How do you roll

How do you roll?

Purpose: Observe and compare the motion of a cart rolling down hill versus a cart rolling up hill. Develop a mathematical model of the position versus time and velocity versus time for these two motions. Determine how the motion depends on the mass of the cart, and the angle at which the track is inclined.

Set up your linear dynamics track as shown:

When you remove the stop from the top of the track to install the motion sensor, be careful not to lose the square nut which fits inside the channel on the track, or the stop will not work when we need it later. Your track already has an angle indicator attached. Adjust the angle to a position between 3^o and 4^o.

Data Studio set-up:

Plug in the motion sensor as in the Match Graph activity and again connect the Xplorer interface to the computer via USB cable.

Open the Data Studio program from your desktop. Click “create experiment” on the opening page. (If the file manager window opens, click “done”). The program will recognize that the motion sensor is plugged in.

Next click on the “Setup” button and the step up screen will appear. The position button should already be selected; you should also select the velocity option. Then set the sample rate to 50 Hz (Hertz = samples per second).

Go to the Sampling Options tab and set a Delayed Start to start recording the position after 3 seconds. Close the set up window.

In Data Studio, position and velocity appear in a window on the left of the screen. Click and drag “velocity” onto the graph (on the right) to add it to the display.

Data Collection:

Press the Start button to begin data collection for the cart rolling down the ramp. Practice pushing the cart up from the bottom of the ramp so that it almost reaches the motion sensor. Try several trials to improve your technique and to make the runs reproducible.

(1) Once you are confident with your technique, pick an angle between 3^o and 10^o and generate position and velocity versus time graphs for the empty cart going down hill.

Apply the appropriate curve fits to each graph:

Highlight the graphical data by clicking and dragging. Then select the appropriate fit from the “fit” menu. Each time you make a fit to position vs. time and velocity vs. time, make sure exactly the same time intervals are selected.

Record the run conditions, and the fit parameters and their meaning (write a formula for position and velocity vs. time in terms of them). Repeat this for the cart going up hill. Sketch or print out the graphs for these two runs only.

Repeat this procedure for the cart going down hill and up hill with a 250 g mass on board, and a 500 g mass on board. Apply the appropriate curve fits to each graph. Record the run conditions and fit parameters and their meaning from each of these four runs.

You should have two graphs per group, and every one in the group should record the run conditions and fit parameters (with one explanation of their meaning) for each of these six runs.

(2) Using an empty cart, pick two angles between 3^o and 10^o different from that you used in (1). Generate position and velocity versus time graphs for the cart going down hill and up hill for each angle.

Apply the appropriate curve fits to each graph.

Record your fit parameters and their meaning for each of these four runs.

Questions (please whiteboard these as a group, and then individually write them up for submission):

(A) Observe your graphs and fit parameters from (1). Does changing the mass affect the motion of cart? Explain. What is the physical meaning of the fit parameters from your fits of your graphs of velocity versus time and position versus time?

(B) Observe the fit parameters for your graphs from the six runs with the empty cart. Does changing the angle affect the motion of the cart? Explain. Which of the fit parameters depends on the angle? Show mathematically how the angle relates to this fit parameter.