Research Question- What is the relationship between the radius of a paper circle and the mass of that circle?
Independent Variable- Radius of paper circle (cm)
Dependent Variable- Mass of paper circle (g)
Control Variables- Material of circles, scale, ruler
It will be easy to keep these values controlled because the circles were already cut out for us and we used the same ruler and scale throughout the lab.
Procedure
Independent Variable- Radius of paper circle (cm)
Dependent Variable- Mass of paper circle (g)
Control Variables- Material of circles, scale, ruler
It will be easy to keep these values controlled because the circles were already cut out for us and we used the same ruler and scale throughout the lab.
Procedure
- Measure the diameter of the paper circle (in)
- Divide by 2 to find the radius
- Convert to centimeters (because we accidentally used a ruler with inches)
- Put that circle on the scale to find its mass (g)
- Repeat with the next circle
- 10 circles in total
- Only 1 trial because the mass of the circles isn't going to change
Radius (cm) |
Mass (g) |
2.223 |
0.360 |
2.667 |
0.500 |
1.016 |
0.080 |
3.239 |
0.750 |
4.064 |
1.140 |
4.826 |
1.740 |
6.604 |
2.980 |
7.938 |
4.460 |
8.382 |
5.070 |
13.018 |
10.200 |
Processed Raw Data- I used 1 inch = 2.54 cm to convert inches to cm
Mass= 0.0446 g/cm^2 * Radius^2 + 0.2433 g/cm * Radius - 0.4174 g
Slope- We used a quadratic form because the relationship between radius and area is quadratic and the relationship between area and mass is linear
Y-intercept- This is incorrect because the mass of a circle with a radius of 0 (nothing) should have a mass of 0.
Conclusion- The relationship between the radius of a paper circle and the mass of that circle is quadratic because circles with small radii have small areas, and then the area increases faster and faster as the radius increases because the formula is A=(pi)(r^2). As area increases, mass increases linearly. The results of this lab were what I expected them to be, with the quadratic model fitting nicely to the data points.
Evaluating Procedures- One weakness of our experiment was that we used a ruler with inches, which may have affected the accuracy of our measurements, especially when we converted them to centimeters. However, we made our measurements as specific as possible on that ruler, so it isn't a substantial difference and can probably be accounted for with my uncertainty bars. A second source of uncertainty would be finding the center of the circle to measure the diameter. Although we did our best, it is difficult to be sure that we are measuring directly in the center of the circle so our radius measurements could be a little smaller than they actually are. Since the y intercept was -0.4174 when it should have been 0, there was definitely some errors on our part during the lab.
Improving the Investigation- Using a ruler with centimeters would have helped, and additionally if we had folded the circles in half exactly to ensure that we were measuring right along the diameter, we would have more accurate measurements for the radii of the circles.
Slope- We used a quadratic form because the relationship between radius and area is quadratic and the relationship between area and mass is linear
Y-intercept- This is incorrect because the mass of a circle with a radius of 0 (nothing) should have a mass of 0.
Conclusion- The relationship between the radius of a paper circle and the mass of that circle is quadratic because circles with small radii have small areas, and then the area increases faster and faster as the radius increases because the formula is A=(pi)(r^2). As area increases, mass increases linearly. The results of this lab were what I expected them to be, with the quadratic model fitting nicely to the data points.
Evaluating Procedures- One weakness of our experiment was that we used a ruler with inches, which may have affected the accuracy of our measurements, especially when we converted them to centimeters. However, we made our measurements as specific as possible on that ruler, so it isn't a substantial difference and can probably be accounted for with my uncertainty bars. A second source of uncertainty would be finding the center of the circle to measure the diameter. Although we did our best, it is difficult to be sure that we are measuring directly in the center of the circle so our radius measurements could be a little smaller than they actually are. Since the y intercept was -0.4174 when it should have been 0, there was definitely some errors on our part during the lab.
Improving the Investigation- Using a ruler with centimeters would have helped, and additionally if we had folded the circles in half exactly to ensure that we were measuring right along the diameter, we would have more accurate measurements for the radii of the circles.