Example Problem: A block of weight w is suspended from a rope tied to two other ropes at point O. Assume the weights of the ropes and the knot are negligible.
One rope is horizontally attached to a wall and the other is fastened to the ceiling. If the weight of the block is 100 N, what is the tension in the ceiling rope?
Solution: This illustration shows the arrangement described in the problem.
All of the tension forces act on the knot at point O.
As always, make a nice drawing to show what's going on. We use this brainless, brute force approach to problems all the time.
Understand the rules, describe them using commands a computer understands, put numbers in, get answers out.Being careful with signs of forces and torques is important in writing the equations! Equilibrium is a special case in mechanics where all the forces acting on a body equal zero.In this practice problem, the vectors are rigged so that the alternate solution is easier than the default solution.The graphical method for addition of vectors requires placing them head to tail. You can calculate all the gravitational force values, and you have the distances of all forces from the pivot A.Hopefully, you can see the progression in solving this kind of problem from drawing the picture, to analyzing the forces, to applying the conditions for equilibrium to writing the equations.The variables have been defined as: T rope and the block.This system is useful because it relates the weight of the block to the tension in the rope.Finally, the direction in which you push is also important.The most effective direction is perpendicular to the door—we push in this direction almost instinctively. Torque is the turning or twisting effectiveness of a force, illustrated here for door rotation on its hinges (as viewed from overhead). (a) Counterclockwise torque is produced by this force, which means that the door will rotate in a counterclockwise due to F.