Determine resultant of two vectors using components of vector

በቬክተሮች ውስጥ ያሉ ችግሮችን ተፈትተዋል - determine resultant of two vectors using components of the vector

1. ረ₁ = 6 N, F₂ = 10 N. Determine resultant vector.

መፍትሔ

F_1x = ረ₁ ኮስ 60^o = (6)(0.5) = 3 N (positive because it has same direction with x axis)

F_2x = ረ₂ ኮስ 30^o = (10)(0.5)√3) = 5√3 = (5)(1.372) = -8.66 N (negative because it has same direction with -x axis)

F_1y = ረ₁ ኃጢአት 60^o = (6)(0.5)√3) = 3√3 = (3)(1.372) = 4.116 N (positive because it has same direction with y axis)

F_2y = ረ₂ ኃጢአት 30^o = (10)(0.5)) = -5 N (negative because it has same direction with -y axis)

F_x = ረ_1x - ረ_2x = 3 – 8.66 = -5.66 N

F_y = ረ_1y - ረ_2y = 4.116 – 5 = -0.884 N

Resultant of these two forces is 5.7 N.

2. ረ₁ = 4 N, F₂ = 4 N, F₃ = 8 N. Determine resultant vector.

መፍትሔ

F_1x = ረ₁ ኮስ 60^o = (4)(0.5) = 2 N (positive because it has same direction with x axis)

F_2x = -4 N (negative because it has same direction with -x axis)

F_3x = ረ₃ ኮስ 60^o = (8)(0.5) = 4 N (positive because it has same direction with x axis)

F_1y = ረ₁ ኃጢአት 60^o = (4)(0.5)√3) = 2√3 N (positive because it has same direction with y axis)

F_2y = 0

F_3y = ረ₃ ኃጢአት 60^o = (8)(0.5)√3) = -4√3 N (negative because it has same direction with -y axis)

F_x = ረ_1x - ረ_2x + ረ_3x = 2 – 4 + 4 = 2 N

F_y = ረ_1y + ረ_2y - ረ_3y = 2√3 + 0 – 4√3 = -2√3 N

Resultant of these three forces is 5.7 N.

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