Teach Fzx Tuesday - Making Mini Engineers

Most of my high school Honors Physics students will never even consider being engineers.  They're not interested.

But it sometimes seems like we're trying to make little engineers by  being all technical and using the 'proper' math and 'proper' symbols.  So let's simplify.  Maybe they'll understand.  Maybe they'll be inspired to become engineers or at least we won't turn them off by making Fzx another math class.

Equilibrium is the easiest example.


Both static and dynamic equilibrium require that the net force in the x- and y-directions sum to zero so we use equation collections like these.

We then force them to use the equations every time telling them that the process will help them to solve the tougher problems.  Since only the toughest problems for the toppest students will ever require substitution or multiple equation system solutions, we can dispense with the technique for the most part.  Sure, it's fun math, but math just ain't fun for most students.

Example - find tensions A and B:

We can solve for A and B by setting up net force X and net force Y equations.  The vector triangle A can be set up using Acos(theta) and Asin(theta).  So

X          Acos(theta) + B = 0
Y          Asin(theta) + 49N = 0

Two unknowns, two equations.  Substitute and solve or find the intersection of the equations or whatever.  It's also easy algebra.  But that approach is DUMB since it relies on algebra more than the brain.  This one is 12.7 times better.

Sketch the FBD, making sure that the equal magnitude vectors are equal in length.  The weight of the 5 kg object is 50 N if g = 10 m/s/s.  I chose a 50 degree angle just for fun.

By inspection Ay is 50N

and if we understand triangles we can divide by sin(theta) to get the value of A

and multiply by cos(theta) to get B since it's the same as Ax by inspection

In other words, we can avoid the official math and solve the problem by inspection and trig trickery - by a basic understanding of the situation and a basic understanding of side ratios of triangles.  This requires some gymnastics training with trig ratios that can be done pretty quickly.

The best thing about this approach is that if the talented engineer type wants to pick up the proper symbology and use the proper equations, it's an easy switch and the understanding is already there.