Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, th

Question

Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown in the figure.(Figure 1) Take F1 = 913N ,F2 = 761N , and F3 = 389N .

A.Find the

Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown in the figure.(Figure 1) Take F1 = 913N ,F2 = 761N , and F3 = 389N Find the x components of each of the three pulls Find the components of each of the three pulls Use the components to find the magnitude of the resultant of the three pulls. Use the components to find the direction of the resultant of the three pulls.

Explanation / Answer

Take F1 = 913N ,F2 = 761N , andF3 = 389N .

A)

F1x = 913*cos(31 deg) = 782.593 N

F2x = -761*sin(32 deg) = -403.268 N

F3x = -389*cos(53 deg) = -234.106 N

B)

F1y = 913*sin(31 deg) = 470.229 N

F2y = 761*cos(32 deg) = 645.364

F3y = -389*sin(53 deg) = -310.669 N

C)

Fnet = (782.593 - 403.268 - 234.106) i + (470.229 + 645.364 - 310.669) j N

Fnet = 145.219 i + 804.924 j N

Magnitude = sqrt(145.219^2 + 804.924^2) = 817.918 N

D)

Direction = arctan(804.924/145.219) = 79.77 degrees

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