Yvonne G.

asked • 05/06/21# Can someone please answer this for me, I have been trying to work it out but I get an incorrect answer. Thank you

An object is objected to two forces: f1=112 lbs at 231degrees from the north clockwise and f2=108 lbs at N 16degrees W .. I have to find the components of F1 and write in standard form, using i and j.

Also, find the magnitude and direction of the resultant force on the object. (using NW, NE, SW, or SE to provide direction)

## 1 Expert Answer

Stanton D. answered • 05/07/21

Tutor to Pique Your Sciences Interest

HI Yvonne G.,

Something doesn't add up in the problem statement. But maybe that "231 degrees from the north clockwise" is intended to be just a directional statement. So you would count off 231 degrees clockwise of North, that's 180 degrees plus another 51 degrees. So slightly beyond SW, right? So relative to E/W, that angle of application is 39 degrees S of W. So the components of f1 are -112*cos(39)i -112*sin(39)j -- in other words, they are both negative_signed components. Remember that force directions, unlike wind directions, are named for the directions they are going towards.

For the f2, N 16 degrees W means, head 16 degrees W of N. So the components are -108*cos(74)i + 108*sin(74)j

I always like to open my angles from the x-axis; that way the i component is always a cos, and the j component always a sin. I'll let you crank out the resultant and consequent direction(s).? -- Cheers. -- Mr. d.

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Ivan V.

I recommend drawing a diagram with your 2 forces as lines pointing away from your object. To solve the components of F1, imagine you have a right triangle with the hypotenuse as 112, and the inner angle as 16 degrees. With this, you can use trigonometry and solve for sin and cosine. To find the magnitude and direction of resultant force, imagine you are adding both forces. Add the x components, add the y components, then solve for the hypotenuse of your triangle. The hypotenuse gives you the magnitude. To find the direction, you need to find the angle, which you can use trig to find.05/06/21