0 B. 4000 C. 400,000 D. 800,000

17. A Brief Review Acceleration: Rate of change of velocity Acceleration: Rate of change of velocity a = velocity change/time of change a = velocity change/time of change a = v/t a = v/t

18. We may have acceleration (i.e. a change in velocity) by We may have acceleration (i.e. a change in velocity) by 1. Changing speed (increase or decrease) 2. Changing direction Units of Acceleration = units of speed/time (m/s)/s = m/s 2 (mi/hr)/day

19. Example: acceleration A sports car increases speed from 4.5 m/s to 40 m/s in 8.0 s. A sports car increases speed from 4.5 m/s to 40 m/s in 8.0 s. What is its acceleration? What is its acceleration?

20. Example: acceleration v i = 4.5 m/s v f = 40 m/s t = 8.0 s v i = 4.5 m/s v f = 40 m/s t = 8.0 s  v = 40 m/s – 4.5 m/s  v = 40 m/s – 4.5 m/s a =  v/  t = (40 m/s – 4.5 m/s)/ 8 s a =  v/  t = (40 m/s – 4.5 m/s)/ 8 s a = 4.4 m/s 2 a = 4.4 m/s 2

21. How many accelerators (ways to change velocity) are there on a car? A. 1 B. 2 C. 3 D. 4

22. Unit Conversion Essentially just multiply the quantity you want to convert by a judiciously selected expression for 1. Essentially just multiply the quantity you want to convert by a judiciously selected expression for 1. For example, 12 in is the same as 1 ft For example, 12 in is the same as 1 ft To convert one foot to inches To convert one foot to inches [1 ft/1 ft] = 1 = [12in/1ft] So 1 ft x [12 in/1 ft] = 12 in The ft will cancel and leave the units you want

23. Convert 27 in into feet. 27 in x [1 ft/12 in] = 27/12 ft = 2.25 ft 27 in x [1 ft/12 in] = 27/12 ft = 2.25 ft Works for all units. If the unit to be converted is in the numerator, make sure it is in the denominator when you multiply. If the unit to be converted is in the denominator, make sure it is in the numerator when you multiply.

24. 1.609km = 1 mi. To find out how many miles are 75 km I would multiply the 75 km by A. [1 mi/1.609 km] B. [1.609 km/1 mi]

25. Convert 65 mi/hr to m/s. 65 mi/hr x [1609 m/1 mi] x [1 hr/60 min] x [1 min/60 s]

26. Convert 65 mi/hr to m/s. 65 mi/hr x [1609 m/1 mi] x [1 hr/60 min] x [1 min/60 s] = 29 m/s

27. Find the speed of light in c = 3 x 10 8 m/s 3 x 10 8 m/s x [100 cm/1 m] x [1 in/2.54 cm] x [1 ft/12 in] x [1 furlong/660 ft] x [60 s/1 min] x [60 min/1 hr] [24 hr/1 day] x [14 day/1 fortnight] = 1.8 x 10 12 furlongs/fortnight

28. 1 hr = 3600 s, 1609 m =1 mi and the speed of sound is 343 m/s, what is the speed of sound given in mi/hr? A. 5.92 mi/hr B. 153 mi/hr C. 767 mi/hr D. 20077200 mi/hr

29. Newton’s Laws

30. I An object won’t change its state of motion unless a net force acts on it.

31. I  A body moving at constant velocity has zero Net Force acting on it

32. II A net force is needed to change the state of motion of an object.

33. II  Defines force: F = ma

34. III When you push on something, it pushes back on you.

35. III  Action-reaction pairs (forces) act on different objects

36. I An object won’t change its state of motion unless a net force acts on it.  Originally discovered by Galileo  Defines inertia: resistance to change  Mass is measure of inertia (kg)  A body moving at constant velocity has zero Net Force acting on it

37. II A net force is needed to change the state of motion of an object.  Defines force: F = ma  Da given force, a small mass experiences a big acceleration and a big mass experiences a small acceleration  Unit of force is the Newton (N)

38. III When you push on something, it pushes back on you.  Forces always exist in pairs  Actin-reaction pairs act on different objects  A statement of conservation of momentum

39. Units of Force: By definition, a Newton (N) is the force that will cause a 1kg mass to accelerate at a rate of 1m/s 2 By definition, a Newton (N) is the force that will cause a 1kg mass to accelerate at a rate of 1m/s 2

40. Example: Rocket pack A 200 kg astronaut experiences a thrust of 100 N. A 200 kg astronaut experiences a thrust of 100 N. What will the acceleration be? What will the acceleration be?

41. A 200 kg astronaut experiences a thrust of 100 N. Acceleration = ? A. 0.1 m/s 2 B. 0.5 m/s 2 C. 2 m/s 2 D. 10 m/s 2

42. Example: Rocket pack A 200 kg astronaut experiences a thrust of 100 N. A 200 kg astronaut experiences a thrust of 100 N. What will the acceleration be? What will the acceleration be? F = ma  a = F/m F = ma  a = F/m 100 N/200 kg = 0.5 m/s 2 100 N/200 kg = 0.5 m/s 2

43. Force due to Gravity Force due to gravity is weight Force due to gravity is weight Dropped objects near Earth’s surface experience g = 9.8m/s 2, regardless of mass Dropped objects near Earth’s surface experience g = 9.8m/s 2, regardless of mass Neglects air friction Neglects air friction Weight is the gravitational force on a mass Weight is the gravitational force on a mass F = ma or W = mg

44. 3. If and object (A) exerts a force on an object (B), then object B exerts an equal but oppositely directed force on A. When you are standing on the floor, you are pushing down on the floor (Weight) but the floor pushes you back up so you don’t accelerate. If you jump out of an airplane, the earth exerts a force on you so you accelerate towards it. You put an equal (but opposite) force on the earth, but since its mass is so big its acceleration is very small

45. When a bug hit the windshield of a car, which one experiences the larger force? A. The bug B. The car C. They experience equal but opposite forces

46. When a bug hit the windshield of a car, which one experiences the larger acceleration? A. The bug B. The car C. They experience the same force, so they experience the same acceleration

47. Four Fundamental Forces 1. Gravity 2. Electromagnetic 3. Weak Nuclear 4. Strong Nuclear Examples of Non-fundamental forces: friction, air drag, tension Examples of Non-fundamental forces: friction, air drag, tension

48. Example Calculations Suppose you start from rest and undergo constant acceleration (a) for a time (t). How far do you go. Suppose you start from rest and undergo constant acceleration (a) for a time (t). How far do you go. Initial speed =0 Final speed = v=at Average speed v avg = (Final speed – Initial speed)/2 V avg = ½ at Now we can calculate the distance traveled as d= v avg t = (½ at) t = ½ at 2 Note: This is only true for constant acceleration.

49. Free Fall Suppose you fall off a 100 m high cliff. Suppose you fall off a 100 m high cliff. How long does it take to hit the ground and how fast are you moving when you hit? How long does it take to hit the ground and how fast are you moving when you hit?

50. Free Fall Suppose you fall off a 100 m high cliff. Suppose you fall off a 100 m high cliff. How long does it take to hit the ground and how fast are you moving when you hit? How long does it take to hit the ground and how fast are you moving when you hit?

51. Now that we know the time to reach the bottom, we can solve for the speed at the bottom Now that we know the time to reach the bottom, we can solve for the speed at the bottom

52. We can also use these equations to find the height of a cliff by dropping something off and finding how long it takes to get to the ground (t) and then solving for the height (d). We can also use these equations to find the height of a cliff by dropping something off and finding how long it takes to get to the ground (t) and then solving for the height (d).

53. In Scotland there is Stirling Bridge. To find out how deep it was I dropped a rock off the bridge. It took them 3 seconds to hit the bottom. How high is the bridge? A. 12 m B. 30 m C. 44 m D. 88 m