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A force of 100 N is acting at 30 degrees to the horizontal. Find the horizontal and...

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abigaile | Student, Undergraduate | (Level 1) Honors

Posted June 15, 2011 at 12:29 AM via web

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A force of 100 N is acting at 30 degrees to the horizontal. Find the horizontal and vertical components of the force.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted June 15, 2011 at 12:37 AM (Answer #1)

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We'll decompose the vector of force to x and y axis. The angle made by the force with x axis is of 30 degrees.

The horizontal component of the force is the adjacent side, next to the angle of 30 degrees.

The vertical component of the force is the opposite side to the angle of 30 degrees.

The given vector of the force represents the hypotenuse of the right angle triangle, whose legs are the components of the vector of force.

We'll determine the component, using the sine and cosine functions.

Let Fx be the horizontal component and Fy be the vertical component.

sin 30 = Fy/F => Fy = F*sin 30 = 100/2 = 50 N

cos 30 = Fx/F => Fx = F*cos 30 = 100*sqrt3/2 = 50*sqrt3N

The requested horizontal and vertical components of the given vector of force are: Fx = 50*sqrt3N and Fy = 50N.

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