Instructors Companion
The Force, Motion, & Scientific Theories Unit has one over-arching purpose: to familiarize students with the consequences of a nonzero net applied force on an object. or, more briefly, F=ma. This, however, is not as simple as it seems, as student's understanding of velocity and acceleration is quite limited. As in other units, we accomplish this goal in four steps. First, we introduce students to the complexity of motion, confronting their initial belief that pushing with constant force results in a constant velocity. Second, students conduct an in-depth exploration into motion, in the process developing definitions of velocity and acceleration. Only then can students begin to characterize the response of a system to an applied force. Finally, students use the ideas developed (F=ma) to understand and explain common forces: gravity and friction.
- 1.1 A First Look At Motion
- 2.1 Position-time Graphs and the Motion Sensor
- 2.2 Velocity: A Combination of Speed and Direction
- 2.3 Developing a Hypothesis: What is the Effect of a Push?
- 3.1 The Effects of Force
- 3.2 Acceleration
- 3.3 Force and Motion: The Verdict
- 4.1 Understanding Gravity as a Force
- 4.2 Multiple Forces and Friction
1.1 A First Look At Motion
In this section students are first confronted with the idea that "motion" may not be a well-defined quantity. The goal is to introduce a question, "how do we describe a moving object", not an answer, and some student frustration is good. It is also designed to get students up and moving around, perhaps their first indication that this is not a normal, passive class. In discussing motion, students should gradually realize that all of their words dance around the concept of distance traveled; the concluding activities lead them to in fact devise a definition for and procedure to measure speed. This necessarily must involve measuring a distance. As simple as this seems, many students don't see speed/velocity as necessarily connected with displacement.
Stumbling Block: Activity 1.1. directs students to push with a constant force. Nevertheless, many will push until their partner reaches a constant velocity and cite this constant velocity as evidence of a constant force, directly contradicting the scale's reading. This is especially a problem if friction is significant (i.e. if you're on carpet). Forcing them to maintain a constant push is important and often quite revealing for the students.
Time Estimate: About 2 hours, or the first class. If necessary, a break can be made after Activity 1.1.2.
2.1 Position-time Graphs and the Motion Sensor
As the title implies, the purpose of this section is to introduce students to the motion sensor, computer software, and position-time graphs. As most of the data students take in this and subsequent sections involve graphs, this is also a relatively painless introduction to graphs. The key idea is that moving with a constant speed produces a straight line on the position vs. time graph. Faster motions produce steeper lines and motion towards/away from the motion detector produces lines that are sloped down/up on the graph.
Technical Tip Technical Tip: Students tend to be sloppy with their predictions, drawing "almost straight" lines. Make sure they take the time to draw straight lines (suggest a ruler). If they believe the slopes of two lines are different, they should put some thought into how different (not just two different lines). Some students associate "straight" only with "horizontal", and you should make sure all students ultimately recognize that straight lines can be up, down, or flat. This may also be the students first experience with "description questions" (2.1.2 question c). Students should not just scribble down a few words here; force them to take the time to write out long-hand, grammatically correct, descriptiosn that will help them study later on. Technical tips on using the motion detector are on page A-14.
Time Estimate: A little under an hour.
2.2 Velocity: A Combination of Speed and Direction
Here the students make the first quantitative connection between position vs. time graphs and velocity. Students should ultimately recognize that the slope of graph gives a quantitative way of comparing motion, must preferred to ambiguous verbal descriptions. The notion of slope is quite difficult for students; many know it only as "rise over run." In this regard, questions b-d in Activity 2.2.1 are very important for setting the tone for the section. A physical meaning for these numbers (rise, run, and slope) takes some time to develop and students should not rush through this process.
Stumbling Block: Question c in Activity 2.2.3 (Do your results make sense?) is one which students tend to rush through. It is not a yes or no question! Students should explicitly describe what they expected, what they saw, and the agreement/disagreement. Even if this is repeating the obvious, the idea is to have them repeat it until they actually believe it.
Time Estimate: About 1 hour.
2.3 Developing a Hypothesis: What is the Effect of a Push?
The purpose of this section is to have students make a very specific, quantitative prediction that can be checked with an experiment. Call attention to the fact that this is how science, in fact, progresses. Hypotheses that cannot be experimentally tested, or those which are too ambiguous to easily test, are not very useful. A discussion could center, for example, on pseudoscientific phenomena (astrology, chakra, ESP, homeopathy), which rarely make careful claims; as a consequence, we cannot scientifically evaluate them.
Stumbling Block Stumbling Block: Make sure that, before moving on to section 3, students have made a test-able prediction. The Force-time graph should have a section where the force is 0 (0-1 seconds); students sometimes overlook this time since the cart isn't moving at that time. Students also tend to draw "semi-straight" lines; make sure they use a ruler if they think the force will be a straight line.
Time Estimate: A little under an hour.
3.1 The Effects of Force
Here the students first encounter quantitatively the effect of a constant force on an object, in effect observing that F=ma. The section begins with students developing a quantitative definition of force. Students have an intuitive understanding of force (everyone knows what it means to "push harder"), but we include this activity to reinforce the idea that a physics understanding of a phenomenon requires more than mere qualitative description. It is not enough to "push harder"; in order to make accurate, quantitative checks on a hypothesis students must have a quantitative way of describing things. Activity 3.1.2 repeats the very first activity of the Motion unit (pushing w/constant force), but now the students have another way of verifying the constant force and are already thinking about how the velocity can change. It is interesting to compare students performance on activity 3.1.2 with that on the earlier activity, 1.1.1. In activity 3.1.3 the students finally test their hypothesis from the earlier section with a fan on a low-friction cart.
Stumbling Block Stumbling Block: The activities here are relatively simple; main pitfall is that students will rush through them and not grasp the nuances. In defining force, students will often not recognize the importance of a quantitative definition. You might want to discuss the importance of communication and verification (how can you communicate your results to another group so they can verify your results) as well as specificity (why are quantitative predictions more powerful). The motion detector and fan attachment work very well together, and the resulting velocity vs. time graph should be very straight. Using four batteries in the cart produces a large enough force so that friction is really negligible.
Time Estimate: A little over an hour.
3.2 Acceleration
Here students develop the idea of acceleration as a quantitative description for a changing velocity, allowing them to quantitatively relate Force and Motion. Acceleration is one of the most difficult concepts for students to master, and the section is designed to lead the students through the following chain of reasoning. First, the slope of the velocity graph tells you how quickly the velocity is changing, be it increasing or decreasing. Specifically, the slope tells how much the velocity changes in one second. Second, because a line with positive slope can be on either side of the x-axis, so to an object with negative velocity can still have an "increasing velocity." Finally, the slope of this line is commonly called the acceleration.
Stumbling Block Stumbling Block: This may be the most difficult section in the unit, as students grapple with concepts that directly contradict their intuitive beliefs. Students frequently struggle with the idea of adding physical meaning to a slope (slope is not just "rise over run"!). Ultimately they must all agree that the slope of a velocity vs. time diagram is how much the velocity changes in one second, do not allow them to "get away" with qualitative words like "rate." Each group should articulate examples of the various combinations of velocity and acceleration (positive acceleration but slowing down, negative acceleration but speeding up, etc.).
Time Estimate: About an hour.
3.3 Force and Motion: The Verdict
By varying the angle of a ramp, students can effectively vary the force applied to a cart (measured with a force sensor). The motion detector then measures the acceleration and students can observe a direct proportionality between force, mass and acceleration. A key idea is that students intuitive guesses about the relationship of force, mass, and acceleration are actually correct. It's a rare occasion where naive guesses are quantitatively correct. By the end of this section students should finally begin to understand "F=ma."
Stumbling Block Stumbling Block: Students sometimes misunderstand the task in activity 3.3.1, rather than doubling the force they want to double the ramp angle (which sort of works for low angles). Then, since they cannot "see" gravity, they struggle with the idea of "force pulling down the ramp." All they need, however, is to recognize that there is a force pulling the cart down the ramp, the specifics of what or how are not important. The question in activity 3.3.3 about being in outer space is difficult, and it is not important that students answer it correctly. Rather, they should just think about how the relationship they have just discovered (Force proportional to acceleration) might manifest in outer space and how friction is always around us here on Earth. Finally, with activity 3.3.5, it is sometimes difficult getting cases where the force is the same on the different masses. Remind the students to take their data carefully and repeat measurements to make sure they are correct.
Time Estimate: About an hour.
4.1: Understanding Gravity as a Force
Students observe tossed objects move with constant acceleration and therefore must be experiencing a constant force, *even at the top when the velocity is momentarily zero*. Since all tossed objects move withe same acceleration, the gravitational force on more massive objects must be greater.
Stumbling Block Stumbling Block: It may take some time for students to understand why the gravitational force must be greater on more massive objects; their naive belief is that "gravity is the same" for all objects. Nevertheless, they take great pleasure in ultimately recognizing this nuance. If students still do not understand how the acceleration can be constant even when the velocity is zero, this gives a final opportunity to clarify the question.
Time Estimate: About 45 minutes.
4.2: Multiple Forces and Friction
Having established the relationship between Force and Motion in cases involving one force, students now look at cases involving two forces. In particular, students now confront the inevitable conclusion that a moving object that is currently experiencing a zero net force continues to move without slowing down. Finally students use their knowledge of force and motion to infer from observations properties of of static and kinetic friction. Finally, students use their understanding of friction to explain the situation posed at the very beginning of the unit with people pushing on a heavy safe.
Stumbling Block Stumbling Block: Students have some difficulty in activity 4.2.2 with the idea that when the ramp is raised the net force on the cart actually goes down. They want to think that the force goes up, since force means (to them) "force from ramp" and they do not combine this with the force from the fan.
Time Estimate: A little over an hour.
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Student Stumbling Blocks: The text following this icon describes some of the stumbling blocks that you might encounter while teaching this section. If you encounter other significant stumbling blocks, please e-mail David Jackson.
Technical/Equipment Tips: The text following this icon describes some technical tip(s) that might be helpful when setting or executing the activities in this section. Often these tips describe the construction or setup of equipment or indicate instances where students might have difficulty with the equipment.
Time Estimates: The text following this icon gives a rough estimate of the amount of time the activities in this section will require.