05202009, 12:23 PM  #1 
Junior Member
Join Date: May 2009
Posts: 5

Rope Pulling
Hi. I'm having difficulty grasping the concept of vectors and displacements. I was wondering if someone could help me with this question:
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. A) How hard must you pull on the third rope to keep the knot from moving? B) In what direction must you pull on the third rope to keep the knot from moving? 
05212009, 10:14 AM  #2 
PHF Helper
Join Date: Feb 2009
Location: India
Posts: 365

First find the resultant of 3 units and 5 units forces. The third force must be equal and opposite to it so that the net force on the knot is zero. To find the resultant R of vectors A and B you can use the formula
R^2 = A^2 + B^2 + 2AB*cos@ where @ is the angle between A and B And the angle @' that the resultant R makes with A can be found by the formula  tan@' = Bsin@/(A+Bcos@) 