1 / 57

MECHANICS

MECHANICS. Motion Along a Straight Line. Ps 41. But First a Review. Significant Figures Non-zero digits are always significant. Any zeros between two significant digits are significant. A final zero or trailing zeros in the decimal portion are significant.

keona
Download Presentation

MECHANICS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MECHANICS

  2. Motion Along a Straight Line Ps 41

  3. But First a Review • Significant Figures • Non-zero digits are always significant. • Any zeros between two significant digits are significant. • A final zero or trailing zeros in the decimal portion are significant. • Ex. 0.002500 has 4 significant figures • Ex. 2,500 has 2 significant figures • Ex. 2.500 x 103 has 4 significant figures • Multiplication/Division – Determined by the LEAST number of significant figures • Addition/Subtraction – Determined by LEAST number of decimal of places in the decimal portion

  4. Vectors • Vectors are physical quantities with both magnitude and direction and cannot be represented by just a single number • Displacement vs. Distance • Velocity vs. Speed • Represented by A • The magnitude of A is represented by |A| or A P2 A P1 P2 B=-A P1

  5. Vector Addition • Tip to tail method or Parallelogram method • Vector addition is commutative (a) (b)

  6. Vector Components • Vector Components

  7. Vector Addition using Components

  8. Example: Young and Freedman Problem 1.31/1.38 • A postal employee drives a delivery truck along the route shown. Determine the magnitude and direction of the resultant displacement.

  9. Example: Young and Freedman Problem 1.31/1.38

  10. Example: Young and Freedman Problem 1.31/1.38

  11. Example: Young and Freedman Problem 1.31/1.38 • DON’T FORGET DIRECTION

  12. Unit Vectors • Unit vectors are unitless vectors with a magnitude of 1. • Primarily used to point a direction. • Represented by • Note scalar times vector

  13. Example

  14. Dot Product • Or scalar product • Using components

  15. Example • What is the angle between the vectors Compute up to 3 sig figs. • Solution

  16. Cross Product • Or vector product • Direction is dictated by the right hand rule • Anti-commutative

  17. Cross Product by Components

  18. Determinant form

  19. Example • Vector A has a magnitude to 5 and lies in the direction of the x-axis. Vector B has a magnitude of 2 and lies along the xy-plane at a 30o angle with the x-axis. Find AxB. • Solution Let

  20. Motion Along a Straight Line Ps 41

  21. Displacement • Is a vector quantity, usually denoted by x. • Change in the position of a point. (we can approximate objects to be a particle) • Remember, since it’s a vector, it’s important to note both magnitude and direction. • Define positive displacement to be a movement along the positive x-axis

  22. Average Velocity P1 • At time t1 the car is at point P1 and at time t2 the car is at point P2 • We can define P1 and P2 to have coordinates x1 and x2 respectively Δx=x2-x1 • Average velocity P2

  23. Velocity • Velocity is the change in displacement per unit time in a specific direction. • It is a vector quantity, usually denoted by v • Has SI unit of m/s • Average velocity can be useful but it does not paint the complete picture. • The winner of a race has the highest average velocity but is not necessarily the fastest.

  24. Instantaneous Velocity • Velocity at a specific instant of time • Define instant as an extremely short amount of time such that it has no duration at all. • Instantaneous Velocity • top speed of 431.072 km/h (Sport version. Picture only shows regular version)

  25. x-t Graph • Average Velocity • Average velocity is the slope of the line between two points • Instantaneous Velocity • Instantaneous velocity is the slope of the tangent line at a specific point x x x2 x1 o o t1 t2 t1 t t

  26. Sample Problem • A BugattiVeyron is at rest 20.0m from an observer. At t=0 it begins zooming down the track in a straight line. The displacement from the observer varies according to the equation a) Find the average velocity from t=0s to t=10s b) Find the average velocity from t=5s to t=10s c) Find the instantaneous velocity at t=10s

  27. Solution • a) • b) • c)

  28. Acceleration • Acceleration describes the rate of change of velocity with time. • Average Acceleration • Vector quantity denoted by • Instantaneous acceleration

  29. WARNING • Just because acceleration is positive (negative) does not mean that velocity is also positive (negative). • Just because acceleration is zero does not mean velocity is zero and vice versa.

  30. Motion at Constant Acceleration • Assume that acceleration is constant. • Generally

  31. Feel Free to use vf, vi, v0 whatever notation you’re more comfortable with • BUT be consistent through out the entire problem

  32. Motion at Constant Acceleration

  33. Seat Work #1 • Using • Derive • Hint: Eliminate time

  34. Giancoli Chapter 2 Problem 26 • In coming to a stop a car leaves skid marks 92 m long on the highway. Assuming a deceleration of 7.00m/s2, estimate the speed of the car just before braking.

  35. Chapter 2 Problem 26 • Ignore negative

  36. Falling Objects • Most common example of constant acceleration is free fall. • Freely falling bodies are objects moving under the influence of gravity alone. (Ignore air resistance) • Attracts everything to it at a constant rate. • Note: because it attracts objects downwards acceleration due to gravity is • Galileo Galilei formulated the laws of motion for free fall

  37. Freely Falling • A freely falling body is any body that is being influenced by gravity alone, regardless of initial motion. • Objects thrown upward or downward or simply released are all freely falling

  38. Example Giancoli 2-42 • A stone is thrown vertically upward with a speed of 18.0 m/s. (a) How fast is it moving when it reaches a height of 11.0m? (b) How long will it take to reach this height? (c) Why are there two answers for b?

  39. Giancoli 2-42 • We can’t ignore negative

  40. Giancoli 2-42

  41. Giancoli 2-42 • Why were there 2 answers to b?

  42. Summary • These 4 equations will allow you to solve any problem dealing with motion in one direction as long as acceleration is CONSTANT! • 1. • 2. • 3. • 4.

  43. Problems from the Book (Giancoli 6thed) • 14- Calculate the average speed and average velocity of a complete round-trip, in which the outgoing 250 km is covered at 95km/hr, followed by a 1 hour lunch break and the return 250km is covered at 55km/hr. Start 95 kph 1 hour break End 55 kph

  44. Chapter 2 Problem 14 • Average speed = change in distance / change in time • For first leg • For return • Total time • Average speed

  45. Chapter 2 Problem 14 • What was the cars average velocity?

  46. Chapter 2 Problem 19 • A sports car moving at constant speed travels 110m in 5.0s. If it then brakes and comes to a stop in 4.0 s, what is its acceleration in m/s2? Express the answer in terms of g’s where g=9.80 m/s2.

  47. Chapter 2 Problem 19 • First find v

More Related