This lab was all about vectors, and finding their components using trigonometry.  I hung a wooden block from a washer and then hung the washer from two different pulleys and put different weights on each pulley so that the set up was NOT symmetric.  The students had to determine the weight of the block from the setup without actually weighing the block.  They knew there were three forces on the washer, the block pulling down with its weight, and the two forces from the strings pulling up at different angles.  Since the washer is NOT accelerating, we know from Newton’s second law, net Force = mass x acceleration, that the net Force on the washer is zero.  So the forces along the vertical must add up to zero and the forces in the horizontal direction must add up to zero.  Students measured the angles of the strings (forces) and wrote down the masses attached to the strings.  Then they calculated the horizontal (x) and vertical (y) components of each force using sines and cosines. Since they know the forces exerted by the string, they just have to solve for the weight of the block.static equilibrium

I explained how I remember the sines and cosines, with Tommy’s Old Aunt Sat On Her Cat And Hollered.   Tan (theta) = Opp/Adj,  Sin (theta)  = Opp/Hyp  and Cos (theta)  = Adj/Hyp.  Here’s a nice webpage that explains what I’m talking about:

We did a number of problems from an old textbook I had, and then I gave them the Trigonometry Pile Up that I found on pinterest.  Its like a brain teaser puzzle but you have to use trig to solve it.  trig pile up The problem consists of pile of triangles and some information is given for each triangle, but you have to work your way up from the bottom to the find the length of the triangle on top of the pile.  Lots of practice using cosines, sines and even pythagorean theorem.  Rounding too soon did make some differences in the final answers so make sure they keep a few extra digits til they get to the top.  This exercise gave them a lot of practice with the trig functions so hopefully they’l know what to do next time they need one.