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UNIT 2 Two Dimensional Motion And Vectors

UNIT 2 Two Dimensional Motion And Vectors. ConcepTest 3.2a Vector Components I. 1) it doubles 2) it increases, but by less than double 3) it does not change 4) it is reduced by half 5) it decreases, but not as much as half.

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UNIT 2 Two Dimensional Motion And Vectors

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  1. UNIT 2Two Dimensional Motion And Vectors

  2. ConcepTest 3.2a Vector Components I 1) it doubles 2) it increases, but by less than double 3) it does not change 4) it is reduced by half 5) it decreases, but not as much as half If each component of a vector is doubled, what happens to the angle of that vector?

  3. ConcepTest 3.2a Vector Components I 1) it doubles 2) it increases, but by less than double 3) it does not change 4) it is reduced by half 5) it decreases, but not as much as half If each component of a vector is doubled, what happens to the angle of that vector? The magnitude of the vector clearly doubles if each of its components is doubled. But the angle of the vector is given by tan q = 2y/2x, which is the same as tan q = y/x (the original angle). Follow-up: If you double one component and not the other, how would the angle change?

  4. ConcepTest 3.2b Vector Components II 1) 30° 2) 180° 3) 90° 4) 60° 5) 45° A certain vector has x and y components that are equal in magnitude. Which of the following is a possible angle for this vector, in a standard x-y coordinate system?

  5. ConcepTest 3.2b Vector Components II 1) 30° 2) 180° 3) 90° 4) 60° 5) 45° A certain vector has x and y components that are equal in magnitude. Which of the following is a possible angle for this vector, in a standard x-y coordinate system? The angle of the vector is given by tan q = y/x. Thus, tan q = 1 in this case if x and y are equal, which means that the angle must be 45°.

  6. ConcepTest 3.3Vector Addition 1) 0 2) 18 3) 37 4) 64 5) 100 You are adding vectors of length 20 and 40 units. What is the only possible resultant magnitude that you can obtain out of the following choices?

  7. ConcepTest 3.3 Vector Addition 1) 0 2) 18 3) 37 4) 64 5) 100 You are adding vectors of length 20 and 40 units. What is the only possible resultant magnitude that you can obtain out of the following choices? The minimum resultant occurs when the vectors are opposite, giving 20 units. The maximum resultant occurs when the vectors are aligned, giving 60 units. Anything in between is also possible, for angles between 0° and 180°.

  8. Tuesday September 20th Vector Operations

  9. TODAY’S AGENDA Tuesday, September 20 • Vector Operations • Mini-Lesson: Vector Operations • Hw: Complete Practice A Problems (all) UPCOMING… • Wed: More Vector Operations • Thurs: Problem Quiz 1 Vectors • Mini-Lesson: Projectile Motion @ 0° • Fri: Projectile Motion @ any angle

  10. Graphical Addition of Vectors 1) 2) 3) 4)

  11. The Resultant and the Equilibrant

  12. The Equilibrant Vector + = The vector –R is called the equilibrant. If you add R and –R, you get zero.

  13. Practice Graphical Subtraction - =

  14. Sample Problem a) b) c)

  15. A + B B A

  16. C A + B + C B A

  17. A - B ‐B A

  18. Trigonometry Refresher: y x q To find the resultant, To find the angle, q

  19. Sample Problem You are driving up a long inclined road. After 1.50 km, you notice that signs along the roadside indicate that your elevation has increased by 175 m. What is the angle of the road above the horizontal? Ө = sin-1(175m/1500m) = 6.70° How far do you have to drive to gain an additional 150 m of elevation? sin(6.70) = (175 + 150)/Length Length(total)= 325m/sin(6.70) = 2785 m Length(additional)= 2785m – 1500m = 1285 m

  20. Sample Problem Rx = (175m)cos(95°) = -15m Ry = (175m)sin(95°) = 174m vx = (25m/s)cos(-78°) = 5.2m/s vy = (25m/s)sin(-78°) = -24m/s ax = (2.23 m/s2)cos(150°) = -1.93 m/s2 ay = (2.23 m/s2)sin(150°) = 1.12 m/s2

  21. Component Addition of Vectors 1) Resolve each vector into its x- and y-components. 2) Add the x-components(Ax, Bx, Cx, etc.) together to get Rx and the y-components (Ay, By, Cy, etc.) together to get Ry.

  22. Component Addition of Vectors 3) Calculate the magnitude of the resultant with the Pythagorean Theorem. Determine the angle with the equation:

  23. Sample Problem In a daily prowl through the neighborhood, a cat makes a displacement of 120.0m due north, followed by a displacement 72.0m due west. Find the displacement required for the cat to returned home. 72.0 m (120.0 m)2 + (72.0 m)2 = 19584 m Ө R = 140 m Ө = tan-1(120m/72m) = 59.0° 120.0 m displacement = 140m @ 59.0° below the x-axis

  24. END

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