3 Evaluating a Claim I

In this lab, you will be presented with a scenario and a statement that makes a claim about the scenario. You will design and conduct an experiment to evaluate the validity of the claim.

Lab 3 Worksheet Evaluating a Claim I

Learning Goals:

1. Determine when you have collected enough data.
2. Use data to test and evaluate a claim.

Evaluating a Claim

Scenario: An IOLab is allowed to roll across a table as shown in the figure below.

Claim: “The friction in the wheel of the IOLab device is small enough that it can be ignored.”

To test this claim, you will need to apply energy conservation to the system. Then you will need to determine when you have collected enough data. One way to do this is by getting a running average. You will also need to come up with a way to determine if the claim is true or false. One way to do this is by performing a z test.

The Measurement 

When considering energy conservation, we see that we are starting off with an initial gravitational potential energy of the suspended mass which is PE = mgh, where “m” is the mass that is suspended. Then when the iOLab device reaches the edge of the table the potential energy has been converted to kinetic energy so we end up with KE = ½ Mv_f², where “M” is the combined mass of the iOLab device and the suspended mass and v_f is the final velocity that the iOLab device has when it reaches the edge of the table. The quantity we have to measure then is the final velocity (v_f) of the iOLab device when it reaches the edge of the table. We can calculate what this final velocity (v_f) should be and then perform the experiment to see what the final velocity (v_f) actually is. To calculate what the final velocity (v_f) should be we first set the initial potential energy equal to the final kinetic energy:

Then we solve for v_f :

To get the mass of the iOLab device, you can calibrate the force sensor and then just pick the device up by the force sensor to get the weight of the device in Newtons. Then you can divide by 9.8 to get the mass in kg.

Read the next part on The Experiment before making this calculation.

The Experiment

Attach some string to the iOLab device and attach some mass to the other end of the string. You will want to use around 50 g to do this. If you don’t have string you could try using floss. For the mass you will attach to the string you can tie some washers if you have some. Or you can put some change in a zip loc bag and tie the string to the bag. Once you have your “mass” you can use the force sensor to weigh it in Newtons. Then divide by 9.8 to have the mass in kg.

You will want to place the device wheel side down so that the suspended mass (see the image above) will cause the device to roll across the table.

Be sure to measure the distance the iOLab device moves in meters. This is the same distance that the mass falls. Be sure to come up with a way to start at the same spot each time. Measure this distance. You can use a measuring tape or the wheel sensor to do this.

Now you can calculate what the velocity should be when the iOLab device reaches the edge of the table.

When you actually perform the experiment you will want to use the wheel sensor and look at the velocity vs time graph to find what the actual velocity is when the device reaches the edge of the table. Find the part of the graph where the device reaches the edge of the table and then hover over that spot with the data tool. Then you can record the velocity displayed in green in the upper left part of the graph.

See the next part called Running Average to determine how many trials you should do.

Running Average

A running average is one way to determine when you have collected a sufficient amount of data. You can make a copy of this Running Average Spreadsheet and enter in your measurements in Column B until you get a low change in average. Below 0.1% is typically considered a reasonable change in average. Most people get to this point around 9 trials.

Z Test

Performing a z test will give us a z score. The z score tells us how man standard deviations from the mean a particular value is. A positive z score tells us that the value is a certain number of standard deviations above the mean. A negative score indicates the value is below the mean.

You can make a copy of the Z Score Spreadsheet and enter your measurements in Column A under “Data”. Then enter the final velocity that you calculated it should be under “x”. You will now get a z score and a probability. We consider a z score of less than 2 or greater than -2 to mean that any randomness is most likely due to chance. This is 2 standard deviations from the mean. If you get a z score that is greater than 2 or less than -2, it means that we cannot consider the calculated velocity and the measured velocity to be the same. So, for instance, if you get a z score of 5 or -5, then you know that the calculated velocity and measured velocity cannot be considered the same and therefore the friction in the wheel cannot be ignored.

Grading Rubric:

Points are assigned for each worksheet question according to the following:

Lab 3 Grading Rubric 131 Manual