11_PartUniversity Physics Solution

11_PartUniversity Physics Solution - Units, Physical...

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Units, Physical Quantities and Vectors 1-11 (b) EXECUTE: Now let . = R AB " "" 1.40 cm 0.95 cm 0.45 cm. xxx RAB =−= + = + 2.425 cm 1.645 cm 4.070 cm. yyy + + = + 22 2 2 (0.45 cm) (4.070 cm) xy RR R =+ = + 4.09 cm R = 4.070 cm tan 9.044 0.45 cm y x R R θ == = + 83.7 = ° Figure 1.43d EVALUATE: The vector addition diagram for ( ) R AB " " " is R " is in the 1st quadrant, with , x y R R < in agreement with our calculation. Figure 1.43e (c) EXECUTE: ( ) −− B A= A B " " " " B A " " and " " are equal in magnitude and opposite in direction. 4.09 cm R = and 83.7 180 264 = °+ °= ° Figure 1.43f
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1-12 Chapter 1 EVALUATE: The vector addition diagram for ( ) =+ R BA " " " is R " is in the 3rd quadrant, with , x y R R < in agreement with our calculation. Figure 1.43g 1.44. IDENTIFY: The velocity of the boat relative to the earth, B/E v " , the velocity of the water relative to the earth, W/E v " , and the velocity of the boat relative to the water, B/W v " , are related by B/E B/W W/E v= v+ v " "" . SET UP: W/E 5.0 km/h = v " , north and B/W 7.0 km/h = v " , west. The vector addition diagram is sketched in Figure 1.44. EXECUTE: 22 2 B/E W/E B/W vvv and 22 B/E (5.0 km/h) (7.0 km/h) 8.6 km/h v = . W/E B/W 5.0 km/h tan 7.0 km/h v v φ == and 36 = ° , north of west. EVALUATE: Since the two vectors we are adding are perpendicular we can use the Pythagorean theorem directly to find the magnitude of their vector sum. Figure 1.44 1.45. IDENTIFY: Let 625 N A = and 875 N B = . We are asked to find the vector C " such that 0 A+B=C= " . SET UP: 0 x A = , 625 N y A =− . (875 N)cos30 758 N x B ° , (875 N)sin30 438 N y B ° . EXECUTE: ( ) (0 758 N) 758 N xx x CA B + =− + . ( ) ( 625 N 438 N) 187 N yy y B + =− − + . Vector C " and its components are sketched in Figure 1.45. 781 N xy CC C = . 187 N tan 758 N y x C C and 13.9 = ° . C " is at an angle of 13.9 ° above the x -axis and therefore at an angle 180 13.9 166.1 −= °° ° counterclockwise from the -axis x + . EVALUATE: A vector addition diagram for A+B+C " " " verifies that their sum is zero. Figure 1.45
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Units, Physical Quantities and Vectors 1-13 1.46. IDENTIFY: We know the vector sum and want to find the magnitude of the vectors. Use the method of components.
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11_PartUniversity Physics Solution - Units, Physical...

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