More on Forces: Challenges and Analogies

Today in Physics was an assortment of challenges related to mass, weight, and friction, ranging from easy to hard. None of the situations was inherently hard, but what makes them hard is seeing the situation for the problem you need to see it as. Students productively struggled, and along the way really strengthened our understanding of static friction, normal force, net force, and Newton’s 2nd Law.

1.  An object hangs from a scale. From a spring scale reading, determine unknown mass.
2.  A mass is suspended from above by a rubberband and below on a surface. The bottom surfaces has a force sensor reading that is shown to students. Students have to predict the force reading for the rubberband above and then check.
3. A mass is pulled by rubber bands both from above and below. Again, students can see the force reading from below, and must predict scale reading above.
4. An object with known mass rests on a rough surface. Students have a force probe and are asked to determine an estimate for coefficient of static friction. Then they are asked to put an unknown mass on top of the first one, and determine the mass of the unknown.
5. Building on task 4, they are also asked to connect the original known mass to a rubber band that pulls up slightly on it (vertically, but not enough to lift it off the rough surface). They can read how much force the rubberband is exerting with a spring scale, and they have to predict how much force it will take to budge the object.
6. A Half-Atwoods setup is shown. Students have a 1.0 kg block, moving along horizontal surface, with hanging mass being equal to 500 g. Students are asked to use a force sensor  and a motion detector to determine a value for the kinetic friction force, and the coefficient of kinetic friction.

Students were encouraged to work all the stations, but had to turn in three carefully worked out problems: Station 2 or 3, and station 4 or 5, and station 6.

For each problem students had to draw a pictorial representation, which identified the object of interest, its boundaries, and the contact forces. They had to draw a free-body diagram that included a separate Fnet vector. They had to include the readings of any data they used. And then show the work they did to arrive at their predictions, and for the ones you could check, how they compared.

Before we did this, we had a short conversation about mass and weight, and reviewed big ideas from forces so far. Over the course of discussing, reviewing, and circling around during the challenges, I made good use of our “forces” and “teams” analogy.

A Fnet Analogy: This is going to drive the force ontology people crazy: 

I’m finding it in class very useful to think of forces drawn on a FBD as showing what individual “players”, and the net force as what the “team accomplishes together”.  We’ve been using this analogy to organize our problem-solving without algorithms.

During the review, I talked about we can extend this analogy since we have learned more about the individual players–their behavior and personalities.  Weight, for example, is a player who always does the same thing, no matter what anyone else is doing. His job is to pull downward with a force of 9.8 Newtons for every kg. He doesn’t change what he is doing in response to what other team members are doing, or in response to what the motion is. Normal is quite different… the normal force is always adjusting what he is doing, depending on what other forces are doing. It’s useful to think of him as being lazy, he will pick up whatever slack is left over, but he will only do what he has to. Tension and normal are pretty similar in this way, except that one only pushes, the other only pulls, and when multiple tensions  and normals are at play, they have to work out a compromise as to who does how much. Finally there is friction, and friction is not so much lazy as “reactive”… Static friction sits around waiting to react to any other player’s efforts to get things moving. But he is only so strong, and can be overpowered. Once static friction is overpowered, he can only rely on a weaker form of himself, kinetic friction, and he works do brings thing to a stop if he can.