Bepaal de vectorcomponenten

Opgeloste problemen met vectoren - determine vector components

1. A force of 20 Newton makes an angle of 30o with the x-axis. Find both the x and y component of the force.

Solving vectors problems – determine vector components 1Het resultaat

Fx = F cos 30o = (20)(cos 30o) = (20)(0.5√3) = 10√3 Newton

Fy = F sin 30o = (20)(sin 30o) = (20)(0.5) = 10 Newton

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2. F1 = 20 Newton makes an angle of 30o with the y axis and F2 = 30 Newton makes an angle of 60o with the -x axis. Find both the x and y components of F1 en F2.

Solving vectors problems – determine vector components 2Het resultaat

F1x =F1 cos 60o = (20)(cos 60o) = (20)(0.5) = -10 Newton (negative because it has same direction with -x axis)

F2x =F2 cos 60o = (30)(cos 60o) = (30)(0.5) = -15 Newton (negative because it has same direction with -x axis)

F1y =F1 zonde 60o = (20)(sin 60o) = (20)(0.5√3) = 10√3 Newton (positive because it has same direction with y axis)

F2y =F2 zonde 60o = (30)(sin 60o) = (30)(0.5√3) = -15√3 Newton (negative because it has same direction with -y axis)

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3. F1 = 2 N, F2 = 4 N, F3 = 6 N. Find both the x and y components of F1, F2 en F3!

Solving vectors problems – determine vector components 3Het resultaat

F1x =F1 cos 60o = (2)(cos 60o) = (2)(0.5) = 1 Newton (positive because it has the same direction with x axis)

F2x =F2 cos 30o = (4)(cos 30o) = (4)(0.5√3) = -2√3 Newton (negative because it has the same direction with -x axis)

F3x =F3 cos 60o = (6)(cos 60o) = (6)(0.5) = 3 Newton (positive because it has the same direction with x axis)

F1y =F1 zonde 60o = (2)(sin 60o) = (2)(0.5√3) = √3 Newton (positive because it has the same direction with y axis)

F2y =F2 zonde 30o = (4)(sin 30o) = (4)(0.5) = 2 Newton (positive because it has the same direction with y axis)

F3y =F3 zonde 60o = (6)(sin 60o) = (6)(0.5√3) = -3√3 Newton (negative because it has the same direction with -y axis)

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  1. Bepaal de resultante van in een lijnvector
  2. Bepaal de vectorcomponenten
  3. Bepaal de resultante van twee vectoren met behulp van de stelling van Pythagoras.
  4. Bepaal de resultante van twee vectoren met behulp van de cosinusvergelijking.
  5. Determine resultant of two vectors using components of vectors

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