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Unformatted text preview: kavo (ak22862) – HW01 – Janow – (12121) 1 This printout should have 15 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. Review assignment on vectors and fields 001 (part 1 of 2) 15.0 points Consider three force vectors vector F 1 , vector F 2 , and vector F 3 . The vector vector F 1 has magnitude F 1 = 45 N and direction θ 1 = 61 ◦ ; the vector vector F 2 has mag nitude F 2 = 31 N and direction θ 2 = − 55 ◦ ; and the vector vector F 3 has magnitude F 3 = 15 N and direction θ 3 = 160 ◦ . All the direction an gles θ are measured from the positive x axis: counterclockwise for θ > 0 and clockwise for θ < 0. What is the magnitude F of the net force vector vector F = vector F 1 + vector F 2 + vector F 3 ? Correct answer: 31 . 8582 N. Explanation: In components, each force vector is F 1 ,x = F 1 × cos θ 1 = 21 . 8164 N , F 1 ,y = F 1 × sin θ 1 = 39 . 3579 N , F 2 ,x = F 2 × cos θ 2 = 17 . 7809 N , F 2 ,y = F 2 × sin θ 2 = − 25 . 3937 N , F 3 ,x = F 3 × cos θ 3 = − 14 . 0954 N , F 3 ,y = F 3 × sin θ 3 = 5 . 1303 N , and therefore the net force is F x = F 1 ,x + F 2 ,x + F 3 ,x = 25 . 5019 N , F y = F 1 ,y + F 2 ,y + F 3 ,y = 19 . 0945 N . Consequently, the magnitude F =  vector F  of the net force vector is F = radicalBig F 2 x + F 2 y = 31 . 8582 N . 002 (part 2 of 2) 15.0 points What is the direction of the net force vector vector F ? State your answer as an angle θ between − 180 ◦ and +180 ◦ . Correct answer: 36 . 8239 ◦ . Explanation: The direction of vector F follows from the ratio of its y and x components, tan θ = F y F x , and hence either θ = arc tan F y F x = 36 . 8239 ◦ or θ = arc tan F y F x ± 180 ◦ = − 143 . 176 ◦ . To resolve the ambiguity, note the component signs: F x > 0, F y > 0, hence 0 ◦ < θ < +90 ◦ , and therefore θ = 36 . 8239 ◦ . Alternatively, the atan2 function gives the unambiguous answer for the direction of any nonzero vector: θ = atan2( F y , F x ) = 36 . 8239 ◦ . Many programming languages have this func tion predefined; if your calculator has it, you should use it. 003 (part 1 of 2) 10.0 points Consider the two vectors vector M = ( a, b ) = a ˆ ı + b ˆ and vector N = ( c, d ) = c ˆ ı + d ˆ , where a = 4, b = 4, c = 4, and d = − 4. a and c represent the xdisplacement and b and d represent the y displacement in a Cartesian xy coordinate system. Note: ˆ ı and ˆ represent unit vectors ( i.e. vectors of length 1) in the x and y directions, respectively. What is the value of the scalar product vector M · vector M ? 1. a 2 − 2 a b + b 2 2. a 2 + b 2 correct 3. a 2 + 2 a b + b 2 4. a + b 5. a 2 − b 2 6. a − b 7....
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 Fall '08
 Opyrchal
 Physics, Cartesian Coordinate System, Force, General Relativity, Correct Answer

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