The helicopter view in the figure below shows two people pulling on a stubborn m

Question

The helicopter view in the figure below shows two people pulling on a stubborn mule. Assume that F1 is 110 N, and F2 is 85 N. The forces are measured in units of newtons (N)

a) Find the single force that is equivalent to the two forces shown

Magnitude

direction

b) Find the force that a third person would have to exert on the mule to make the net force equal to zero.

Magnitude

Direction

I keep getting the magnitude for both A and B, 180.4 N. For the direction in A I get 85.5, and the direction for B, 265.54. My homework website says the directions are both in correct, off by 10% of the correct value. Any help would be helpful.

Explanation / Answer

a)

here

F1x = 110 * cos(60) = 55 N

F1y = 110 * sin(60) = 95.26 N

F2x = - 85 *cos( 75) =- 22 N

F2y = 85 * sin(75) = 82.1N

then

Fx = F1x + F2x = 55 - 22 = 33 N

Fy = F1y + F2y = 95.26 + 82.1 = 177.36 N

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

F = sqrt( 33^2 + 177.36^2 ) = 180.4 N

so the magnitude of the force equivalent to the two forces is 180.4N

then for the direction the angle will be

theta = tan^-1 (Fy / Fx)

theta = tan^-1 ( 177.36 / 33)

theta = 79.46 degree

b)

To make the net force zero a third person would pull with a force = 180.4 N and at an angle od 79.46 +180 = 259.46 degree

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