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Three forces with magnitudes of 70 pounds, 40 pounds, and 60 pounds act on an object at angles of -35 degrees, 45 degrees, and 135 degrees, respectively, with the positive x-axis.

Find the direction and magnitude of the resultant of these forces.

Answer :

The magnitude of the resultant force is 69.66 pounds and it makes an angle of -53.81° with the positive x-axis.

Given,

F1:

Magnitude = 70 pounds

Angle = -35°

Fx = 70 cos(-35) = 57.34 pounds (to the right)

Fy = 70 sin(-35) = -40.40 pounds (downward)

F2:

Magnitude = 40 pounds

Angle = 45°

Fx = 40 cos(45) = 28.28 pounds (to the right)

Fy = 40 sin(45) = 28.28 pounds (upward)

F3:

Magnitude = 60 pounds

Angle = 135°

Fx = 60 cos(135) = -42.43 pounds (to the left)

Fy = 60 sin(135) = -42.43 pounds (downward)

Now, we can add up the x and y components of the forces separately to find the net force.

Net Fx = F1x + F2x + F3x

= 57.34 + 28.28 - 42.43

= 43.19 pounds.

Net Fy = F1y + F2y + F3y

= -40.40 + 28.28 - 42.43

= -54.55 pounds.

Using the Pythagorean theorem and inverse tangent function we can find the following:

Magnitude:

|F| = sqrt((Net Fx)^2 + (Net Fy)^2)

= sqrt((43.19)^2 + (-54.55)^2)

= 69.66 pounds.

Direction:

theta = atan(Net Fy / Net Fx)

= atan(-54.55 / 43.19)

= -53.81.

Therefore, the magnitude of the resultant force is 69.66 pounds and it makes an angle of -53.81° with the positive x-axis.

To learn more about vector addition, refer to:

https://brainly.com/question/2927458

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