You need to purchase an elliptical table for your dining room. You remember that

Question

You need to purchase an elliptical table for your dining room. You remember that you liked your friend's table in their house and go to visit them. They forgot where they purchased the table from and to it is up to you to determine the dimensions of the table: the largest radius (a), the shortest radius (b), and area (A) Your friend, who owns a tape measure, helps you measure the table. You know that the area of an ellipse is: A - rob and the smallest division on the tape measure is 1 mm. The following are the values determined from your multiple measurements, you and your friend each measure the dimensions twice: a. Why do you and your friend get different values for the measured lengths each time? b. Determine the dimensions of the table with a range of uncertainty from the recorded data. Also determine the area of the table with a range of uncertainty. Be sure to include random and instrumental uncertainty. If you having trouble deciding which value to use, refer to the Weakest Link portion of the Experimental Uncertainties document. c. After a little hunting around, you find the same table online with the dimensions of a 95.25 cm and b = 55.245 cm. Are your calculated values consistent with what you found online?

Explanation / Answer

Part a

This is because uncertainty in a measurement may creep in due to various reasons. Uncertainties in a measurement can be of instrumental type or random type. Instrumental uncertainty mainly consists of least count uncertainty while random uncertainty may have so many reasons like imperfection in measuring techniques, random and unpredictable variation in experimental conditions etc and many more.

Part b

From the given information we can clearly say that instrumental uncertainty is 0.05 cm (as the smallest division on the scale is 0.1 cm and least count = smallest division/2).

The average value of a = 95.425 cm

While the average random uncertainty in a= 0.525 cm

The average value of b = 55.3 cm

While the average random uncertainty in b= 0.35 cm

As the values of random uncertainties are much larger than the instrumental uncertainties hence instrumental uncertainty is irrelevant. So

The a = (95.425 ± 0.525) cm

b = (55.30 ± 0.35) cm

And A = (95.425)(55.30) = 16569.78785 cm2

And uncertainty in A = (95.425)(0.35)+(55.30)(0.525) = 62.43125 cm2

So A = (16569.78785 ± 62.43125) cm2

Part c

We can see that the values of a and b are in the range mentioned above. So yes, the values of a and b are consistent with the measured values.

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