lab_1

- To take data using a computer and signal interface
- To use computer software programs to interpret data
- To observe the distance-time relation for motion at constant velocity

- Motion sensor
- Pasco dynamics track and cart
- Computer with Signal Interface and Data Studio

The position of an object moving along a line is indicated by its displacement. The displacement is the positive or negative distance from a point of reference called the origin, the numbers being positive to the right of the origin and negative to the left. In Figure 1 displacement is labeled as x, time as t, and velocity as v. We can express displacement with equation (1):

<math>x = vt + x_{0}</math> **(1)**

The initial displacement x_{o} is the starting position when time t equals zero. This value is where the line crosses the vertical axis and is called the y-intercept. In a graph of displacement x (on the vertical axis) versus time t (on the horizontal axis) the velocity of the motion v is equal to the slope of the line.

<math>v = \mathrm{slope} = \frac{\mathrm{rise}}{\mathrm{run}} = \frac {x_{2} - x_{1}}{t_{2} - t_{1}}</math> **(2)**

Consider the following two cases:

A. Motion away from the origin | B. Motion towards the origin |
---|---|

Cart has an initial position at +50 cm, travels for a time duration of 2 seconds, at a constant velocity of +50 cm/s | Cart has an initial position at +50 cm, travels for a time duration of 2 seconds, at a constant velocity of −50 cm/s |

Draw graphs in your e-journal (using the draw tools) of what you think the motion will be for these two cases, plotting the displacement x versus the time t. Then answer the following questions for both cases:

- Will the graph be straight or curved?
- Will the graph slope up or down?
- If it is curved will it curve up or down?

Explain your reasoning for each of these answers.

- Plug the motion sensor’s phone plugs into channels 1 and 2 with the yellow banded plug in channel 1.
- Mount the motion sensor at the end of the track.
- Align the sensor so that it is pointing down the track.
- Level the track (if you have a bumper at the end of the track use the screw to level the track).

**Setup Data Studio: (See Figure 2)**

- Open DataStudio (in the start menu and on the desktop)
- Click on Create Experiment.
- Click on channel 1 (left-most yellow circle on the science workshop picture) and choose Motion Sensor from the list that appears (Figure 3). In the menu that appears below the signal interface, set the Sample Rate to 50 Hz.
- Click on the Sampling Options, go to third tab, Automatic Stop, and set the time to 3 seconds.
- On the left side, drag the Graph icon onto position vs. time.
- Arrange the various windows as needed.

**Data Collection:**

- Place the cart on the track near the sensor.
- Make sure that the spring end of the cart is facing
**away**from the motion sensor (Figure 4). NEVER allow the cart to run into the motion sensor!!! - Click on the Start button as your lab partner pushes the cart away. Wait until data collection stops.

**Automatic Fitting:**

- Highlight the straight-line region of your position vs. time graph by clicking on the graph and dragging the cursor over the region you want (the clean straight portion of the graph).
- Click on the Fit button and choose Linear Fit for a (straight-line) model.
- Record the values of the slope m, y-intercept b and the Root Mean Square Error in your journal.
- Use the print screen button on the keyboard to paste a picture the graph into your e-journal.

**Manual Fitting:**

- Calculate the slope between the two points using the rise over run approach.

<math>m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}}</math>**(3)**

- Obtain the y-intercept by plugging in one point and the value of m from above into equation (4) and solving for b.

<math>b = y_{1} - mx_{1}</math>**(4)**

**Analyzing Results:**

Calculate the percent difference between the values you obtained in your manual fit, with the automatic fit values (compare the automatic fit's slope with the manual slope and the automatic fit's y-intercept with the manual y-intercept).

<math>\%\mathrm{Diff} = \frac{|m_{\mathrm{automatic \, fit}} - m_{\mathrm{manual \, fit}}|}{m_{\mathrm{automatic \, fit}}} \times 100 \%</math>

- Return to the Data Studio window and repeat the experiment, placing the cart on the end opposite the motion sensor and pushing it toward the sensor.
- Make sure to stop the cart before it hits the sensor.
- Repeat the Manual Fitting, Automatic Fitting and Analyzing Results sections above.

*Instructions*

- Copy and paste this entire eJournal Report section into a blank WORD file.
- Complete the report in WORD.
- You may wish to modify borders in the tables.
- Submit your report by uploading the WORD in our class D2L site. If the D2L site is down, email the completed report file directly to a lab TA or to physics@andrews.edu.

- Title:
- Names: (Put 'scribe' beside the name of the person writing the abstract, conclusion, etc. This will be a different person each week as you and your lab partner exchange duties!!)
- Date
- Time In & Out:

- Personalized Statement of Objectives:
- Methods Used: (Insert a labeled webcam image of apparatus. Describe what and how measurements are made.)
- Predictions Made: (Include sketches, plots, and descriptions of expected results.)

**Automatic Fitting**

- Record the value of the slope, m…
- Record the value of the y-intercept, b…
- Record the value of the Root Mean Square Error…
- Paste a copy of your graph here:

**Manual Fitting**

- Using the x-y tool record x
_{1}, x_{2}, y_{1}, y_{2} - Record your slope using a manual fit…

<math>m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}}</math>

- Record your y-intercept using…

<math>b = y_{1} - mx_{1}</math>

**Analyzing Results**

- %Diff for slope using:

<math>\%\mathrm{Diff} = \frac{|m_{\mathrm{automatic}} - m_{\mathrm{manual}}|}{m_{\mathrm{automatic}}} \times 100 \%</math>

- %Diff for y-intercept using:

<math>\%\mathrm{Diff} = \frac{|b_{\mathrm{automatic}} - b_{\mathrm{manual}}|}{b_{\mathrm{automatic}}} \times 100 \%</math>

**Questions**

- How does your observed curve compare with your predicted curve?
- What is the speed of the cart?
- How far from the detector is the cart when the detector begins measuring its motion?
- What does the value of the Mean Square Error indicate?

**Automatic Fitting**

- Record the value of the slope, m…
- Record the value of the y-intercept, b…
- Record the value of the Root Mean Square Error…
- Paste a copy of your graph here:

**Manual Fitting**

- Using the x-y tool record x
_{1}, x_{2}, y_{1}, y_{2} - Record your slope using a manual fit…

<math>m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}}</math>

- Record your y-intercept using…

<math>b = y_{1} - mx_{1}</math>

**Analyzing Results**

- %Diff for slope using:

<math>\%\mathrm{Diff} = \frac{|m_{\mathrm{automatic \, fit}} - m_{\mathrm{manual \, fit}}|}{m_{\mathrm{automatic \, fit}}} \times 100 \%</math>

- %Diff for y-intercept using:

<math>\%\mathrm{Diff} = \frac{|b_{\mathrm{automatic \, fit}} - b_{\mathrm{manual \, fit}}|}{b_{\mathrm{automatic \, fit}}} \times 100 \%</math>

**Questions**

- How does your observed curve compare with your predicted curve?
- What is the speed of the cart?
- How far from the detector is the cart when the detector begins measuring its motion?
- What does the value of the Mean Square Error indicate?

**Further Questions:**

- How are the results for parts A and B similar?
- How are the results for parts A and B different?

*Good points to address are:*

- What have you concluded about the distance-time relation for motion at a constant velocity?
- What significance does the slope of a position vs. time graph hold?
- What is the cause for difference in measured and calculated conclusions?
- ect…

This is a formal statement of what this laboratory experiment was all about.

Included in this paragraph should be something about:

- The Objectives
- Your Results
- Your Conclusions

- Document your completion of this lab with your partner by inserting a webcam photo of yourself, your partner, your apparatus, and your TA.

- Complete the lab and upload your eJournal Report in D2L before the scheduled end of the lab period.

lab_1.txt · Last modified: 2015/04/16 15:38 (external edit)