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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.
Several familiar factors determine how effective you are in opening the door. First of all, the larger the force, the more effective it is in opening the door—obviously, the harder you push, the more rapidly the door opens. If you apply your force too close to the hinges, the door will open slowly, if at all.
Most people have been embarrassed by making this mistake and bumping up against a door when it did not open as quickly as expected.
This type of problem pops up in many situations and is important in engineering and physics.
This equilibrium example problem illustrates how to determine the different forces acting on a system of forces acting on a body in equilibrium.
Note in the illustration how the ceiling rope’s force is broken into its horizontal and vertical components. The key to this type of problem is to isolate your systems and locate all the forces acting on individual parts.
This will make it easier to add up all our forces along our coordinate system. Since the system is in equilibrium, the sum of all these forces will be equal to zero.
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.