03_P26InstructorSolution

03_P26InstructorSolution - 3.26. Visualize: Solve: (a) θ E...

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Unformatted text preview: 3.26. Visualize: Solve: (a) θ E = tan −1 ⎛ 1 ⎞ = 45° ⎜⎟ ⎝1⎠ 2 θ F = tan −1 ⎛ 1 ⎞ = 63.4° ⎜⎟ ⎝⎠ Thus φ = 180° − θ E − θ F = 71.6° (b) From the figure, E = 2 and F = 5. Using G 2 = E 2 + F 2 − 2 EF cos φ = ( 2) 2 + ( 5) 2 − 2( 2)( 5)cos(180° − 71.6°) ⇒ G = 3.00. sin α sin(180° − 71.6°) = ⇒ α = 45° 2.975 5 Since θ E = 45° , the angle made by the vector G with the +x-axis is θG = (α + θ E ) = 45° + 45° = 90°. (c) We have Furthermore, using Ex = +1.0, and E y = +1.0 Fx = −1.0, and Fy = +2.0 Gx = 0.0, and ⇒G = ( 0.0 ) G y = 3.0 2 + ( 3.0 ) = 3.0, 2 and θ = tan −1 |G y | |Gx | ⎛ 3.0 ⎞ = tan −1 ⎜ ⎟ = 90° ⎝ 0.0 ⎠ That is, the vector G makes an angle of 90° with the x-axis. Assess: The graphical solution and the vector solution give the same answer within the given significance of figures. ...
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This note was uploaded on 12/10/2011 for the course PHYS 1211 taught by Professor Geller during the Fall '09 term at University of Georgia Athens.

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