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

#### Topic 8: Force and Motion in Two Dimensions

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:  This week, we can finally understand the lay-up jump, and any other two-dimensional motion (or three-dimensional).

1. An object can move at constant velocity even though the vector sum of forces on it are perfectly balanced. (It just can't accelerate).
2. If the vector sum of forces acting on an object are not perfectly balanced, the object will either speed up or slow down or change the direction of its motion.
3. The change in the velocity of an object when a given force is applied depends on the object's mass.

Demonstrate how to extract data from the video. Graph (x,y) displacement pairs for the approximate center of mass of a player taking a jump shot. Emphasize that these are vector distances from an origin. Move the origin. Discuss negative displacements.

Students have problems realizing that forces don't always speed things up or slow them down: they can also change direction of motion at constant speed. The best way to discuss these concepts is by recalling and explaining some examples that are likely to be familiar to the students. Here are some examples:

• When a car goes around a corner at a constant speed, its velocity is changing (direction, not magnitude) The force that causes this is produced by friction between the tires and the road. (If the car goes too fast, or the roadway is slippery, the frictional force is too small and the car skids.)
• When you swing a rock on a rope you can feel the rock "trying to get away." What you're feeling is the force necessary to accelerate the rock and make it travel in a circle. (There's also the force required to keep the rock from falling.) If you were to cut the rope, the rock would fall vertically but continue to move in a straight line horizontally in whatever direction it was traveling when the force of the rope went away.

Investigations: Have the students produce simulations 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.

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