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6_PartUniversity Physics Solution

6_PartUniversity Physics Solution - 1-6 1.31 Chapter 1...

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1-6 Chapter 1 1.31. I DENTIFY : Draw each subsequent displacement tail to head with the previous displacement. The resultant displacement is the single vector that points from the starting point to the stopping point. S ET U P : Call the three displacements A " , B " , and C " . The resultant displacement R " is given by R = A+ B + C " " " " . E XECUTE : The vector addition diagram is given in Figure 1.31. Careful measurement gives that R " is 7.8 km, 38 north of east # . E VALUATE : The magnitude of the resultant displacement, 7.8 km, is less than the sum of the magnitudes of the individual displacements, 2.6 km 4.0 km 3.1 km + + . Figure 1.31 1.32. I DENTIFY : Draw the vector addition diagram, so scale. S ET U P : The two vectors A " and B " are specified in the figure that accompanies the problem. E XECUTE : (a) The diagram for C = A+ B " " " is given in Figure 1.32a. Measuring the length and angle of C " gives 9.0 m C = and an angle of 34 θ = ° . (b) The diagram for D = A B " " " is given in Figure 1.32b. Measuring the length and angle of D " gives 22 m D = and an angle of 250 θ = ° . (c) ( ) A B = A+ B " " , so A B " " has a magnitude of 9.0 m (the same as A+ B " " ) and an angle with the x + axis of 214 ° (opposite to the direction of A+ B " " ). (d) ( ) B A = A B " " " " , so B A " " has a magnitude of 22 m and an angle with the x + axis of 70 ° (opposite to the direction of A B " " ). E VALUATE : The vector A " is equal in magnitude and opposite in direction to the vector A " . Figure 1.32 1.33. I DENTIFY : Since she returns to the starting point, the vectors sum of the four displacements must be zero. S ET U P : Call the three given displacements A " , B " , and C " , and call the fourth displacement D " . 0 A+ B + C + D = " " " " . E XECUTE : The vector addition diagram is sketched in Figure 1.33. Careful measurement gives that D " is144 m, 41 south of west. #
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Units, Physical Quantities and Vectors 1-7 E VALUATE : D " is equal in magnitude and opposite in direction to the sum A+ B + C " " " . Figure 1.33 1.34. I DENTIFY and S ET U P : Use a ruler and protractor to draw the vectors described. Then draw the corresponding horizontal and vertical components.
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