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9/24 Vectors!!!!

9/24 Vectors!!!!. Pick up Problem Sets Physics HW 11 & 12 2D Kinematics AP Vectors More Practice Tests are not graded. But I did sleep in a Holiday Inn last night. Bonus Opportunity. 9/25 Vectors!!!! Pick up a piece of graph paper. Yesterday you picked up

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9/24 Vectors!!!!

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  1. 9/24 Vectors!!!! Pick up Problem Sets Physics HW 11 & 12 2D Kinematics AP Vectors More Practice Tests are not graded. But I did sleep in a Holiday Inn last night. Bonus Opportunity

  2. 9/25 Vectors!!!! Pick up a piece of graph paper Yesterday you picked up Physics HW 11 & 12 2D Kinematics AP Vectors More Practice Tests are graded, but not entered. Bonus Opportunity

  3. 9/26 Vectors!!!! Yesterday we worked thorough ex 3 and 5. Today you will complete the pirate vector lab You will work in pairs. Supplies: Book cover Metric ruler Protractor Colored Pencils or markers Lab directions There are 12 clues Test Corrections if below a 70 AP Bonus opportunities

  4. 9/29 Vectors!!!! Friday we did the pirate lab. See me if you were absent. Today we will look at the Girl Scout problem (this is typically referred to as the river boat problem) and we will consider Force as a vector (push or pull) Test Corrections if below a 70 AP Bonus opportunities

  5. 9/30 Vectors!!!! Get the calculator that matches your blue tag on your desk Monday we did the Girl Scout problem (ex 6) and two Forces at right angles (ex 7) Today we will look at components, multiple vectors and learn the component method. If time we will look at problems that require correction of motion (ie 15,16, & 19 on HW #12) Test Corrections if below a 70 (This mon-thur) AP Bonus opportunities

  6. Pirate Vector LabSolve graphically (using a metric ruler and a protractor) Read the story and follow the directions exactly. Additional instructions: you must Include arrows and units for each vector Draw your resultant in a different color Determine resultant magnitude and direction graphically (using a metric ruler and a protractor) Record answer (with units) and secret rule on blank area of your map. Box your answer. Rubric: Name-Scale 1

  7. Pirate Vector Lab Rubric: 1 Name-Scale

  8. Vectors and Scalars AP Physics B

  9. Scalar A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it. Magnitude – A numerical value with units.

  10. Vector A VECTOR is ANY quantity in physics that has BOTH MAGNITUDE and DIRECTION. Vectors are typically illustrated by drawing an ARROW above the symbol. The arrow is used to convey direction and magnitude.

  11. Applications of Vectors VECTOR ADDITION – If 2 similar vectors point in the SAME direction, add them. • Example: A man walks 54.5 meters east, then another 30 meters east. Calculate his displacement relative to where he started? + 54.5 m, E 30 m, E Notice that the SIZE of the arrow conveys MAGNITUDE and the way it was drawn conveys DIRECTION. 84.5 m, E

  12. Applications of Vectors VECTOR SUBTRACTION - If 2 vectors are going in opposite directions, you SUBTRACT. • Example: A man walks 54.5 meters east, then 30 meters west. Calculate his displacement relative to where he started? 54.5 m, E - 30 m, W 24.5 m, E

  13. Non-Collinear Vectors When 2 vectors are perpendicular, you must use the Pythagorean theorem. A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT. Finish The hypotenuse in Physics is called the RESULTANT. 55 km, N Vertical Component Horizontal Component Start 95 km,E The LEGS of the triangle are called the COMPONENTS

  14. BUT……what about the direction? In the previous example, DISPLACEMENT was asked for and since it is a VECTOR we should include a DIRECTION on our final answer. N W of N E of N N of E N of W E W N of E S of W S of E NOTE: When drawing a right triangle that conveys some type of motion, you MUST draw your components HEAD TO TOE. W of S E of S S

  15. BUT…..what about the VALUE of the angle??? Just putting North of East on the answer is NOT specific enough for the direction. We MUST find the VALUE of the angle. To find the value of the angle we use a Trig function called TANGENT. 109.8 km 55 km, N q N of E 95 km,E So the COMPLETE final answer is : 109.8 km, 30 degrees North of East

  16. What if you are missing a component? Suppose a person walked 65 m, 25 degrees East of North. What were his horizontal and vertical components? The goal: ALWAYS MAKE A RIGHT TRIANGLE! To solve for components, we often use the trig functions sine and cosine. H.C. = ? V.C = ? 25 65 m

  17. Example 1 A bear, searching for food wanders 35 meters east then 20 meters north. Frustrated, he wanders another 12 meters west then 6 meters south. Calculate the bear's displacement. 23 m, E - = 12 m, W - = 14 m, N 6 m, S 20 m, N 14 m, N 35 m, E R q 23 m, E The Final Answer: 26.93 m, 31.3 degrees NORTH of EAST

  18. Example 2 A boat moves with a velocity of 15 m/s, N in a river which flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north. 8.0 m/s, W 15 m/s, N Rv q The Final Answer : 17 m/s, @ 28.1 degrees West of North

  19. Example 3 A plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate the plane's horizontal and vertical velocity components. H.C. =? 32 V.C. = ? 63.5 m/s

  20. Example 4 A storm system moves 5000 km due east, then shifts course at 40 degrees North of East for 1500 km. Calculate the storm's resultant displacement. 1500 km V.C. 40 5000 km, E H.C. 5000 km + 1149.1 km = 6149.1 km R 964.2 km q The Final Answer: 6224.14 km @ 8.91 degrees, North of East 6149.1 km

  21. Practice adding vectors Ex 5 • Draw the following to scale: • Indicate scale. • Make sure you draw tail to tip for the two vectors. • Indicate the resultant with a dotted line. The tip of the resultant meets the tip of the second vector. • You walk 5 m to the north and then 8 m east • Determine your resultant displacement graphically. • What did you get? I got 9.7m. • Determine your resultant displacement using the Pythagorean formula. • Did you get 9.43 m?

  22. Practice adding vectors Ex 5 • Draw the following to scale: • Indicate scale. • Make sure you draw tail to tip for the two vectors. • Indicate the resultant with a dotted line. The tip of the resultant meets the tip of the second vector. • You walk 5 m to the north and then 8 m east • Determine your resultant displacement graphically. • What did you get? I got 9.7m. • Determine your resultant displacement using the Pythagorean formula. • Did you get 9.43 m?

  23. Ex 5 8 m 5 m

  24. Ex 5 • “θ” or Theta, is any unknown angle but in this case it is the angle between the two vectors • Use a protractor to determine the angle “θ” of your resultant. • Place the protractor along the axis of the initial vector. Take the reading in reference to the resultant. • Refer to diagram on next slide

  25. Ex 5 8 m 5 m θ

  26. Ex 5 • What value did you get with your protractor? • I got 59° • This would be described as 59° east of north since the resultant is east of the north axis. • How could you do this mathematically? • Use SOH CAH TOA • Label the sides in reference to θ. • I would suggest using tan since you calculated the hypotenuse.

  27. Ex 5 Opp 8m Adj 5m θ

  28. Ex 5 • Using Tan: • Tan θ = opp/adj • Tan θ = 8m/5m • Tan θ = 1.6 THIS IS NOT THE ANGLE!!! • Find inverse tan. • Enter 2nd tan (1.6) enter • You should get 58.0° The direction is still East of North • This is in the same range as what we got with the protractor.

  29. Example 6 A girl scout elects to swim across the river. The river is 37.5 meters wide. A current flows downstream at a rate of 0.66 m/s. If she initially swims towards the boy scout camp (directly cross the river) at a rate of 1.73 m/s, how long will it take her to reach the far shore?

  30. ] 37.5m 1.73 m/s Remember what the question asks. How long does it take her to swim across? To solve for time, what do we need to know? Use velocity and displacement but only in reference to crossing the river.

  31. ] 37.5m 1.73 m/s v = d/t t = d/v t = 37.5m÷1.73m/s t = 21.7 s

  32. Example 6 ] 37.5m 1.73 m/s Where exactly does the girl scout end up on the far shore? What do we need to know? To determine displacement we need velocity and time but only in reference to downstream.

  33. 0.66m/s To find where she ends up, what is the downstream velocity? 0.66m/s What is the time? 21.7 sec Time is the same for both cross stream and downstream. 14.3 m downstream

  34. When working with multiple vectors remember they are independent of one another although they have a net effect. In the case of the girl scout, her overall (think resultant) velocity and direction changed. Do you know how to solve for the apparent resultant velocity and direction?

  35. 0.66m/s 1.73 m/s c θ Resultant velocity? Make sure you only use velocity vectors! c2 = 1.732 + 0.662 c = 1.85 m/s Which angle for direction? tan θ = 1.73/0.66 = 2.62… θ = 69.1° vr = 1.85 m/s at 69.1° downstream in respect to shore

  36. Fix next slide

  37. 0.66m/s 1.73 m/s c θ What angle should the girl scout enter the water upstream to end up at the boy scout camp?? Expand this

  38. How are force vectors drawn? • Tail to tail

  39. Resultant Force • The resultant force of concurrent forces can be calculated using the parallelogram method or using the component method. • We will use the parallelogram method first.

  40. F1 and F2 are: • concurrent forces. • FR is the • Resultant force. • FR’ is the • equilibrant force. • The mathematical method used with such diagram is called the parallelogram method.

  41. EX 7 One force of 7.75 N is exerted on point R in the direction of direct south. A second force of 15.50 N is exerted on R in the direction of 90.0 west of south. What is the magnitude and direction of the resultant force in reference to the larger force? θ 15.50 N tan θ = 7.75 N / 15.50 N θ = 26.6° south of west 7.75 N (15.50 N)2 + (7.75 N)2 = FR2 17.3 N = FR

  42. EX 8 A sled is being pulled up and to the right at an angle of 27.00to the horizontal. If the person is pulling with a force of 165.0 N, what are the horizontal and vertical components of the force? Determine Y using sin O= SH = sin(27)(165 N) A = 74.91 N 165.0 N 27º Determine X using cos A= CH = cos(27)(165 N) A = 147.02 N

  43. What happens if the concurrent vectors are not at right angles? • We will the component method • We will solve for resultant in respect to the X axis in Quadrant I

  44. What are the values for X & Y in each quadrant ? X is Y is X is Y is X is Y is X is Y is

  45. What are the values for X & Y in each quadrant ? X is - Y is + X is + Y is + X is + Y is - X is - Y is -

  46. Ex 8 Two forces act on point Q. The first, of 435 N, heads 18.0° north of east. The second, of 220 N, is directed due west. Determine magnitude and direction of the resultant force using the component method.

  47. Ex 9 Two forces act on point Q. The first, of 435 N, heads 18.0° north of east. The second, of 220 N, is directed due west. Determine magnitude and direction of the resultant force using the component method. 435 N 18º 220 N West

  48. Ex 9 Two forces act on point Q. The first, of 435 N, heads 18.0° north of east. The second, of 220 N, is directed due west. Determine magnitude and direction of the resultant force using the component method. Describe any angles outside of quad 1 in reference to x axis of quad 1 180º 435 N 18º 220 N West

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