Unit 5 Blog - Unbalanced Forces

Blog Post – Unit 5: Unbalanced Forces

Friction Model:  We began this unit with an attempt to model the friction force.  By using a large dial spring scale and a block, it was evident that when pulling the block, the force acting on it grew to a maximum value and then reduced slightly once motion began.  We then posed the question:  What are the factors that you could change to that might affect the friction between the block and the table?   The list of factors we generated were:  surface area, mass (or weight) of block, surface texture, angle of pull, speed.  Different groups chose a different factor to test and then we white boarded the results. 

What we found is that friction was affect by the two surfaces in contact, and that there was a linear (direct) relationship between the force of friction and the force pushing the surfaces together. We then named the slope of the friction vs surface force the coefficient of friction. 

We then moved into our “paradigm lab” which explored the factors that might affect the acceleration of an object.  A question was asked:  “what factors could you adjust to affect the acceleration of the cart?”  The factors we determined were:   Applied force, mass (or weight) of cart, angle of pull, angle of ramp.  Each group was asked to pick two of the factors and run an experiment using logger pro, newton scales (or force sensors) and motion sensors.  We found that acceleration varied directly with applied force and inversely with mass (Newton’s 2^nd law).  

We went through a fairly confusing method of combining two generic relationships found experimentally and then determining the value of a new coefficient introduced to make the combined relationship an equality.

The coefficient was found to be “1”, which allowed us to write our equation as (a = f/m) which was verified on Google to be Newton’s 2^nd law.  

Elevator Ride:   After a brief discussion about what a bathroom scale reads (which was decided to be how hard the floor or scale pushes up on the person) each group determined the acceleration of the elevator as it traveled from 2^nd floor to 1^st floor, and then from 1^st floor to 2^nd floor.  This was done by recording the reading of a scale (or force sensor) that was measuring the “weight” (really apparent weight) of the object as the elevator moved between floors.  From these recorded “weight” changes, we used 2^nd law to compute the accelerations of the elevator.  

Modified Atwood’s Machine Analysis:  We spent considerable time analyzing the modified atwood’s machine and learned an interesting and, I think, powerful method of analyzing this as a “system” as opposed to treating objects separately and writing a system of equations to solve.  One difficulty I had with this system when I first studied it in college was how to determine whether the tension force was greater than, less than, or equal to the weight of the hanging object when the system accelerates.   Conceptually, this proved very challenging to me as I had a poor conceptual understanding of mechanics at this time.  I visualized replacing the hanging mass with my hand and pulling on the cart.  This led me to think that the force of tension would be greater than the weight of the object, which is opposite of the correct interpretation.  I could see having students place a force sensor on the cart and comparing the tension force with the weight of the object when accelerating.  This would cement, once and for all, that the net force and acceleration are in the same direction…so the tension force must be less than the weight! 

How I feel about it:  I like how the relationships that we typically use in the classroom can be developed by the student through experiment.  However, I’m uncertain whether or not the development of the relationships experimentally will have much impact on their ability to interpret and use them in real life (or classroom story problem) situations.  If nothing else, however, this would allow the student some concrete experience on which to draw upon when solving problems later on.  I really like the elevator ride scenario and have done this numerous times in my own classroom.  The difficulty I’ve always had was obtaining accurate results, but the use technology as demonstrated in this modeling session seems to ease this concern.

How I intend to implement:  I can envision doing all these activities in my classroom, however, I’m not sure of the order at this time.  In the past, I have covered friction models near the end of the forces unit, and in the modeling class, friction came first. 

Difficulties I see:  As I mentioned, I’m not sure that experimental development will aid in problem solving ability, so I envision students will still struggle with apply the 2^nd law to classroom problems.  I also am not certain that students will understand (or appreciate) how the two relationships for acceleration were merged into one relationship, nor will they appreciate the meaning or interpretation of the 3^rd coefficient being a value of one.