Express the two forces in Cartesian vector form. Determine the magnitude and coordinate direction angles of the resultant.

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Question

Express the two forces in Cartesian vector form. Determine the magnitude and coordinate direction angles of the resultant.

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Answer 1

Answer #1

a )

given F₁ = 250 N , F₂ = 400 N

and

= 120⁰ , = 45⁰ , = 60⁰

and also = 25⁰ , = 35⁰

now

F₁ = 250 X ( cos35 X sin 25 i + cos 35 X cos25 j - sin35 k )

F₁ = 86.54 i + 185.59 j - 0.5735 k

F₂ = 400 X ( cos120 i + cos45 j + cos 60 k )

F₂ = -200 i + 282.84 j + 200 k

F = F₁ + F₂

F = - 113.46 i + 468.43 j + 199.4265 k

F = 113.46² + 468.43² + 199.4625²

F = 521.61 N

b )

cos = -113.46 / 521.61

= 102.56⁰

cos = 468.43 / 521.61

= 26.09⁰

cos = 199.4625 / 521.61

= 67.51⁰

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Answer 2

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Express the two forces in Cartesian vector form. Determine the magnitude and coordinate direction angles of the resultant.