physics

In physics, we are interested in why things change (and sometimes why they don’t). Models are how we explain this. Before trying to explain it with a model, however, we need to make careful observations that will hopefully lead to patterns from which we can build the model. Observations can be represented in various ways.

For a given motion, we want to ask: What observations can we make? What is changing? What makes it change?

One way to represent an observation of motion is a motion diagram, which typically includes:

Dots representing the object.

Velocity arrows connecting the dots.

Acceleration information (which we will not worry about today).

Representing Observations of Motion: Motion Diagrams

Open the Motion Diagram simulation at http://physics.bu.edu/~duffy/HTML5/motion_diagrams.html . Make sure the both the Red and Blue Car are set to initial position = 0 m, initial velocity = 5 m/s, and acceleration = 0 m/s2. (Whenever the acceleration is zero, the simulated car acts like the motorized cart.) Press PLAY to watch the motion.

In the box below, record the motion diagram for the top (Red) car. Then, complete the motion diagram by drawing velocity arrows between each dot (don’t worry about acceleration yet).

Increase the speed of the Red Car to 10 m/s, and draw its motion diagram in the box below, including velocity arrows.

Now let’s try making these representations for a different type of motion. Set the initial velocity to 0 m/s and the acceleration of the Red Car to 2 m/s2. (Once the acceleration is not zero, the simulated car acts like the Fan Cart).

Representing Observations of Motion: Graphs

A graph is a collection of points and each point corresponds to a pair of related numbers. One number in the pair represents a horizontal value and the other represents a vertical value. One way to determine changes in this type of representation is to compare two points on the graph. We can compare two points by looking at the change in their vertical values and the change in their horizontal values. The change in the vertical values is called the rise. The change in the horizontal values is called the run.

In the salary example, we looked at the run at two different locations on the graph. Choosing the run to be 1 year long made the comparing the change in the salary easier.

However, you can only compare the rise if the run at both locations is the same. Rather than always comparing two numbers (is the run the same? How do the rises compare?), we can instead compare a single number: the ratio of these values. The ratio of the rise to the run is called the slope:

Figures 2a-d are all examples of graphs of different shapes.

A particular shape for the graph is determined by whether the value of the slope changes or not at different locations on the graph. The shape of a graph tells you something about the relationship between the numbers.

Our runs in this lab will be related to time, so a run is a time interval which is always positive.

A rise is positive if the shape is generally upward from left to right (as in Figures a and b), and negative if the shape is downward from left to right (as in Figures c and d).

Go to the simulation at http://physics.bu.edu/~duffy/HTML5/1Dmotion_constantv_constanta.html . For the Red Car, set the initial position to 0 m and the initial velocity to 5 m/s. Set the acceleration of the Blue Car to 0 m/s2.

On the graphs below, sketch the Capstone position and velocity graphs displayed on the screen for the Red Car.

You only need to make a sketch of the shape of the graph, so don’t worry about any numbers. (You can switch between position and velocity graphs by using the Graph: “Position vs time” and “Velocity vs time” buttons at the bottom of the simulation.)

Fill out the following chart. If it asks for a value, find the number by reading it off of the y-axis. If it asks for the slope, find it by doing a rise/run calculation (find places where the line crosses the grey lines for the most accuracy).

Repeat, but change the initial velocity of the Red Car to 10 m/s.

Building the Model from Observations

Using variables instead of numbers in a model lets you apply the model to many different situations. We will use these variables:

d = displacement

t = time interval

v = velocity

We’ll test this model next time!

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Lab #2: Motion I « Page of »

Lab #2: Motion I « Page of »