# A Modeling Approach to Mechanical Advantage

Posted on: April 24, 2012

Let me start by saying that I have yet to take a course in teaching through modeling.  I want to, and I will.

I never loved my pulley lab.  I was never pleased with the learning, the kids seem to focus on trying to set up the pulleys and not on what is happening.

Two days ago I handed them this revised instruction sheet:  Pulley Lab Rev D – Discovery Lab.  The instructions are simple, “Your job is to come up with a set of rules that explains what is happening with the pulleys, ropes, and weights.”

Besides the ring stand, support, pulleys, weights, and string, I gave each group a Vernier and force meter.  They set to work trying to figure out what is going on.

After they finished with the first setup, I asked them to tell me what happened.  The weight was the same, so what was the purpose?  Finally one of them said it changed the lifting up to pulling down.  So a single pulley can be used to change directions.  I gave them a few applications, like pulling something up into a tree or the mast of a ship.

Next they started on the other pictures.  They noticed the force changed.  I mentioned that there is a cost to the reduced force, what is the cost?  Their response was less work.  No, work is conserved.  Keep going.

When they got through picture 3, I explained that they were experiencing Mechanical Advantage.  If you hang by one arm, you hold all of your weight.  Add the second arm and you are splitting the weight.  Add a third arm… you get the picture.

As they got through the rest of the diagrams, two challenges remained:  1) what is the cost, and 2) figure out how to rig this up to get a mechanical advantage of 5.  I gave them a hint – picture 2.  They worked for a while without success.  End of the first day.

I came into class and was pleasantly surprised to see all of the groups were already set up and working.  They were twisting the ropes all over the place.  I gave them 15 minutes to play.  They still didn’t understand the cost, so I drew the solution for the MA of 5.  We put a bunch of weights on the pulleys, almost 10 lbs, and I had them all take a turn lifting.  I wanted them to experience the mechanical advantage.  Then we measured how far the weights moved and how much string was pulled to make this happen.

That was all it took, they got it.  In a perfect system, work is conserved.  This led to a discussion of efficiency and how a lever also provides a mechanical advantage.  It was a good day.

Note:  Here is the solution to the challenge at the end of the lab:  MA 5 Solution

### What’s New in 2013/2014?

Every year brings a change, this one is no exception.

I will be picking up the sophomore honors Algebra II class to keep them separate from the juniors. This should help accelerate them and put them on a stronger track towards Calculus. Looks like there will be only one section each of Physics and Calculus, but still two of Robotics & Engineering.

Hot topics this year are going to be the Common-Core Standards, Standards-Based Grading (SBG), improving AP Calculus scores, and somehow adding Python, maybe as a club.

### Polls in the sidebar

Just a quick poll to help me understand who is stopping by my blog.