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Motion I

This brief review provides an overview of motion, kinematics, and Newton's laws, including basic quantities to describe motion, vectors and scalars, speed and velocity, acceleration, unit conversion, and Newton's three laws of motion.

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Motion I

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  1. Motion I Kinematics and Newton’s Laws

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

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

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

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

  6. 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.

  7. A Brief Review • 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.

  8. Distance traveled in 1 hour • 35 m • 103 m • 2100 m • 126,000 m

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

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

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

  12. Track is 4000 m (2.5 mi)

  13. Is the Daytona 500 race a spped race or a velocity race? • Speed • Velocity

  14. What is the displacement for the race (200 laps)? • 0 m • 4000 m • 400,000 m • 800,000 m

  15. What is the velocity for the race (200 laps)? • 0 • 4000 • 400,000 • 800,000

  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? • 1 • 2 • 3 • 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. 1.609km = 1 mi. To find out how many miles are 75 km I would multiply the 75 km by • [1 mi/1.609 km] • [1.609 km/1 mi]

  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]

  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] = 29 m/s

  26. 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

  27. 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? • 5.92 mi/hr • 153 mi/hr • 767 mi/hr • 20077200 mi/hr

  28. Newton’s Laws

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

  30. I An object won’t change its state of motion unless a net force acts on it. • A body moving at constant velocity has zeroNet Force acting on it

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

  32. II A net force is needed to change the state of motion of an object. • Defines force: F = ma

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

  34. III When you push on something, it pushes back on you. • Action-reaction pairs (forces) act on different objects

  35. 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

  36. 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)

  37. 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

  38. 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

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

  40. A 200 kg astronaut experiences a thrust of 100 N. Acceleration = ? • 0.1 m/s2 • 0.5 m/s2 • 2m/s2 • 10 m/s2

  41. 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

  42. Force due to Gravity • Force due to gravity is weight • Dropped objects near Earth’s surface experience g = 9.8m/s2, regardless of mass • Neglects air friction • Weight is the gravitational force on a mass F = ma or W = mg

  43. 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

  44. 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

  45. When a bug hit the windshield of a car, which one experiences the larger acceleration? • The bug • The car • They experience the same force, so they experience the same acceleration

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

  47. 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.

  48. 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?

  49. 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?

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

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