This page last changed on Jul 07, 2008 by kbell.

#### Topic 6: Separation of Forces.

Standard 8PC2.d. Students know how to identify separately the two or more forces that are acting on a single static object, including gravity, elastic forces due to tension or compression in matter, and friction.

Classroom discussion.  Start with the most common situation of all: an object (a book, say) sitting on a table. Ask students to identify all the forces acting on the book. Common answers: gravity, friction, upward force of table. In each case, ask what direction does the force point, and how large is the force (compared to other forces). There will be differences of opinion, presumably, among the students. Try to bring these out and encourage the students to argue with each other and to try to convince each other. Introduce a MW model of a table and book in gravity where it is possible to see the sagging of the table and to eventually break the table. This directly responds to the standard phrase "elastic forces due to tension or compression in matter." The MW model can include a switch to turn off gravity. Since the book will now fly up, this gives another way that the force of the table on the book is manifest. We may be able to make a MW model that shows the forces on the book, including gravity and the net force of the table.

Next, push on the book and make it slide at a constant speed across the table. Again, ask the students to identify all the forces acting on the book, and their directions and magnitudes. This introduces friction. A probe demo can show that friction causes heating. (Embed a penny in Styrofoam and push this across more Styrofoam--most of the heat then goes into the penny.) Again, demonstrating a molecular model of friction might help show the molecular basis of frictional heating.

Investigations.  Using the simulation environment, students draw force vectors that represent their mental model of the forces acting on the book in the two situations: stationary and moving at constant speed. In each case, the activity forces them to take a snapshot of the arrows before they can run the experiment (to encourage them to think about their own mental model before committing to it). After they run the model the activity asks them whether they are pleased with the result or whether they want to change the input parameters and try again.
Extensions:  Students investigate the effect of changing the weight of the object or the nature of the two surfaces -- e.g., wood against sandpaper, wax paper against steel. Guiding question(s): how do these changes affect the behavior of the model? What changes and what stays the same?
Suggested lab:  Same experiments, but with the addition of strain gauges to measure forces. So the students measure the weight of the object (the book, or whatever it is that's moving) by hanging it from a strain gauge and then for the initial experiment they put a strain gauge between the book and the table. The first strain gauge is measuring the downward force of gravity on the book, the second is measuring the upward force of the table. (They should be the same, within experimental error.) For the moving book, the students can measure the force that produces the motion by pulling or pushing the book with a strain gauge. The opposing force seems a little harder to measure directly (though one could have the "table" on wheels and measure the force required to keep it from rolling with the book).

Assessments:  With the computer-based investigations: do they ever get it "right" (i.e., keeping the book from moving in the first place, keeping it from accelerating in the second) and if so, how many trials does it take them and do they converge on the right answer (e..g, if the book is accelerating in the direction of the external force, do they know to increase the frictional force to reduce the acceleration?

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