This hands-on activity is a part of a series of challenge-based, experiential learning modules for use in an undergraduate Dynamics course.  The modules follow the STAR Legacy Learning Model, an inquiry based method based in the How People Learn (HPL) theory. 

Pulley Panic

Problem Challenge

Students are asked to compare two designs for a new elevator system for a high-rise building.  Because the owner would like to have an efficient and quick elevator, students are first asked to evaluate which of the two provided alternatives, if either, has the quickest free fall acceleration.

Class Activities

PREDICT

Students are posed the problem at the beginning of the class period. Students are then asked to predict the solution independently.  They must commit their prediction in writing along with a justification for why they believe their solution is correct. Students are given the opportunity to volunteer their prediction and justification and share with the rest of the class.

EXPLORE PERSPECTIVES

In small groups, students are presented with a physical model that represents the system being analyzed.  The model is a two mass system connected by a string draped over a pulley.  The students can then measure the fall rate of the system using a stopwatch or phone timer.  Students are encouraged to repeat for data consistency.  Then, students repeat the process with a different mass system.  The key part is the net difference between the two masses should be the same as in the first system.  Student measure the fall time again, and now a comparison can be made.  (Note: For a more dramatic change in fall time, keep the net difference in mass as small as possible.)

After the physical model, students then construct a mathematical model.  Students can work in teams to build the equations of motion and solve for the acceleration of the two systems.

REFLECTIONS

Students are then asked to reflect on the activity.  They should identify if their original guess was a misconception and accurately describe the true phenomenon.  Instructors should ask for example reflections to be shared with class to make sure no-one is walking away with a misunderstanding.

Enhanced Module

This activity can easily be expanded beyond a single lecture module.  The pictured model above includes a 3D printed pulley (STL file provided).  The pulley has slots for 1/4"-20 hex nuts, and additional weight can be added to the pulley to investigate the effects of mass on a ridged body.  Some enhanced challenges that can be posed to students that would require a little more time and exploration:

• Predict the effect of adding mass to the perimeter of the pulley.
• Design a pully that would result in the slowest elevator descent.
• Design a motor that would provide a specified travel time over a set rise.
• Change mass ratios between the two unbalanced masses and predict the effect.