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05 Midterm 1 Solutions Ch. 1-3

05 Midterm 1 Solutions Ch. 1-3 - 1 Units and Vectors(8...

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Version A 1. Units and Vectors (8 points) a. In SI units, energies are measured in units called Joules, where 1.00 Joule = 1.00 kg m 2 /s 2 . An alternative unit of energy is the Dyne: 1.00 Dyne = 1.00 g cm 2 /s 2 . How many Dynes are there in 2.50 Joules? 2 3 2 2 2 7 2 2 10 g 10 cm 1Dyne 2.50 kg m /s 2.50 10 Dynes kg m 1.00 g cm /s × × × = × A: 2.50×10 7 Dynes B: 4.25×10 7 Dynes C: 6.50×10 7 Dynes D: 6.50×10 7 Dynes b. The vector A has a magnitude of 5.00 m, and is oriented at an angle of +30.0° from the x axis. Find a vector B (in the form B x i + B y j ) so that A B has a magnitude of 4.00 m and is oriented in the direction of the positive y axis. ( ) ( ) ( ) ( ) ( ) ( ) ( ) 4.00 m 5.00 m cos 5.00 m sin 0 5.00 m cos 4.33 m 4.00 m 5.00 m sin 4.00 m 1.50 m 4.33 m 1.50 m y x y x x x x x y y y y y y A B C j C j A A C A B B A C A B B A C B i j θ θ θ θ = = + = = = = = = = = + = = = = = − = + + − G G G G G G G G A: B x = 4.33 m, B y = -1.50 m B: B x = 4.60 m, B y = +0.857 m C: B x = 6.58 m, B y = +0.394 m D: B x = 0.867 m, B y = -2.50 m

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