Motion and Newton's Laws: Understanding Basic Quantities

1. Motion I Kinematics and Newton’s Laws

2. Basic Quantities to Describe Motion • Space (where are you)

3. Basic Quantities to Describe Motion • Space (where are you) • Time (when are you there)

4. Basic Quantities to Describe Motion • Space (where are you) • Time (when are you there) • Motion is how we move through space as a function of the time.

5. Newton’s Definitions: • Space: Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. • Time: Absolute true and mathematical time, of itself, and from its own nature, flows equably, without relation to anything external, and by another name is called duration.

6. A Brief Review • Vectors Scalars • Size Size only • Direction

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

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

9. Example • 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.

10. A Brief Review • Given the speed, we can also calculate the distance traveled in a given time. distance = (speed) x (time) x = v x t Example: If speed = 35m/s, how far do we travel in 1 hour. x=(35 m/s)(3600 s)=126,000 m = 126,000m x [1mi/1609m]=78.3 mi

11. A Brief Review • Velocity: Rate of change of displacement • v = displacement/time of movement • Displacement is a vector that tells us how far and in what direction • v = x/t

12. Velocity • Velocity tells not only how fast we are going (speed) but also tells us the direction we are going.

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

14. EXAMPLE: Daytona 500 • Average speed is approximately 200 mi/hr, but what is average velocity? • Since we start and stop at the same location, displacement is zero • Velocity must also be zero.

15. Car keeps changing direction so on average it doesn’t actually go anywhere, but it is still moving quickly

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

17. We may have acceleration (i.e. a change in velocity) by • Changing speed (increase or decrease) • Changing direction Units of Acceleration = units of speed/time (m/s)/s = m/s2 (mi/hr)/day

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

19. Example: acceleration • vi = 4.5 m/s vf = 40 m/s t = 8.0 s • Dv = 40 m/s – 4.5 m/s • a = Dv/Dt = (40 m/s – 4.5 m/s)/ 8 s • a = 4.4 m/s2

20. How many accelerators (ways to change velocity) are there on a car? • a) 1 • b) 2 • c) 3 • d) 4

21. Unit Conversion • 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 • 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

22. Convert 27 in into feet. • 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.

23. I know that 1.609km = 1 mi. If I want to find out how many miles are 75 km I would multiply the 75 km by • [1mi/1.609km] • [1.609km/1mi]

24. 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

25. Find the speed of light in • c = 3 x 108 m/s • 3 x 108 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 1012 furlongs/fortnight

26. Given that 1 hr=3600 s, 1609 m=1 mi and the speed of sound is 330 m/s, what is the speed of sound given in mi/hr? • a) 12.3 mi/hr • b) 147 mi/hr • c) 738 mi/hr • d) 31858200 mi/hr

27. Newton’s Laws

28. 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

29. 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)

30. 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

31. Units of Force: • By definition, a Newton (N) is the force that will cause a 1kg mass to accelerate at a rate of 1m/s2

32. Example: Rocket pack • A 200 kg astronaut experiences a thrust of 100 N. • What will the acceleration be? • F = ma a = F/m • 100 N/200 kg = 0.5 m/s2

33. Force due to Gravity • Near the surface of the earth, all dropped objects will experience an acceleration of g=9.8m/s2, regardless of their mass. • Neglects air friction • Weight is the gravitational force on a mass F = ma = mg =W Note the Weight of a 1kg mass on earth is W=(1kg)(9.8m/s2)=9.8N

34. 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

35. When a bug hit the windshield of a car, which one experiences the larger force? • The bug • The car • They experience equal but opposite forces.

36. When a bug hit the windshield of a car, which one experiences the larger acceleration? • The bug • The car • Since they have the same force, they have the same acceleration.

37. Four Fundamental Forces • Gravity • Electromagnetic • Weak Nuclear • Strong Nuclear • Examples of Non-fundamental forces: friction, air drag, tension

38. Example Calculations • 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 vavg= (Final speed – Initial speed)/2 Vavg = ½ at Now we can calculate the distance traveled as d= vavg t = (½ at) t = ½ at2 Note: This is only true for constant acceleration.

39. Free Fall • 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?

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

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

42. While traveling in Scotland I came across Stirling Bridge. To find out how deep it was I dropped rocks off of the bridge and found that it took them about 3 seconds to hit the bottom. What was the approximate depth of the gorge? • 15m • 30m • 45m • 90m