This page last changed on Jul 07, 2008 by kbell.
Topic 5: Forces
- 8PC2.a. Students know a force has both direction and magnitude.
- 8PC2.b. Students know when an object is subject to two or more forces at once, the result is the cumulative effect of all the forces.
Classroom discussion. One or more students pulling (with ropes) on an object with wheels (e.g., a rolling chair or a wagon). First question: if Paul pulls on the chair in this direction, what will happen? Answer (obvious): the chair will move in that direction. Better answer (not so obvious): the chair will accelerate momentarily in that direction, and continue to accelerate as long as the force is applied (and not counteracted by some other force). Guide discussion about what the second answer means (initially, no velocity; later, velocity in some direction; change in velocity implies acceleration) but don't overdo it, since this example seems so trivial. Second situation: Paul pulls in one direction, Bob pulls in the opposite direction. What will happen? Everyone knows: tug of war -- the chair will move (OK, accelerate!) in the direction of the stronger pull; if the pulls are equal the chair will remain at rest. Third situation: While Bob and Paul are pulling to either side, Ken comes along and pulls in a direction perpendicular to that of Bob and Paul. What happens? Answer: if Bob and Paul continue to pull in opposite directions (which will require walking along with the object), they will "cancel each other out" and the chair will move (accelerate) in the direction of Ken's force. If Bob and Paul stay where they are, the chair will move slighly in the direction of Ken's force and then stop. What's with that? Can the students figure out why the chair moved and then stopped? What governs how far it moves? (Hint: are Bob and Paul really pulling in opposite directions now?)
Investigations: Set up the situations we just did in the classroom, check that the model does pretty much what you observed, take snapshots and describe what 's going on. Second investigation: Here are two forces: what do you think will happen when you run the model? (Forces initially co-linear but unequal in magnitude, later equal in magnitude but not co-llinear.) Third investigation: Here are two forces; add a third force that will cancel out the first two (forces initially co-linear but unequal in magnitude, later equal in magnitude but not co-llinear).
Extensions: For "extra credit," solve the gneral problem: show that the sum of any number of forces is always equal to some other force (or no force at all) and find out how to figure out what that force is. Guided exploration in the simulation world in which the force vectors can be detached from the object and placed head-to-tail, or two forces can be added by the "parallelogram rule." To add more than two forces, start with two, figure out the resultant (by either method), then replace the original forces by their resultant, add another one, and repeat the process. We'd need to scaffold this process quite tightly.
Suggested lab: Divide the students into groups of three, give every student a rope and a strain gauge, and give the group an object to pull on. Challenge 1: try to each pull the same amount (as measured by your individual strain gauge) while keeping the object stationary. Challenge 2: have two students pull the same amount and the third pull twice as hard while keeping the object stationary. in each case, report (in your lab notebooks) what the configuration was that made it possible.
Assessments: To assess the simulation activity we need a way to evaluate the student's answers to the questions, as well as a way to distinguish when she accomplishes the task. The latter is easy, the former involves some way of determining what prediction the student is making. We could do this, for example, by having her drag the object in the direction she thinks it will go. Again, the reporting involves: did she answer correctly (on such and such a subtask) the first time, if not, did she recognize that her answer was incorrect and either change it or make some changes and run the model again, and how many such tries did it take for her to get it right?
Include forces on atoms and galaxies.