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 = 905 N ,F2 = 783 N , and F3 = 341 N .

1.

Find the x components of each of the three pulls.

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

2.

Find the y components of each of the three pulls.

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

3.

Use the components to find the magnitude of the resultant of the three pulls.

Express your answer in newtons to three significant figures.

4.

Use the components to find the direction of the resultant of the three pulls.

Express your answer as the angle counted from +x axis in the counterclockwise direction.

Explanation / Answer

1)

for the forces ,

F1x = 905 * cos(31) = 775.7 N

F2x = - 783 * sin(32) = -414.9 N

F3x = -341 * cos(53) = -205.2 N

2)
for the y - component


F1y = 905 * sin(31) = 466.11 N

F2y = 783 * cos(32) = 664 N

F3y = -341 * sin(53) = -272.3 N

3)

Now , for the resultant of the forces is F

Fx = 775.7 - 414.9 - 205.2

Fx = 155.6 N

Fy = 466.11 + 664 -272.3

Fy = 857.8 N

magnitude = sqrt(155.6^2 + 857.8^2)

magnitude = 871.9 N

the magnitude of resulttant is 871,9 N

4)

direction = arctan(857.8/155.6)

direction = 79.7 degree

the direction of net force is 79.7 degree

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.