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 Jun 23rd 2010, 06:24 PM #1 Junior Member   Join Date: May 2010 Posts: 15 vectors Figure P3.47 shows three ropes tied together in a knot. One of your friends pulls on a rope with 6 units of force due east and another pulls on a second rope with 8 units of force toward the northwest, 120° from the first friend. How hard and in what direction must you pull on the third rope to keep the knot from moving? This is a question on a sample test given to us. I have used up all my submissions for this one, but I was basically just guessing. I'm not really sure how to do this and I couldn't find the problem online anywhere. I know this is an easy one, but I guess I have just forgotten since the start of the semester. I feel like I need to use the Pythagorean Theorem here but I'm not sure where. Any help would be appreciated.
Jun 27th 2010, 12:20 PM   #2
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Join Date: Aug 2008
Posts: 113
 Originally Posted by Sterlingm Figure P3.47 shows three ropes tied together in a knot. One of your friends pulls on a rope with 6 units of force due east and another pulls on a second rope with 8 units of force toward the northwest, 120° from the first friend. How hard and in what direction must you pull on the third rope to keep the knot from moving? This is a question on a sample test given to us. I have used up all my submissions for this one, but I was basically just guessing. I'm not really sure how to do this and I couldn't find the problem online anywhere. I know this is an easy one, but I guess I have just forgotten since the start of the semester. I feel like I need to use the Pythagorean Theorem here but I'm not sure where. Any help would be appreciated.
sketch the three vectors on a set of axes such that the 6 unit vector lies on the + x-axis.

the 8 unit force is the hypotenuse of a 30-60-90 triangle, and has components 4 units in the negative x-direction (to the left) and 4\sqrt{3} units in the positive y-direction.

since the system is in equilibrium, the unknown vector must have a component of 2 units in the negative x-direction and 4\sqrt{3} units in the negative y-direction.

use these two components to find the magnitude and direction of the unknown vector.

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