Question

The helicopter view in the figure below shows two people pulling on a stubborn mule. (Take  F₁ = 111 N and F₂ = 87.0 N.)

An illustration shows the helicopter view of a mule being pulled along a forked road in two directions by two men. An x y coordinate system is overlaid on the image, with the origin at the mule's nose, and the mule facing in the positive y-direction. The man on the right is pulling the mule toward the right-side forked road with a force F₁. This force vector makes an angle of 60.0° with the horizontal drawn right in front of where the mule is standing. The man on the left is pulling the mule toward the left-side forked road with a force F₂. This force vector makes an angle 75.0° with the horizontal.

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

magnitude
direction

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

magnitude
direction

Answer 1

(a)

In x - direction

Fx = 111 * cos 60 - 87 * cos 75 = 32.983 N

In y - direction,

Fy = 111 * sin 60 + 87 * sin 75 = 180.2 N

so,

F = sqrt ( 32.983² + 180.2² )

F = 183.2 N

and

direction = arctan ( 180.2 / 32.983)

direction = 79.63 degree

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(b)

F₃ = 183.2 N

direction = 259.63 degree