Topic 7: Force and Motion in One Dimension

Standards

1. 8PC2.c. Students know when the forces on an object are balanced, the motion of the object does not change.
2. 8PC2.e. Students know that when the forces on an object are unbalanced, the object will change its velocity (that is, it will speed up, slow down, or change direction).
3. 8PC2.f. Students know the greater the mass of an object, the more force is needed to achieve the same rate of change in motion.

*Classroom discussion:  * There are three new ideas to be added to the content of last week:

1. An object can move at constant speed even though the forces on it are perfectly balanced. (It just can't accelerate).
2. If the forces acting on an object are not perfectly balanced, the object will either speed up or slow down (in one dimension).
3. The change in the speed of an object when a given force is applied depends on the object's mass.
   Explain what is meant by one-dimensional motion. Next week will take up the situation in more dimensions.

Of these, hardest by far is to recognize that forces can be balanced even when an object is moving. The best way to discuss these concepts is by recalling, explaining, and demonstrating some examples that are likely to be familiar to the students. Here are some examples:

• A swimmer traveling through water at constant speed has zero total force applied to it -- in particular, the energy required to swim creates a force that exactly compensates for the drag force.
• When a sky diver falls she very quickly reaches terminal velocity -- the speed at which the frictional force from air exactly equals the weight of the skydiver. At that point, the skydiver no longer accelerates and the sum of all the forces on it is exactly zero. Scrunching up into a ball increases the terminal velocity.
• When you pull your little brother in a wagon you mostly go at a constant speed and the force that you apply is exactly countered by gravity and friction.

Some situations of one-dimensional accelerated motion should also be demonstrated and discussed. In each case, emphasize the connection between the change in speed and the direction and magnitude of the force. We could easily make simulations of each of these, or use PhET ones.

• Drag race.
• Bungee jumping.

Investigations: Have the students produce simulations (using our version of SimCalc) of some or all of the familiar examples of constant or accelerated motion discussed in class. The simulations should include all the forces acting on the moving object (so in the case of the first example, the boat should have a force due to gravity that is cancelled out by a buoyant force, and a force due to the motor that is cancelled out by the drag caused by its motion through the water) and the motion of the object should include acceleration or not, as discussed in class. It might be best to break the class into small groups, and assign one example to each group. The group is given 20 minutes, say, to produce the simulation, at which point each group will be called upon to demonstrate and describe its example to the rest of the class. (As usual in such situations, the individual chosen to give the presentation will be selected at random by the teacher from among the members of each group, and group's performance (and grade) will be judged on the basis not only of the completeness of the simulation but also on the skill and knowledge of the presenter.) It might also be a good idea to have each group write an "annotation" for its example prior to the presentation to the class, with the option to revise the annotation based on comments during the presentation. We'd keep track of both versions, of course, and report them to the teacher.

Extensions: Challenge students to come up with examples of their own and build animations representing them. The examples should illustrate either balanced forces acting on a body in motion, unbalanced forces acting on a body in rotational motion at constant speed, unbalanced forces acting to accelerate or decelerate an object but keep it moving in the same direction, or the effect of increasing or decreasing the mass of an object while keeping constant the force applied to it.
Suggested lab: For any of the examples studied above, create a real-world example using strain gauges to measure all the relevant forces. Collect information from the strain gauges in real time, and annotate the resulting graphs to explain any anomalies or interesting features.
Assessments: If the kids select the animation they are trying to make from a popup menu, they we can automatically evaluate whether their model has the rirht properties (e.g., does the motor boat accelerate? Does the rock on the end of the string change its speed?) If they have a chance to revise a "broken" model (say, after they have heard the class discussion of it) they we have information regarding whether they were able to act on advice to fix it, We can't score their annotations automatically, but when they select certain regions of their graphs as being worthy of annotation, we can certainly learn from that what they think is important.