Question

In: Physics

Suppose that you have cut circles of different diameters from the same uniform sheet of paper.You...

Suppose that you have cut circles of different diameters from the same uniform sheet of paper.You measure the diameter and mass of each circle and collect the following data:

Mass of Circles as a Function of DiameterD (cm) (m) (g)10.0 0.624 12.0 0.886 14.0 1.148 16.0 1.429 18.0 1.859 20.0 2.307

As an exercise you will now make a graph of vs. in Excel. Note that when you are asked to make a graph in the form " vs ", the first variable mentioned is graphed on the vertical axis and the second variable is graphed on the horizontal axis. To complete the following exercises youwill need to explore the Excel menu system, you may get help from another student or me whennecessary. Note that when you right-click on most items a contextual menu will appear.1. Enter the values in column-A (which is horizontal by default) and the values in column-B (which is vertical by default). Start your entries in Row-3 so you can produce a table similar tothe one above that has a title and column headings.2. Select your data and use the Excel "Chart" feature to turn this into a "Marked Scatter" graph.You do not want to connect the points with any curve at this time.3. Remove any reference to "Series-1" that may appear on your graph by clicking on it anddeleting it. The graph will resize.4. By default Excel shows horizontal grid lines. See if you can insert vertical grid lines too.5. Add the chart title "Mass of Circles as a Function of Diameter" above the chart.6. Add the horizontal axis title "D (cm)" below the horizontal axis.7. Add a rotated vertical axis title "m (g)" to the left of the vertical axis.8. Add a second-order polynomial trend-line to the chart. Select the "Display equation on chart"and "Display R-squared value on chart" options.9. Force Excel to display the polynomial coefficients to 6 decimal places.

Expert Solution

Solution:

The data corresponding to the mass of the circle as a function of its diameter is given as follows

Diameter, D (cm)	Mass, m (g)
10.0	0.624
12.0	0.886
14.0	1.148
16.0	1.429
18.0	1.859
20.0	2.307

A graph is plotted between the diameter of the circle and mass with the help of excel and is shown below.

Here, we have taken the diameter on the x-axis and the mass on the y-axis and is fitted with the second-order polynomial and the corresponding equation is shown on the graph.

Here, the blue solid circles represent the data points and the solid red line represents the second-order polynomial fit to the given data.

It shows that the data is properly fitted with the second-order polynomial resulting a good R² values (close to 1).

The equation with which we have fitted the data is given below.

The same equation we can write in terms of the mass of the circle as a function of its diameter as follows

Where

Hence, we have expressed the mass of the circle as a function of its diameter.

genius_generous answered 2 years ago

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