Teach Fzx Tuesday - EZr Equilibrium - Sample Problem

Static Equilibrium.  Structures.  Balanced Forces.

IF those topics are taught, students are generally presented with equations like this 

and they are expected to do lots of algebra.

Let's ignore the second condition for now and just deal with net forces in the x- and y- directions.  Remember that the net force is zero in each direction.

Here's a sample problem with my method.  It's easier than algebra.

Left tension is given as 200 N

First, I want my students to sketch a good free body diagram - ONE object and all the FORCES acting ON it.  It must be scaled so that larger forces are longer arrows and angles less than 45 degrees don't look like angles greater than 45 degrees.

Free Body Diagram

Then they find the components of each vector not already parallel to an axis using this method

Finding Vector Components

and remember that vector components are vector replacements.

Vector Components are Vector Replacements

After labeling the diagrams with all the force values they can, 

Completed Free Body Diagram

I then have them LOOK AT IT

and find the x-force that BALANCES the situation.  Then the y-force that balances the situation.  No fancy algebra equations, just looking and thinking and adding and subtracting.  

Right force by inspection: horizontal net force = 0

Sometimes they have to use the quadratic equation or a trigonometric equation like this to find another vector in the triangle

Using trig to solve for Tension

or use the vector component method in the video above to find the vertical component.

Finding vertical component

Then they LOOK AT IT again to find the final forces.  It's easy in this case since the two up forces must be balanced by the single downward weight.  Sometimes they'll construct a final force triangle showing the direction of the last force that puts the object in equilibrium.

Finding Weight by inspection: vertical net force = 0

My method depends on a good Free Body Diagram and simple addition to zero for static equilibrium.  They tend not to forget the method as quickly since my approach is less formulaic and more intuitive.  Less algebra is better.