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Homework Format

Homework Format. Cover Page. Staple at 45 0. NAME PHY 108.002 Date Problems Grade. Cover Page, Example. Staple at 45 0. Harry Downing PHY 108.002 1-28-09 Ch 11 – 2, 6, 9, 16 Grade 5, 4, 5, 3. Pass out some example engineering pad paper and take pictures.

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Homework Format

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  1. Homework Format

  2. Cover Page Staple at 450 NAME PHY 108.002 Date Problems Grade

  3. Cover Page,Example Staple at 450 Harry Downing PHY 108.002 1-28-09 Ch 11 – 2, 6, 9, 16 Grade 5, 4, 5, 3 Pass out some example engineering pad paper and take pictures.

  4. What are the x and y components of the force shown? y y Name Problem # x x

  5. Chapter 1Speed, Displacement, Velocity:An Introduction to Vectors

  6. N • Imagine that you have a map that leads you to a buried treasure. • This map has instructions such as 15 paces west northwest of the skull. • The 15 paces is a distance and west northwest is a direction.

  7. A SCALAR QUANTITY • A quantity that has nothing to do with spatial direction. • Examples of scalars in physics are mass time distance or length density work energy temperature charge

  8. DISTANCE (l) • A distance traveled, a path length, etc.

  9. AVERAGE SPEED Average Speed = distance/time Units - m/s, ft/s, etc.

  10. Speeding Little Old Lady Sorry, Ma’am, but you were doing 45 mph in a 30 mph zone. But I haven’t driven 45 miles yet. Okay, okay, would you believe that I haven’t been driving for an hour yet?

  11. 30 mph 2 miles ? Example of Average Speed B A • You take a trip from A to B and back to A. • You want to average 60 mph for the round trip A to B to A. From A to B you average 30 mph. What is your average speed on the return trip from B to A?

  12. Average Speed

  13. INSTANTANEOUS SPEED Instantaneous Speed is the speed you would read from a speedometer.

  14. Slope of a distance versus time curve

  15. A VECTOR QUANTITY • A quantity that can be specified completely only if we provide both its magnitude (size) and direction. • Examples of vectors in physics are displacement velocity acceleration force momentum angular momentum

  16. The math associated with scalars is familiar to everyone. • The math associated with vectors is more involved.

  17. THE DISPLACEMENT When an object moves from one point in space to another, the displacement is the vector from the initial location to the final location. It is independent of the actual distance traveled.

  18. VELOCITY • Average Velocity = Displacement/time Units - m/s, ft/s, etc. • Instantaneous Velocity of an object is its instantaneous speed plus the direction it is traveling. • Velocity is a vector.

  19. Displacement and Average Velocity Distance traveled is the length of the path taken. Average velocity =

  20. Average Velocity

  21. INSTANTANEOUS VELOCITY

  22. THE ADDITION OF VECTORS The resultant is the sum of a number of vectors of a particular type. Example: Force Vectors Displacement Vectors

  23. THE TIP-TO-TAIL (OR POLYGON) METHOD • Let’s use a treasure map again as an example of the addition of vectors. • Let’s imagine the instructions tell you to go 4 miles east then 3 miles north.

  24. 5 miles 3 miles 36.90 4 miles

  25. In this case you could have gone 3 miles north first and then 4 miles east next and still end up at the same location. • Your final position is 5 miles at 36.90 north of east. • It would have saved time if that had been the one distance and one direction traveled in the first place.

  26. We say that the 5 miles at 36.90 north of east is the vector sum of the 4 miles east vector and the 3 miles north vector. • The order of the addition does not matter. • Examples of addition of vectors follows. The method used will be the head-to-tail.

  27. N E W S

  28. N 900 1800 00 E W 2700 S Resultant Equilibrant

  29. PARALLELOGRAM METHOD

  30. PARALLELOGRAM METHOD

  31. SUBTRACTION OF VECTORS

  32. THE TRIGONOMETRIC FUNCTIONS hypotenuse C opposite-q B q adjacent-q A

  33. hypotenuse C opposite-q B q adjacent-q A

  34. hypotenuse C opposite-q B q adjacent-q A

  35. A COMPONENT OF A VECTOR y x

  36. y x

  37. COMPONENT METHOD FOR ADDING VECTORS • Resolve each vector into components along the axes used. Remember that components along the negative direction of an axis will be considered negative in the following additions. • Add all the x-components together. • This will be • Add all the y-components together. • This will be • Add all the z-components together. • This will be • Then In two dimensions

  38. z y x

  39. y x

  40. UNIT VECTORS y x Consider a vector that has unit length along the x-axis direction. Call it the i unit vector. Consider a vector that has unit length along the y-axis direction. Call it the j unit vector. In general a vector has components along three mutually perpendicular axes (a k unit vector along the z-axis direction) and thus can be written as Then the x-component of R becomes The y-component of R becomes

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