A detailed physics lesson example

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Constructing a JiTT Physics Lesson: A Detailed Example

The content topic: Application of Newton’s Laws

This is a lesson toward the end of a topic. It also involves problem analysis and computation.

The lesson parts.

Do students remember what the three laws actually are. Anticipate problems with the understanding of the third law. Practice constructing free body diagrams. Atwood machine analysis and demonstration. Practice in-class worksheets.

New concepts

none –

However, based on experience, a substantial review will probably be needed. The Third law is probably not understood or is misunderstood, particularly if it has to be used in an analysis. Likewise, the notion of NET FORCE may need work


Equations

2nd Law: Fnet = Ma 3rd Law: FAB = - FBA

Warmup questions

1. Two objects, 3 kg each, are suspended from a string which is passing over pulleys as in the picture above. Tiny scales are spliced into the string as shown. The weights of the scales are small and can be neglected.

What is the reading on each of the three scales? Suppose you cut the rope above the object on the left. What would the scales read now?

Scales.jpg

This is the heart of the assignment. The responses to this question will guide the review of the laws, the construction of the free body diagrams and the analysis of dynamics problems.

2. Estimate the acceleration you subject yourself to if you walk into a wall at normal walking speed. Make a reasonable estimate of your speed and of the time it takes you to come to a stop. (You can use the estimate from the first warm up if you wish).

The first warmup dealt with constant acceleration kinematics. Sending the student back to a previous warmup is trying to encourage taking the warm-ups as a learning tool seriously.

Now estimate the force the wall has to exert on your body to stop you. Compare this force to your weight. This question will start the lesson. It’s an attention grabber and it’s an unusual take on the force law.


3. Which is correct?
If action always equals reaction, a horse cannot pull a buggy because the action of the horse on the buggy is exactly cancelled by the reaction of the buggy on the horse. The buggy pulls backward on the horse just as hard as the horse pulls forward on the buggy, so they cannot move.
a. The horse pulls forward slightly harder on the buggy than the buggy pulls backward on the horse, so they move forward.

b. The horse pulls before the buggy has time to react, so they move forward.

c. The horse can pull the buggy forward only if the horse weighs more than the buggy.

d. The force on the buggy is as strong as the force on the horse, but the horse is joined to the earth by its flat hoofs, while the buggy is free to roll on its round wheels.

e. The force on the buggy is as strong as the force on the horse, but the horse is joined to the earth by its flat hoofs, while the buggy is free to roll on its round wheels.

This is a variant of the familiar third law question. It will be used throughout the lesson whenever understaning the meaning of the third law becomes an issue.


Anticipating the student responses

Question 1.

Students have to realize that the scales can be calibrated in force units or in mass units. So the first issue to look for is: in answering the question, which calibration did the student use. You may say, the scales ought to be calibrated in newtons and that’s that but that is not helpful. There are scales out there calibrated in mass units. So we have to deal with that.

Next, students have to be aware that the reason for the tension in the strings is gravity. Therefore, regardless of the calibration issue the question requires an understanding of the action of forces.

As set up, the system is in equilibrium (ask the class what that means and how do they know?) so the net force on anything (one of the masses, a piece of the string, any of the scales) has to be zero. What does that tell us about the tension in the string? Based on every day experience with lay people (even if you never taught this) you can expect some of the students to believe the tension to be zero (despite the fact that heavy enough weights would break the string), some believe that the tension is the sum of the two weights (that’s why, to draw and quarter victims, people used four horses instead of one strong horse and three stakes in the ground. Think about it!), and there will be a smattering of values somewhere in between. Anticipate that an actual set up in the classroom is essential. Seeing is believing. If students actually see the readings on the scales they may be willing to give up their preconceptions.

When it comes to predicting the readings when the string is cut, there is little that common experiences can provide as a guide. We anticipate that most students will guess; the most popular guesses being zero or the force equal to one of the weights, with not much justification.

Question 2.

Likely to fare better. It obviously calls for F=Ma. There will be various attempts at getting that acceleration, but this is the second time they meet this question so it should not be too hard.

Question 3.

This question is ubiquitous and students have to be forced to take it seriously. The prediction is that most of the choices will have takers. To get the students to leave the lesson with real understanding is a challenge. They may memorize the answer without either understanding it or even believing it. Another possibility is that students will simply look up the answer. Most commonly used questions face run that risk.


Lesson flow

Start with the estimation question. If the responses are good move on quickly to the “scales” question. If need be, engage the class in a discussion of force, inertia and acceleration. Bring in familiar examples from daily life, the sports, amusement rides, …
The “scales” question. Show a response arguing for the reading to be zero. Ask the author(s) for justification. Ask for any rebuttals. Try to see if a short “peer instruction” will change any opinions.

Move on to “twice the weight” answer. Ask the author(s) for justification. Ask for any rebuttals. Try to see if a short “peer instruction” will change any opinions.

Now you have to deal with the calibration. Will the class agree that (at least in the equilibrium case) we have to deal with forces (weights of the hanging objects) rather than their masses? When would the masses play a role? Do the masses play any role at all in the equilibrium case?

Review the units. Review the relation between mass and force and between kilogram and newton.

Check the scales in the demo setup.

(It’s preferable to bring in newton scales even though either calibration would work in principle even though, in practice, using scales calibrated in kg, or worse yet in grams, adds an unnecessary and distracting complication.)

Now bring in the responses that were closer to the correct answers. Again, ask the author(s) for justification. Ask for any rebuttals. Try to see if a short “peer instruction” will change any opinions.

Time for the demo. (use weights that are much heavier than the scale)

Have a student hang one weight from one scale, attach a string to the other end of the scale and suspend the system from his/her finger. Ask the rest of the class to predict the reading. Have the demonstrator read off the scale reading. How many forces on the hanging weight? How many forces on the scale? How many forces on the string between the weight and the scale? How many forces on the string between the scale and the finger?

Now conenct two scales in series and repeat. There are three string segments now.

Visit the horse and buggy question. Show the distribution of responses and ask for another vote. Don’t reveal the correct answer.

Go back to one scale, one weight set up and reproduce the right side of the diagram (the side with scale C) and replace scale B with the demonstrator’s finger. Ask the rest of the class to predict the reading. Have the demonstrator read off the scale reading. How many forces on the hanging weight? How many forces on the scale? How many forces on the string between the weight and the scale? How many forces on the string between the scale and the finger? Splice in scale B and repeat the exercise with the demonstrator’s finger holding on to scale B.

Tie a string to the left side of scale B and pass it over the right pulley. Repeat the exercise.

Visit the horse and buggy question. Show the distribution of responses and ask for another vote. Don’t reveal the correct answer. Have the class work the problem #1 and question #3 on the worksheet (appended to this document.) Back to the demo. Set up the demo complete except for the left weight. Make the demonstrator hold the string below scale A. Repeat the exercise. It should go very quickly now.

Complete the demo and gave the demonstrator read of all the readings.

Have the students draw the free body diagrams for the two masses and the four string segments. Identify and label all the forces.

Now have the class “cut” the string somewhere in the diagram and repeat the free body diagram exercise.

Predict the accelerations of each of the masses.

Work the rest of the problems and questions on the worksheet.

Extensions of the lesson (next class if necessary, or homework or next warmup):

Replace on of the weights with a 5 kg weight. Do the free body analysis.

Replace scale B with a mass, sliding on a frictionless table, and repeat the analysis.

Replace scale B with a mass, sliding on a table with friction, and repeat the analysis.

Replace scale B with a mass, sliding on a frictionless inclined table, and repeat the analysis.

Replace scale B with a mass, sliding on an inclined table with friction, and repeat the analysis.



Actual (unedited) student responses, selected for display in class. The responses are from Dr. Novak’s class at IUPUI, February 9, 1998. These were selected from a set of 28.

Question 2. (remember, it was decided to start with that one.)

1. I walk at an acceleration of approximately 1.66 m/s so hitting the wall would be an acceleration of - 1.66m/s.

2. 170 lb = 77.1 kg walking speed = 5.0 m/s stopping time = 2.0 s acceleration = 2.5 m/s using F = ma F = 192.75 N F of wall = 192.75 N weight = 755.6 N

3. v = 1 m/s t = .5 s a = 2 m/s2 F = 190 x 2 = - 380 N = twice my weight

4. Using a walking speed of 5.72 ft/sec and assuming it takes 2 sec to stop, my acceleration would be 2.86 ft/sec sq. Using Newton’s law I figured that the wall must exert a force of 10.725 lb in order to stop me.


5. If I walk at an initial speed of 0.5 m/s and it takes me 1 second to come to a stop when I hit the wall, my acceleration will be –0.5 m/s^2. It would take a force of 34 N to stop me. My weight is 666.4 N.


Question 1.

1. Assuming that the middle scale can measure weight from either direction: The downward forces on each side will cancel each other out giving the middle scale a measurement of 0. The other scales will both measure 3 kg. If you cut the rope, the weight would fall to the earth. Because the scales require an upward force of enough to suspend the object being weighed in order to give a measurement, the scales would read 0.

2. On scale B the reading would be zero because it has the same pull from each side so this equals the scale out. On scale A and scale C the readings are going to be zero because the force on the scale from the left is the same as on the right of the two scales. (If you cut the string) scale A, B, and C would read 3 kg times the force of gravity.

3. A and C will read 3 kg and B will read 6 kg. If the rope is cut the whole thing will crash and the scale will read 0.

4. A and C would both equal 29.4 N. Since A and C are equal, both forces should cancel each other and give a reading of 0 for B. If the rope was cut at A, there would be no opposing forces. I think A and B would equal 0 and C would equal 29.4 until it hit the ground.

5. Scale A reads 29.4 N. Scale C reads 29.4 N. Scale B reads 58.8 N because it has 29.4 N pulling to the left and right of it. (no answer to the second part.)

6. After drawing the free body diagrams I saw that the forces on the strings holding the two objects must be equal to the weight of the object, only in the upward direction. Therefore the scales A and C must each read 29.4 N. Since the objects are in equilibrium the free body digram for scale B shows force on each end heading away from the scale. Since each force is 29.4 N scale B must read 58.8 N. If the rope was cut just below scale A then using Newton’s laws all three scales would read zero.


Question 3. (only 18 students gave a response)

3 students chose b, 15 students chose e

The lesson flow based on the responses

The responses to question 1 were pretty much as expected. The representative sample shows some problems with units. If the class cooperates this can be handled fairly quickly (5 minutes.)

The representative responses show that estimation skills need honing. Many students overestimate the stopping time.

The responses to question 3 raises the suspicion that the students looked up the answer. It is a familiar question. Since the responses to question 2 do not corroborate the understanding of the third law, the horse and buggy problem will be left on the board throughout the lesson and a free body diagram will be provided as the analysis of question 2 proceeds.

The responses to question 2 are as expected and the lesson flow will proceed as outlined in part 7. Of course, particular attention will be paid to the wording of the responses. For example, response #5 provides an opportunity to reflect on the vector nature of the force.