Statics: Equilibrium in 2 dimensions, Part III

 This lecture continues the one from part 2, shown here. 

Again, we sum up the force and moments and make sure they are equivalent to 0. 

CCW means counter clockwise and CW means clockwise. Don't forget the moment arm, and you do things relative to the MOMENT ARM not the distance. This is why for the 400mm this clockwise arm is about the lever. For any dimension any force, we have a general case that is very useful to us making some things much easier if you remember it. 

For any two-force member, the two forces must be colinear. It should me lying on the same straight line. We're going to be doing lots of bridges in the future.

Doesn't matter if it's irregular shaped, just need to be on the same line. We need an equal and opposite force to get a force balance, and if you pull on a device it's going to turn until the forces are colinear and equal and opposite. 

We can generalize this to areas with 3 forces:

For any 3-force member the force must have lines of action that intersect at a single point. AKA the lines are not parallel. 

We can use these simple facts to take away some of the unknowns. 

Remember, all of the forces must sum to 0 at a single point. 

In a free body diagram, N represents the normal force or weight, and we are looking for the forces. 

The length AB also needs to be in equilibrium, because equal and opposite because it's the reaction forces to each other. 

Now we have 3 forces now. 

This is a 3-force member and they MUST intersect at the normal. By symmetry if the normal is in the center, each side is a 45 degree angle. Then, by symmetry, B = C.  Here's the explanation with the equation: 

Let's solve a pulley problem with a cord and we will use this pulley to try to lift a big mass. For reference sake, we will label these. Say that the masses of all the pulleys are the same, and we are trying to find the tension in the line as a function of the amount of mass that we are raising. So T, the tension of the line, is a function of that mass. We assume the rope doesn't break and we want to find T.

We start where T is and keep working where we find it. Remember draw the free body diagram. Think the pulleys are vertical. Remember ropes exert pull in their own direction so you have forces there as well. Remember we want force equilibrium. 

Pulley C has a weight (mg). Will mention later.