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Old Jun 23rd 2010, 07:24 PM   #1
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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.
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Old Jun 27th 2010, 01:20 PM   #2
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Originally Posted by Sterlingm View Post
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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