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Physics is the Science of Measurement

Weight. Time. Physics is the Science of Measurement. Length. We begin with the measurement of length: its magnitude and its direction. B. A. Distance: A Scalar Quantity. Distance is the length of the actual path taken by an object. A scalar quantity:

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Physics is the Science of Measurement

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  1. Weight Time Physics is the Science of Measurement Length We begin with the measurement of length: its magnitude and its direction.

  2. B A Distance: A Scalar Quantity • Distance is the length of the actual path taken by an object. A scalar quantity: Contains magnitude only and consists of a number and a unit. distance = 20 m

  3. B D = 12 m, 20o A q Displacement—A Vector Quantity • Displacement is the straight-line separation of two points in a specified direction. A vector quantity: Contains magnitude AND direction, a number,unit & angle. (12 m, 300)

  4. D 4 m,E 6 m,W Distance and Displacement • Displacement is the change of position based on the starting point. Consider a car that travels 4 m, E then 6 m, W. Net displacement: D= 2 m, W What is the distance traveled? x= -2 x= +4 10 m !!

  5. N 60o 50o W E 60o 60o S Identifying Direction A common way of identifying direction is by reference to East, North, West, and South. (Locate points below.) Length = 40 m 40 m, 50o N of E 40 m, 60o N of W 40 m, 60o W of S 40 m, 60o S of E

  6. N 45o N W E W E 50o S S Identifying Direction Write the angles shown below by using references to east, south, west, north. 500 S of E Click to see the Answers . . . 450 W of N

  7. y (-2, +3) (+3, +2) + + x - Right, up = (+,+) Left, down = (-,-) (x,y) = (?, ?) - (-1, -3) (+4, -3) Rectangular Coordinates Reference is made to x and y axes, with + and -numbers to indicate position in space.

  8. R y q x Trigonometry Review • Application of Trigonometry to Vectors Trigonometry y = R sin q x = R cos q R2 = x2 + y2

  9. 300 90 m Example 1:Find the height of a building if it casts a shadow 90 m long and the indicated angle is 30o. The height h is opposite 300 and the known adjacent side is 90 m. h h = (90 m) tan 30o h = 57.7 m

  10. R y q x Finding Components of Vectors A component is the effect of a vector along other directions. The x and y components of the vector (R,q) are illustrated below. x = R cos q y = R sin q

  11. N 400 m y = ? 30o E x = ? R y q x Example 2:A person walks 400 m in a direction of 30o N of E. How far is the displacement east and how far north? N E The x-component (E) is ADJ: x = R cosq The y-component (N) is OPP: y = R sinq

  12. N 400 m y = ? 30o E x = ? The x-component is: Rx = +346 m Example 2 (Cont.):A 400-m walk in a direction of 30o N of E. How far is the displacement east and how far north? Note:x is the side adjacent to angle 300 ADJ = HYP x Cos 300 x = R cosq x = (400 m)cos30o = +346 m, E

  13. N 400 m y = ? 30o E x = ? The y-component is: Ry = +200 m Example 2 (Cont.):A 400-m walk in a direction of 30o N of E. How far is the displacement east and how far north? Note:y is the side opposite to angle 300 OPP = HYP x Sin 300 y = R sinq y = (400 m) sin 30o = + 200 m, N

  14. N The x- and y- components are each + in the first quadrant 400 m Ry = +200 m 30o E Rx = +346 m Example 2 (Cont.):A 400-m walk in a direction of 30o N of E. How far is the displacement east and how far north? Solution: The person is displaced 346 m east and 200 m north of the original position.

  15. Resultant of Perpendicular Vectors Finding resultant of two perpendicular vectors is like changing from rectangular to polar coord. R y q x R is always positive; q is from + x axis

  16. R +40 m f -30 m Example 3:A woman walks 30 m, W; then 40 m, N. Find her total displacement. q = 59.1o N of W R = 50 m (R,q) = (50 m, 126.9o)

  17. 1. Start at origin. Draw each vector to scale with tip of 1st to tail of 2nd, tip of 2nd to tail 3rd, and so on for others. Component Method 2. Draw resultant from origin to tip of last vector, noting the quadrant of the resultant. 3. Write each vector in x,y components. 4. Add vectors algebraically to get resultant in x,y components. Then convert to the total vector (R,q).

  18. N B 3 km, W 4 km, N C E A D 2 km, E 2 km, S Example 4.A boat moves 2.0 km east then 4.0 km north, then 3.0 km west, and finally 2.0 km south. Find resultant displacement. 1. Start at origin. Draw each vector to scale with tip of 1st to tail of 2nd, tip of 2nd to tail 3rd, and so on for others. 2. Draw resultant from origin to tip of last vector, noting the quadrant of the resultant. Note: The scale is approximate, but it is still clear that the resultant is in the fourth quadrant.

  19. N B 3 km, W 4 km, N C E A D 2 km, S 2 km, E 5. Convert to resultant vector See next page. Example 4 (Cont.)Find resultant displacement. 3.Write each vector ini,jnotation: A = +2 x B = + 4 y C = -3 x D = - 2 y 4.Add vectors A,B,C,D algebraically to get resultant inx,ycomponents. -1 x + 2 y R = 1 km, west and 2 km north of origin.

  20. Resultant Sum is: R = -1 x + 2 y N B 3 km, W 4 km, N C E D A 2 km, S 2 km, E Ry= +2 km R f Rx = -1 km Example 4 (Cont.)Find resultant displacement. Now, We Find R,  R = 2.24 km  = 63.40 N of W

  21. Conclusion of Chapter 3B - Vectors

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