The four forces F1, F2 F3, and F4 can be combined into one resultant force that

Question

The four forces F1, F2 F3, and F4 can be combined into one resultant force that we will call F. What are the x and y components of the net force. F. that the cables exert on the crate? Express your answers, separated by a comma, to three significant figures and include the appropriate units. As shown a crate of unknown mass is suspended in the air by four cables and is at rest. Three of these forces have magnitudes F1 = 300 N f2 = 400 N. and F3 = 350 N with angles theta 1 = 20.0 degree, theta 2 = 36.0 degree, and theta 3 = 22.5 degree, respectively. The magnitude of F4 Is unknown, but its angle is the same as that of the 3-4-5 triangle.

Explanation / Answer

Given F1 = 300N, F2 =400N, F3 = 350N a1 = 20 degrees, a2 = 35 degrees, a3 = 22.5 degrees, a4 = a degrees given that mass is at rest ie., Fx = 0 From the diagram we have Fx = F4 cos a + F3 cos(90-22.5) - F1 cos (20) - F2 cos (90-35) = 0 ===> F4 cos a = -350 cos(90-22.5) + 300 cos (20) + 400 cos (90-35) ===> F4 cos a = 377.39 N Fy = F4 sin a + F3 sin(90-22.5) - F1 sin (20) - F2 sin (90-35) ====> Fy = F4 sin a + 350 sin(90-22.5) - 300 sin (20) - 400 sin (90-35)

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