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 = 926 N ,F2 = 643 N , and F3 = 375 N .

Find the x components of each of the three pulls.

Find the y 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.

Express your answers in newtons to three significant figures separated by commas.

Explanation / Answer

F_x=F_1 cos 31 - F_2 sin 32-F_3 cos 53=227.32N

F_y=F_1 sin 31 - F_2 cos 32-F_3 sin 53=-443.33N

F=(F_x^2+F_y^2)^.5=498N

theta =arc tan(F_y/F_x)=-62.85 degree=297.14 degree from positive x

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