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 1) The total force that they exert on the post is zero. One of them pulls directly north with F1 = 500 N . Another pulls with F2 = 400N in a direction 60.0 degree west of north. Find the magnitude and direction of the force F3 rightarrow exerted calculate the magnitude of the force exerted by the third person. Express the magnitude of F3 rightarrow in newtons to three significant figures. Determine the direction in which the third person is pulling. Express the angle in degrees (0 theta

Explanation / Answer

Let's use a Cartesian grid for our diagram, where the: • positive x-axis is East • negative x-axis is West • positive y-axis is North • negative y-axis is South ... and denote "?" as meaning "vector": ?F (Force in N; Angle ? in degrees) ?F1 = (500; 90º) ?F2 = (400 N; 150º) ?F3 = (F3 N; ?3º) We are also told that the resultant vector sum, ?R = ?F1 + ?F2 + ?F3 = 0 ? ? ?R(H) = ?F1(H) + ?F2(H) + ?F3(H) = 0, (where "H" represents "horizontal") ? 500cos90º + 400cos150º + F3(cos?3) = 0 ? 0 – 343.41 + F3cos?3 = 0 ? F3cos?3 = 343.41 ? F3 = 343.41 ÷ cos?3 ? ?R(V) = ?F1(V) + ?F2(V) + ?F3(V) = 0, (where "V" represents "vertical") ? 500sin90º + 400sin150º + F3(sin?3) = 0 ? 500 + 200 + F3sin?3 = 0 ? F3sin?3) = –700 ? F3 = –700 ÷ sin?3 ? 343.41 ÷ cos?3 = –700 ÷ sin?3 ? sin?3 ÷ cos?3 = –700 ÷ 343.41 ? tan?3 = –700 ÷ 343.41 ? ?3 = atan(–700 ÷ 343.41) = –63.86... = –63.9º (n. 10th º) ? from ?, F3 = 343.41 ÷ cos?3 = 343.41 ÷ cos(–63.9º) = 779.69... = 780 N (n. 1) ? ?F3 = (F3 N; ?3º) = (780 N; –63.9º) ? The third person must exert a force of 780 N in a direction 63.9º South of East

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