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Vector Combination and Fundamentals of 2D forces handout 1

Vector Combination and Fundamentals of 2D forces handout 1. Homework and Review Questions. Draw a picture for each vector shown: 25 m [N 37 W] 14.3 m/s (197 °) 7.45 N [ SE ] 890 m/s 2 ( 342°) 76.5 N [ E 49.7 S] 9.34 m [ S 6.0 W ]. Write the direction value for each vector shown:.

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Vector Combination and Fundamentals of 2D forces handout 1

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  1. Vector Combination and Fundamentals of 2D forces handout 1 Homework and Review Questions

  2. Draw a picture for each vector shown: 25 m [N 37 W] 14.3 m/s (197°) 7.45 N [ SE ] 890 m/s2 ( 342°) 76.5 N [ E 49.7 S] 9.34 m [ S 6.0 W ] Write the direction value for each vector shown: Homework 57.5 m 9.6° 7) 9) 8) 19 N 65° 27° 48 m/s

  3. Q10 • An explorer walks 13 km due east, then 18 km north and finally 3 km west. • What is the total distance walked (in km)? • What is the resultant displacement (in km) of the explorer from the starting point?

  4. Q11 • While flying due east at 120 km/h is also carried northward at 45 km/h by a wind blowing due north. What is the plane resultant velocity?

  5. Question 12 • A hike leaves camp and , using a compass walks 4 km [E], 6 km [S], 3 km [E], 5 km [N], 10 km [W], 8 km [N] and 3 km [S]. At the end of 3 days, the hiker is lost. By drawing a diagram, compute how far the hiker is from camp and which direction should be taken to get back to camp.

  6. Vector combination Handout 2

  7. Q1 • Find the resultant vector of the following: • 5m/s [N] • 6 m/s [E] • 7 m/s [S] • 8 m/s [W] • 19 m/s [E] • 46 m/s [N]

  8. Q2 • Determine the components of the following vectors: • A) 30 N [ S 35 E] • B) 47 m [N74 W]

  9. Q3 • How do you add the following vectors? • 4 m [N] + 5 m [S 30 E]

  10. How would you combine these • 20 m [N] + 25 m [SE] ?

  11. Question 4 • Dave rows a boat directly across the river at 4.0 m/s [N]. The river flows at 6.0 m/s [E] and is 360 m across. a) In what overall direction does Dave’s boat go? b) How far downstream is Dave’s landing point c) How much time does it take for Dave to cross the river, and would the time be different if there was no current in the river?

  12. Q5 Drunken Man Problem • A tipsy man staggers out of a bar and moves with the following 3 vectors: • A) 50 m [N] • B) 47 m [NE] • C) 90 m [S 76 W] • What is the man’s overall displacement from the bar door?

  13. Question 6 • Dan applies a force of 92 N on a heavy box by using rope held at an angle of 45° with the horizontal. What are the vertical and horizontal components of the 92N force?

  14. Question 7 • A 40 kg crate is pulled across the ice with a rope. A force of 100 N is applied at an angle of 30 ° with the horizontal. Neglecting friction, calculate • The acceleration of the crate • The upward force the ice exerts on the crate as it is pulled

  15. Question 8 (picture) T1 30° T2 Eat at Joe's

  16. Question 8 • Joe wishes to hang a sign weighing 750 N from the cables shown in the picture. Calculate the tension in both cables

  17. Question #5 • An object is equilibrium has 3 forces exerted on it. A 33 N force pushing [N], a 44 N [E 60 N] and an unknown third force. • What is the magnitude and direction of the third force?

  18. Find the equilibriant…. 52 m/s [ S 79 E]

  19. Homework • Page 121 • Problem 1-4

  20. Today • Homework • 90-94

  21. Example: • Combine the following vectors: 17 m/s [N 33 W] + 8.5 m/s [S] + 4.6 m/s (201°)

  22. Homework • Page 121 problems 1-4 combination of vectors • Page 125, problems 5-9 components of vectors

  23. Homework • Page 121 problems 1-4 combination of vectors • Magnitude means size • Pythagorean with right angles • Law of Cosines with non right angles • Law of cosines if you know more about the angles than sides

  24. Weekend homework • Page 125, problems 5-9 components of vectors

  25. Add the 2 vectors • 15.56 m [N] and 26.7 m [E]

  26. Add the vectors • 87.6 m/s (30 degrees North of West) • 70.2 m/s [W]

  27. Find the components of the following vector • 96.8 m/s2 (37.8 degrees South of East)

  28. Find the components of the following vector • 327.5 N [ S 82 W]

  29. Subtract • 51.6 m [N] – 45.7 [W]

  30. Subtract • 36.9 m/s [ S] – 48.6 [ S 47 W]

  31. Subtract • 36.9 m/s [ S] – 48.6 [ S 47 W]

  32. Add the vectors • 87.6 m/s (30 degrees North of West) • 70.2 m/s [W] • 56.2 m/s [N]

  33. Monster problem • Combine the following and determine the resultant vector. • 545 N [NW] • 329 N [E] • 871 N [S 63.6 E] • 734 N [N] • 456 N [73.6 degrees West of North]

  34. What is the net force acting on the ring? • Force 1: 500 N [N 50 W] • Force 2: 400 N [N 40 E]

  35. Question • Alfredo leaves camp and, using a compass, walks 4 km E, then 6 km S, 3 km E, 5 km N, 10 km W, 8 km N, and finally 3 km S. • Compute the distance and displacement of Alfredo. • Determine which direction he should take to get directly back to camp

  36. Can you answer this question… • Suppose a 2105 kg truck is stalled and motionless at an icy intersection. • A blue car hits the truck with a force of 3450 N [ S] at the exact same time as a… • Red car hits the truck with a force of 2590 N [ E 40 N] What is the net force? What is the acceleration of the truck? How far does the truck move in ½ a second?

  37. Answer this question as well… • A 15,800 kg sailboat glides through the water without friction. • The only force applied to the sail is a steady breeze of 17,640 N pushing at a 30 degree angle to the horizontal. What is the amount of force applied to the sail that pushes it forward? If the sailboat begins at rest, how fast will the boat travel after 1 minute?

  38. Class Problem #3 • A 110 N force and a 55 N force both act on an object at point P. The 55 N force acts at 0%. What is the magnitude and direction of the resultant force? Point p 55 N 110 N

  39. Answer • Since the boat moves with constant acceleration and velocity (a = 0) • Use equation D = vit + ½at2 • 136 = (16) t + ½ (0) t2 • t = 8.5 s • The 9 m/s [N] has no bearing on what happens [E] 0

  40. Class Problems • An explorer walks 13 km due east, then 18 km north and finally 3 km west. • What is the total distance walked (in km)? • What is the resultant displacement (in km) of the explorer from the starting point?

  41. Class problem #2 • While flying due east at 120 km/h (in km/h) is also carried northward at 45 km/h (in km/h) by a wind blowing due north. What is the plane resultant velocity?

  42. Class Problem #3 • A 110 N force and a 55 N force both act on an object at point P. The 55 N force acts at 0%. What is the magnitude and direction of the resultant force? Point p 55 N 110 N

  43. Class Problem • Two ropes are pulling on a log. What is the net force? • 1st force = 12.0 N at 10° • 2nd force = 8.0 N at 120°

  44. Crazy Rocket problem

  45. Lawn mover/ sled problem types

  46. Example Q. #5 • A plane moves with a velocity of: • 250 m/s [N 30 E] How fast is the plane moving directly North?

  47. Determine the resultant of the following vector values: 48 m [ N ] 67 m [ S 61 W]

  48. Find the equilibrant to the following combination: 59 m/s [ N] - 67 m/s [E] + 49 m/s [ S ] - 16 m/s [W]

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