Phys 141_HW Sol_Ch3&4_W08

Phys 141_HW Sol_Ch3&4_W08 - Cal Poly State University,...

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Cal Poly State University, SLO D. Niebuhr Physics Department Winter 2008 Phys 141 Homework Solutions Chapter 3, 4 Assigned Problems: Chapter 3 : 3, 7, 10, 18, 22, 26, 31, 45, 47 Chapter 4 : 4, 5, 8, 16, 25, 28, 32, 34, 41, 46 3.3. Visualize: Solve: (a) C = A - B if B r is directed in the same direction as A r . Size does not matter, except that A B because C as a magnitude cannot be negative. (b) C = A + B if B r is directed opposite to the direction of A r . Size does not matter. 3.7. Visualize: The figure shows the components v x and v y , and the angle θ . Solve: We have, sin40 , y v v = - ° or 10 m/s sin40 , v - = - ° or 15.56 m/s. v = Thus the x -component is cos40 (15.56 m/s ) cos40 11.9 m/s. x v v = ° = ° = Assess: Note that we had to insert the minus sign manually with y v since the vector is in the fourth quadrant. 3.10. Visualize:
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Cal Poly State University, SLO D. Niebuhr Physics Department Winter 2008 Phys 141 We will follow the rules given in the Tactics Box 3.1. Solve: (a) (2 km)sin30 1 km x r = - ° = - (2 km)cos30 1.73 km y r = ° = (b) (5 cm/s)sin90 5 cm/s x v = - ° = - (5 cm/s)cos90 0 cm/s y v = ° = (c) 2 2 (10 m/s )sin40 6.43 m/s x a = - ° = - 2 2 (10 m/s )cos40 7.66 m/s y a = - ° = - (d) (50 N)sin36.9 30.0 N x F = ° = (50 N)cos36.9 40.0 N y F = ° = Assess: The components have the same units as the vectors. Note the minus signs we have manually inserted according to the Tactics Box 3.1. 3.18. Visualize: Solve: ( a) We have 5 2 A i j = + r and 3 5 . B i j = - - r This means 2 10 4 A i j = + r and 3 9 15 . B i j = - - r Hence, 2 3 E A B = + r r r ± 1 11 . i j = - (b) Vectors A r , , B r and E r are shown in the above figure. (c) From the E r vector, 1 x E = and 11 y E = - . Therefore, the magnitude and direction of E v are 2 2 (1) ( 11) 11.05 E = + - = 1 1 1 tan tan 5.19 | | 11 x y E E φ - - = = = ° Assess: Note that is the angle made with the y -axis, and that is why 1 tan ( /| |) x y E E - = rather than 1 tan (| |/ ) y x E E - which would be the case if were the angle made with the
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Phys 141_HW Sol_Ch3&4_W08 - Cal Poly State University,...

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