Determine the direction in which the third person is pulling. Learning Goal: To

Question

Determine the direction in which the third person is pulling.

Learning Goal: 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 1) The total force that they exert on the post is zero. One of them pulls directly north with F1 = 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. Part C Determine the direction in which the third person is pulling. Express the angle in degrees (0 Theta

Explanation / Answer

consider north as y-axis
and east as +x-axis

F1x= 0 N
F1y = 500 N
F2 = 400 at (90+60) angle
F2x = F2cos150 = ?346.4 N
F2y = F2sin150 =200 N
given that net force is zero
F1x+F2x+F3x =0
F3x = -F1x-F2x = 0 - (?346.4 N ) = 346.4 N
from y-components
F1y+F2y+F3y =0
F3y = - F1y - F2y = -500 - 200 = -700 N
direction = tan-1(-700/346.4) = -63.6 = 360 - 63.6 = 296.32 degrees counter clockwise from +x-axis

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