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# Howework 1 - 1 For each vector system drawn write all the...

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- 1 - 30 o A = 20 3 N 60 o B = 20 N 45 o A = 30 2 m 30 o B = 10 3 m C = 10 m 1. For each vector system drawn, write all the vectors in Cartesian (X-Y) notation. (i) (ii) 2. For each of the vector systems above, write the resultant vector in both Cartesian (X-Y) format and polar form. 3. For each of the following equations, solve for all the variables: (i) 2 3 2 5 = + x x (ii) 3 4 5 = + y x and y x 5 11 = + (iii) 1 = + + z y x and 4 3 5 2 = z y x and 2 3 = + z y 4. Five lightweight plastic spheres labeled A through E are suspended from threads as shown. Each sphere holds either positive charge +Q, negative charge –Q, or zero charge. When each sphere is moved closed to another, the following behavior is noticed: Sphere A attracts ALL the other spheres. Sphere B attracts spheres A, C, and D only, and has no effect on sphere E. A positive charge repels sphere C. A B C D E N y 3 10 x 10 - ) y sin60 x (-cos60 N 20 N y 3 10 x 30 ) y sin30 x (cos30 N 3 20 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ + = + = + = + = B A r r m y -10 C m y 3 5 x 15 - ) y sin30 x (-cos30 m 3 10 m y 30 x 30 ) y sin45 x (cos45 m 2 30 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ = + = + = + = + = r r r B A For (i) N y 3 20 x 20 ˆ ˆ + + = + B A r r magnitude = N 40 3 20 20 2 2 = + ) ( ) ( angle = o 1 - 60 20 3 20 tan = = θ For (ii) m y ) 3 5 20 ( x 15 ˆ ˆ + + + = + + C B A r r magnitude = m 3 32 3 5 20 15 2 2 . ) ( ) ( = + + angle = o 1 - 4 62 15 3 5 20 tan . = + = θ Cross-multiply 3(x+2) = 5(x-2) 3x + 6 = 5x – 10; 2x = 16; x = 8 Substitute x = 5y-11 5(5y-11) + 4y = 3; 25y – 55 + 4y = 3; 29y = 58; y=2 so then x = -1 Substitute x = 1-y-z into eqn 2 to get 2(1-y-z) -5y -3z = 4 or 2 -7y -5z = 4

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Howework 1 - 1 For each vector system drawn write all the...

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