Newton’s Second Law

 

This lesson is an extension of work that should already have been done on Newton’s Second Law, and motion of objects with and without friction. The lesson can be used as a simpler assignment for more advanced students or adapted to be a longer, more engaging assignment for beginner students or students in a less advanced class. The advanced students will be presented with this situation:

 

A block of mass M1 sits on a table with coefficient of friction μ. The block is attached to a weight of mass m2 with a rope of negligible mass which hangs off the table over a frictionless pulley. (Only the two masses are to be considered, for now we ignore the rotation of the pulley system). 

 

 

 

 

The students will solve for the acceleration of the system when m2 is released in algebraic terms only. 

 

A more engaging way to explore the problem would be this: Michael and Melissa are two mountain climbers attempting to scale Mount Everest. They have attached a rope between themselves as they scale a particularly dangerous trek. Unexpectedly, the ground below Michael gives out and he plummets towards a ledge only a small distance blow. As he falls, he pulls Melissa by the rope attached between them. If the coefficient of friction of the mountain is μ, what is the acceleration of both Michael (m2) and Melissa (m1)? Students should solve for this in only algebraic terms.

 

Once this is completed the students will then be joined in small groups and given access to computers where they will visit this website:

 

 

This site contains a java application which simulates the above situation. Each group will be given a slip of paper containing a time in seconds on it. This variable is the amount of time for a block to reach the end of the table, or for Michael to reach the ledge below. The groups must then from that time deduct the acceleration of the system. They then must deduce values for the remaining variables (M1, m2, and μ) that will give that acceleration. There are many possibilities for correct answers but there must be the stipulation that no variable can equal zero. Students will be able to run the simulation with their discovered values to see if they were correct.

 

Instructional Goals:

 

 

Materials Needed:

The initial part of the lesson needs only traditional supplies. Students will need pencil and paper to work through the algebra. It would help to have a classroom where the desks and computers are separated as the website gives the answer to the first part and it is desired that they work it out on their own. Students should not be allowed access to the computers until the initial section is completed. Once this section is done, computers with internet access and java applications are needed. There should be at least one computer for every 3 students. The students may also want a calculator. These could be allowed but it should also be noted that most computers have such an application.

 

Standards Met:

 

MOTIONS AND FORCES

D.12.7 Qualitatively and quantitatively analyze* changes in the motion of objects and the forces that act on them and represent analytical data both algebraically and graphically

D.12.8 Understand* the forces of gravitation, the electromagnetic force, intermolecular force, and explain* their impact on the universal system

 

Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology. Students:

Use models and simulations to explore complex systems and issues.

 

Description of Learners

This lesson is intended for students in a high school physics course; possible advanced or AP as an early lesson. Special education students should be given extra time and resources as needed. The goal of the lesson is not to learn about or how to access the internet application. If it becomes apparent that students are having difficulty with that, they should be directed to the website by a teacher or classmate. 

 

Prior Learning

This lesson is an advancement of topics already discussed with regards to Newton’s second law. When giving the introduction, the teacher should refer to prior class periods where that topic was introduced and studied at length as well as class periods where the motion of objects and friction were considered. The simulation will build on this prior learning by putting the theories into practice. If resources are available, it is possible to build an actual apparatus in the classroom which would definitely get the students engaged. If not, the simulation should do the trick.

 

Instructional Procedures

The teacher should begin with a brief review of previous classes on Newton’s Second Law. Questions to the class like “What is Newton’s Second Law?” and “How do we generally use it/ what are we usually looking for?” (acceleration) would suffice for this. 

 

The teacher will then present them with the problem. Individual assignment sheets should be handed out to each student with the picture, description of variables, and question posed: What is the acceleration of the system when m2 is released? These sheets could contain space to do the work or the students could use their notebooks. The teacher will then give the students time to work individually on the problem. This should take no longer than 10 minutes (5 in more advanced classes). The teacher should walk amongst the students and make himself or herself available for questions the students may have.   

 

Once the students have completed the question, the teacher should go over the correct answer to make sure everyone has it and understands the easiest, though not only, way to get to it. The teacher will then break the class into groups of three and hand each group a slip of paper. On the paper should be the web site address and a certain time in seconds. The teacher should explain that the simulation has the capability to change the height of the table (distance the masses move). The students should set the LB (as the application calls it) to s=1 meter. They will then use the motion equation presented above to find the acceleration of the system. Once they have acceleration they should be instructed to find appropriate values of masses and friction so that when they run the simulation, it will take as close to exactly as long as their groups time. While this is happening the teacher again should be intermingling with the groups, discussing any problems. 

 

One issue that may come up is that if the student put the weight of the first block too big, the system will not move. They should, or the teacher should help them realize why this is so they can proceed without this problem. 

 

Each group’s time should be different so the groups cannot work together. There could be a prize of some sort for the group whose simulation runs closest to their time but the teacher should be prepared for the possibility of multiple groups getting the exact time.

 

This lesson is designed to be completed in one class period. In longer classes, this may end up being short so the teacher should be prepared with another topic in the possible case the entire class finishes early. 

 

Assessment

 

This lesson has the feel of an assignment. While the students are constructing their own knowledge, they have essentially learned the basics in previous lectures and are now only applying what they know. As such, much of the assessment involved here is based of off whether they get the “right” answer or not. The first, and very technology based type of assessment will be seeing if the students can find the right combination of variables to make the block drop in the time assigned to them. They will have time to decipher the correct arrangement, and can call over the teacher when they have figured it out and then run the simulation on their computer. They are essentially in charge of their own assessment here because they know the expectations (the time given) and can change the parameters based on what they know about the physics until they arrive at the correct answer.

 

For another form of assessment, I could use a short answer question form to see if the students got the main points of the assignment. Questions would include things like:

What was the effect of increasing the coefficient of friction?

What happened when you made the block on the table too heavy and why?

What ways did you find to make the blocks move the fastest? The slowest?

I’m more a fan of group discussions so perhaps after trying this lesson a few times this pen and paper assessment could be turned into class discussion where the students talk together about what worked and what didn’t and why. The goal of this assessment and the goal of the lesson in general would be to determine if the kids understand how the different variables affected how Newton’s 2^nd Law applied. I would be hoping to determine if the students were simply guessing or knew how to apply the math behind the physics to get the right answers. Another possible way to determine this would be to involve some sort of short answer or journaling technique. This writing assessment would ask the students about their thought processes as they went through the activity. What numbers did they try first? Did this work? Why or why not? What did they try next, why? This assessment should explain whether the students were guessing at random or understood what changes needed to be made in the variables to make the scenario work out.