# Unit 4: Balanced Forces Particle Model

The fourth unit introduces Forces. It takes about two and one-half weeks. It begins with a series of Bowling Ball Activities; e.g. make the ball speed up, slow down, turn $90^{\circ}$, move in a circular arc. In the previous unit, a simplified “Interaction Diagram,” what many call a “System Schema.” As we begin to use this diagram, we see that multiple interactions are occurring.

Students are asked to make a quick sketch of momentum vs. time for the bowling ball starting from rest, being pushed by the broom, and then rolling at “constant” velocity. Most agree that it should be a horizontal line at $p = 0$, then a diagonal line as it is speeding up, and then a horizontal line at the final constant velocity.

In previous units, students saw the slopes are often important quantities, so they are asked to try to figure out what this slope of momentum vs. time represents. Usually, with little guidance, they can figure out that this slope represents the rate at which momentum is swapping, which we define as a “Force.” Thus, if an interaction is the swapping of momentum, it’s derivative is a Force.

From there we introduce the different types of interactions present during our activities. We identify three contact forces: push (Normal), pull (Tension), and slide (Friction). We also name one non-contact force, Gravity. From there, these types of interactions are added to the interaction diagram. Then show how this interaction diagram, can be used to make Force Diagrams.

We conclude the day by noticing that multiple interactions can balance out, thus multiple forces on a single particle or systems can balance out. We go on to notice that the system will only accelerate when the forces are unbalanced, which I mention is Newton’s 1st Law (when in an inertial frame of reference).

So the next step in the sequence is Worksheet 1 in which they practice making the Interaction Diagram with forces included and Force Diagrams. They are aided by a reading that help show in greater detail how to create Force Diagrams including equality marks.

From there, we do a lab to try to begin to understand the non-contact force of gravity by hanging various masses on a spring scale. Thus finding the relationship between mass and the force of gravity.

Once that’s complete we add this calculation to begin to add numerical values into Force Diagrams in worksheet 2. Along with a second reading, we end the unit with worksheet 3 as we add component forces into the mix.

The student goals for this unit are:

1. can draw a properly labeled free body diagram of all the forces acting on an object including equality marks
2. given one interaction between two objects, determine the direction of force exerted on each object
3. determine the direction of acceleration of an object from a free body diagram
4. determine whether or not the forces are balanced given information about the motion of the object
5. determine the force of gravity on an object within a gravitational field