Part 2

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19 Part 2

Determine $I_0$ , the moment of inertia of the shaft and crossbar. Also at this point, there should be no masses on the cross arm (i.e., remove $m_1$ and $m_2$ ).

PROCEDURE

1. Connect a Rotary motion sensor to the interface.

2. In PASCO Capstone, go to:

a. Hardware setup,

b. Rotary motion sensor > Properties,

c. Linear accessory,

d. Select ‘medium pulley (groove)’ > ‘ok’.

e. Exit out of the hardware setup by clicking ‘Hardware setup’ again.

3. In PASCO Capstone, set up your graphs of position, linear velocity, and angular velocity vs. time.

a. Click on the graph area, and a bar should appear.

b. Next, click the button in the top bar called ‘add new plot area to the Graph display.’ Click that button until 3 graphs are shown.

c. Click on the y-axis of each, selecting the three quantities (one for each): position, linear and angular velocity.

4. **IMPORTANT** Make sure that your driving mass starts at the same height for each run. We recommend winding up the wheel three times for each experiment to ensure that you have a consistent starting height. The driving mass should be 15 g. That is why the additional 10 g mass is added to the one attached to the string.

5. Wind the cord evenly on the shaft. Click on Record.

6. Release the mass and let it fall down. Click STOP a few seconds after the mass reaches the lowest position. Perform the analysis described below and report your results in Table 1.

7. After you have completed the checkpoint below, repeat steps 4, 5 and 6 five additional times. Report your results in Table 1.

Make sure you understand how to perform steps 4, 5 and 6 correctly, as they will be the primary procedure for the rest of the lab.

ANALYSIS

Consider the three curves obtained from the procedure of PART 2. Where on each graph is the starting point when the driving mass is released? Remember that it is very important to make sure the initial height of the falling mass remains the same every time a measurement is taken throughout the rest of the lab.

Question 2.

Identify the point on each curve at which the driving mass is at its lowest position. Make sure to explain your reasoning. It may be helpful to describe the location of the point on both axes relative to the position of the extrema in position, linear velocity or angular velocity. Think carefully about this question, keeping in mind that the rotary motion sensor determines position, linear velocity and angular velocity from the speed of rotation of the rotating shaft.

The time $t$ that you need to determine is the amount of time it takes the mass to fall from its initial height to its lowest point. You will determine this from the graph on PASCO Capstones’ program with the following steps.

1. Find the starting time, $t_0$ , by identifying on your graph the point right before the mass begins to drop. Click on the point on the graph to see the time $t_0$ .

2. Next, find the point in time where the mass has reached its lowest height, $t_1$ . Double click on your position-time curve to bring up the coordinate box.

a. Use the left and right arrows on your keyboard to move the pointer around until you reach the minimum.

3. Your time $t$ is then $t_1-t_0$ . Record in your Excel sheet and the Results section for Part 2.

Question 3.

How did you determine the starting time for each measurement from the software? With that in mind, what would the uncertainty in time be based on the software?

CHECKPOINT

(Ask the TA to check your graphs for the first run, point out where the driving mass is at its lowest point as well as when the experiment starts on the graph)

Double click on the points $h(t_1)$ , $v(t_1)$ , and $\omega(t_1)$ in order to see the precise coordinates of these points, and record these values in your table in the Results section, and in your Excel sheet. Remember that the position, velocity and angular velocity in your graphs are relative to the starting height. So, to record the correct values of height, speed, and angular speed, you can simply ignore the negative sign in your y co-ordinates.

Recall that $I_0$ is the moment of inertia of the shaft and crossbar.

One may calculate $I_0$ with Equation 9 using values of $r$ , $h$ , and $t$ , (Let’s call it Method 1), or with Equation 5 using values of $\omega(t_1)$ , $v(t_1)$ , and $t_1$ (Method 2). Recall that $h=h_0-h(t_1)$ . However, since in the Capstone measurements $h_0$ is assumed to be zero, the total run $h$ is practically equal to $h_1$ . Therefore, in the Part 2 tables in Excel and Report (and later in Part 3) we use value of $h_1$ for $h$ . Record your values in the Part 2 Results section.

Repeat steps 4 to 6 of the procedure for five additional runs, recording all of your data in the Part 2 Results section and in your Lab 3 Excel workbook.

1. Calculate $I_0(t_1)$ using both methods (Equation 9 and Equation 5) once by hand, and compare it to the value in your excel sheet.

2. In order to obtain uncertainties of the evaluation of $I_0$ , repeat the calculation 5 times for the additional runs, and calculate the standard deviation for both Method 1 and Method 2. The Excel sheet will calculate the standard deviation of both methods for you. In your Results section, report the average value from both Methods as that Method’s $I_0$ , and the standard deviation as the uncertainty for that respective method.

From now on we will use Method 2 (Equation 5) for all calculations of the moment of inertia.

Question 4.

Compare the results obtained between Method 1 and Method 2. Which method is more precise, and why (explain)?

19 Part 2

PROCEDURE

ANALYSIS

CHECKPOINT

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