To practice Problem-Solving Strategy 1.3 Vector Addition. Three people pull hori

Question

To practice Problem-Solving Strategy 1.3 Vector Addition. Three people pull horizontally on ropes attached to a post, as shown in the figure.(Figure J.) The total force that they exert on the post is zero. One of them pulls directly north with Fy = 500N . Another pulls with F2 = 400N in a direction 60.0 degree west of north. Find the magnitude and direction of the force F3 exerted by the third person so that the sum of the three forces is zero. Add vectors to the diagram below to indicate the vector sum of the three forces acting on the post: R = F1 + F2 + F3 = 0. Use the conventional choice of coordinates, with the +x axis as east and the +y axis as north. Draw vectors F1, F2, and F3 on the diagram below such that F1 + F2 + F3 = 0. Draw F1 starting from the origin of the axes provided. Each unit on the graph is 100 N.

Explanation / Answer

So you want the forces to sum up to zero and we are given 2 of the forces (F1,F2) and need to find the third (F3).

So sum the forces in the y direction:

F1 + F2cos(60) - F3y = 500 + 400cos(60) + F3y = 0... Thus F3y = -700N

sum the forces in the x direction:

F3x - F2sin(60) = F3x - 400sin(60) = 0... Thus F3x = 346.41N

Thus F3 is sqrt(346.41^2 + 700^2) = 781N

Then to find its angle from 90 east.

arctan(346.41/700) = 26 degress from 90 east.

So just draw the first two with the given measurements and angles, then draw the third with the measurements we found.

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