shows three ropes tied together in a knot. One of your friends pulls on a rope w

Question

shows three ropes tied together in a knot. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force.

shows three ropes tied together in a knot. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force. How hard must you pull on the third rope to keep the knot from moving? Express your answer using two significant figures. In what direction must you pull on the third rope to keep the knot from moving? Express your answer using two significant figures. counterclockwise from the left direction

Explanation / Answer

ut the knot at 0,0 and the 3 unit force along the x axis. The 5 unit force goes into the second quadrant

Sum the Forces Horizontally (the two known ones.

3 units * cos(0o) = + 3 units
5 units * cos(120o) = -2.5 units.
Resultant = +3 - 2.5 = 0.5 units.

Sum the forces vertically
3*sin(0o) = 0
5*sin(120o) = 4.33 units
Resultant + 4.33 vertically

Find where you should be.
F = sqrt(Fx^2 + Fy^2)
F = sqrt(4.33^2 + 0.5^2)
F = sqrt(19)
F = 4.35 N

So you must pull with 4.35 units of force.

Now for the angle
The angle = 180 + Tan-1(vertical/horizontal) = 180 + tan-1(4.33/0.5) = 263.4 o from the + x axis.

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