Hw1_solution

Hw1_solution - PROBLEM 4.5.44 GOAL To express each force in...

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Unformatted text preview: PROBLEM 4.5.44 GOAL : To express each force in vector notation. GIVEN : Sketch of forces applied to a hook. ASSUME : None necessary. DRAW : FORMULATE EQUATIONS and SOLVE : Using equations (4.7) and (4.11): For F 1 : F 1 = 400 N ( − cos 60 ◦ ˆ i + cos 60 ◦ ˆ j + cos 45 ◦ ˆ k ) F 1 = ( − 200 ˆ i + 200 ˆ j + 282 . 8 ˆ k ) N For F 2 : F 2 = || F 2 || (cos θ x ˆ i + cos θ y ˆ j + cos θ z ˆ k ) cos θ x = (sin φ )(cos θ ) cos θ y = (sin φ )(sin θ ) cos θ z = cos φ F 2 = || F 2 || ((sin φ )(cos θ ) ˆ i + (sin φ )(sin θ ) ˆ j + cos φ ˆ k ) F 2 = 600 N ((sin 120 ◦ )(cos 45 ◦ ) ˆ i + (sin 120 ◦ )(sin 45 ◦ ) ˆ j + cos 120 ◦ ˆ k ) F 2 = (367 . 42 ˆ i + 367 . 42 ˆ j − 300 ˆ k ) N RESULTS : F 1 = ( − 200 ˆ i + 200 ˆ j + 282 . 8 ˆ k ) N F 2 = (367 . 42 ˆ i + 367 . 42 ˆ j − 300 ˆ k ) N CHECK : Visually check the direction, and ensure the magnitudes of the forces are correct....
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Hw1_solution - PROBLEM 4.5.44 GOAL To express each force in...

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