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GROUP # _______

PHYS 110 Lab #2: Motion II

The big idea:

Does the motion model always work?

Last week you made a model for motion based on the observation that the value of the slope of the position graph was the same as the velocity. The model looked like this:

	What kinds of motion did you observe in the previous lab or have observed in your everyday life that you are confident that you can describe with the model? What kinds of motion do you think the model won’t apply to or are not sure if it applies. Provide at least three of each. Be prepared to share your ideas with the class.
	Model will apply:	Model doesn’t apply:

QUESTION 1: The table below shows how we extract information from position and velocity graphs. How would our model predict how we could extract displacement information from a velocity graph? (Hint: For equations, what you want to solve for should be by itself to the left of the equal sign.)

Your result for Question 1 is the same model for motion but expressed in a different way.

Your model should work!

First, let’s investigate the model in a situation where we’re confident it will work—motion that’s similar to the kind of behavior you derived the model from.

Open the simulation at http://physics.bu.edu/~duffy/HTML5/1Dmotion_constantv_constanta.html . For the Red Car, set the initial position to 0 m, the initial velocity to 4 m/s. For the Blue Car, set the acceleration to 0 m/s2.

On the graphs on the next page, sketch the 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. Use the dark line on the graphs below as the reference point for the vertical axis, but don’t worry about any numbers.

Motorized cart LOW Speed away from sensor:

Extract the following data from the position graph. For the slope, use the rise/run. For the time interval, read it off of the horizontal axis. For the displacement, read it off the vertical axis. For the area, find the area of a square and count squares (you’ll have to estimate for the bits that are part of a square). Include units!

the slope:
the run (time interval, t) for the entire motion:
the rise (displacement, d) for the entire motion:
the area enclosed by the graph line:

Extract the following data from the velocity graph:

the mean:
the run (time interval, t) for the entire motion:
the rise for the entire motion:
the area enclosed by the graph line:

QUESTION 2: You’ve already seen that the slope of the position graph and the mean of the velocity graph have the same value and units. What other information listed above from the velocity graph matches the information from the position graph in both value and units?

THIS IS A GOOD PLACE HAVE YOUR INSTRUCTOR CHECK YOUR ANSWER!

QUESTION 3: Is the matching information (your answer to Question 2) consistent with your version of the model from Question 1? Justify your answer.

Does the model work for all motion?

Let’s see if the model still works for a very different sort of behavior.

Set the velocity of the Red Car to 0 m/s and the acceleration of the Blue Car to 1.5 m/s2.

On the graphs below, sketch the position and velocity graphs of the Blue Car displayed on the screen. You only need to make a sketch of the shape of the graph, don’t worry about numbers.

High Fan-speed Cart away from sensor:

Extract the following data from the position graph:

the run (time interval, t) for the entire motion:
the rise (displacement, d) for the entire motion:

Extract the following data from the velocity graph:

the run (time interval, t) for the entire motion:
the rise (velocity change) for the entire motion:
the area enclosed by the graph line:

Use the time interval, t, and the velocity change (rise) in your model (d=vt) to calculate d. Show your work below:	NOTE: The value of the velocity changes so it’s not clear which value to use for v. We’ll try the change of velocity, because that includes the whole range of velocity values.

QUESTION 4: Is your calculation using the model consistent with your fan cart data? Justify your answer.

QUESTION 5: For the motorized cart, you saw that the displacement from the position graph and the area under the velocity graph have the same value and units. Is that also true for the fan cart? Justify your answer.

	Make a model for the cart’s motion in terms displacement, time and velocity. Start with your answer to Question 5.

NEW VERSION OF THE MODEL:

THIS IS A GOOD PLACE HAVE YOUR INSTRUCTOR CHECK YOUR ANSWER!

time

velocity

Use the new version of the model to find the displacement for the motion shown in the graph above. Your result will have the variables d, v0, vf, and t.

Your answer above is written in terms displacement, time and velocity. Your book has the same model written like this:

Find a way to make your model look like the book’s. (HINT: ) The book’s version is the most used version.

Testing the New Model

Now that you’ve developed a new model, it’s time to investigate it, as well as the kinds of motion it can describe, more fully.

Watch the videos for each of these behaviors:

PREDICTION 1:

Push in positive direction: Suppose you take data in the following way: With the fan on high speed, give the fan cart a short, gentle push in the positive direction (away from the sensor). The cart should move away from you, turn around and come back to you. Ignoring the push, sketch your predictions for the graphs of this motion on the next page.

PREDICTION 2:

Push in negative direction: Suppose you take data in the following way: With the fan on high speed, give the fan cart a short, gentle push in the negative direction (towards the sensor). The cart should move away from you, turn around and come back to you. Ignoring the push, sketch your predictions for the graphs of this motion on the next page.

You can skip the acceleration graphs when you make your predictions.

PREDICTION for Fan Cart push in positive direction	PREDICTION for Fan Cart push in negative direction

Look at the graphs provided for each of the motions of the cart, and sketch them below. Skip the acceleration graphs.

DATA for Fan Cart push in positive direction	DATA for Fan Cart push in negative direction

Let’s try to understand this motion before we apply the model.

For the fan cart pushed in the positive direction:

As the fan cart moves AWAY from the sensor, does it speed up or slow down?
As the fan cart moves AWAY from the sensor, is the value of the acceleration positive, negative or zero?
As the fan cart moves TOWARDS the sensor, does it speed up or slow down?
As the fan cart moves TOWARDS the sensor, is the value of the acceleration positive, negative or zero?

Draw a motion diagram the fan cart moving AWAY from the sensor:

308D070.tmp

Draw a motion diagram for fan cart moving TOWARDS the sensor:

308D070.tmp

For the fan cart pushed in the negative direction:

As the fan cart moves TOWARDS the sensor, does it speed up or slow down?
As the fan cart moves TOWARDS the sensor, is the value of the acceleration positive, negative or zero?
As the fan cart moves AWAY from the sensor, does it speed up or slow down?
As the fan cart moves AWAY from the sensor, is the value of the acceleration positive, negative or zero?

Draw a motion diagram for fan cart moving TOWARDS the sensor:

308D070.tmp

Draw a motion diagram for fan cart moving AWAY from the sensor:

308D070.tmp

QUESTION 6: Is the acceleration always positive if the cart speeds up? What evidence do you have to support your answer?

Now, let’s test the model for this motion.

Using the graphs, record data for the push in the positive position:

QUESTION 7: Is the data above consistent with your version of the model? Justify your answer. (Include calculations!)

QUESTION 8: For constant motion, you found that the slope of the position graph was the same as the value of the velocity. Is this still the case for accelerated motion? Use data from the positive and negative pushes to justify your answer.

Lab #3: Motion II Group Worksheet | Page of