- Research Question: What is the relationship between the radius of a paper circle and the mass of that circle?
- Independent Variable:
- The size of the paper circle
- Dependent Variable
- The mass of the paper circle
- Control Variables
- Scale used
- Use the same scale for all circles
- Thickness of the circles
- Use the provided circles
- Type of paper used in the circles
- Use the provided circles
- Ruler used
- Use the same ruler
- Scale used
- Data Collection
- Measure the diameter of the circle in inches with ruler then measure the mass of the same circle then repeat for all circles
- Procedure
- Sort circles in order of size
- Starting with the smallest circle measure its diameter in inches (IV)
- Measure and record the mass of that same circle (DV) using the electronic scale
- Repeat for all circles
- Convert diameter in inches ot radius in cm
- Lab Diagram
Data
Diameter (Inches)
7/8 1 3/4 2 1/8 2 1/2 3 1/4 3 7/8 5 1/8 6 1/4 6 3/4 10 1/4 |
Mass (grams)
0.08 0.36 0.50 0.75 1.14 1.73 3.00 4.45 5.05 11.57 |
Radius (Centimeter)
1.10 2.22 2.70 3.18 4.13 4.92 6.50 7.94 8.57 13.0 |
Conversion from Diameter in inches to radius in Cm
r=(D*2.54)/2 |
Graph
Mass = 0.06867 Radius^2 + 0.01277 Radius - 0.01714
Conclusion
The relationship between the radius of a paper circle and the mass of that circle is directly related with the equation Mass = 0.06867 Radius^2 + 0.01277 Radius - 0.01714 showing this relationship. It is quadratic because as the circle gets larger adding the same distance to the radius accounts for much more paper and mass being added. This is backed up by the data and a strong relationship to the quadratic line of best fit on the graph.
Uncertainty Analysis
The two largest sources of uncertainty in this were the ruler only having inches and the lack of multiple trials. The ruler only having inches and being marked for 1/8 of inches led to rounding being needed to be done that then would make the centimeters off when converted. If a ruler with cm and mm was used we would have been able to collect more precise data. Using a cm and mm ruler would improve this lab and make the data more precise. Another possible area of uncertainty was that we only had one person measuring each circle once. To account for any errors here we could have had them measure each circle twice or had somebody else measure the circle to confirm the initial measurement. I