In an experiment, two variable quantities, x and y were measured. The relation between x and y is thought to be: y= 4(pi)b(x)^3
x(cm) +/- 0.02cm
0.67
0.80
0.90
0.95
y(g) +/- 0.25g
2.25
4.00
5.52
6.60
a) Draw a complete table that allows you to plot the graph which could be used to verify the relation between x and y.
b) Calculate the value of b using the a graphical method.
What is your question. The instructions are clear. If you think it is a cube power, frankly, I would plot it on log paper (logy=log 4PIb + 3logx) So on log-log paper, it will be a straight line scatter plot). 1x1 cycle should do it for that data.
http://www.printablepaper.net/preview/log-portrait-letter-1x1
Can I make my x value as 3sqrtx, I will get the same straight line? Is that possible, if I use log and the 3sqrtx i get different values of b, which one is more accurate?
a) To draw a complete table that allows you to plot the graph, you need to arrange the measured values of x and y in a table format. Include the errors or uncertainties in the measurements as well. Here is the table:
```
x (cm) +/- 0.02cm | y (g) +/- 0.25g
-------------------------------------
0.67 | 2.25
0.80 | 4.00
0.90 | 5.52
0.95 | 6.60
```
This table shows the measured values of x and y along with their respective uncertainties.
b) To calculate the value of b using a graphical method, you need to plot the values of y against the values of (pi * x^3). By doing this, you will be able to determine the slope of the line, which corresponds to the value of b in the relation y = 4(pi)bx^3.
Follow these steps:
1. Plot the values of (pi * x^3) on the x-axis.
2. Plot the values of y on the y-axis.
3. Use a scatter plot to represent the data points.
4. Draw a straight line that appears to fit the majority of the data points.
Make sure to label the axis with the appropriate units (cm^3 and g) and include a title for the graph.
5. Determine the slope of the line by measuring the vertical change (∆y) and the horizontal change (∆(pi * x^3)) between any two points on the line.
6. The slope of the line corresponds to the value of b in the equation y = 4(pi)bx^3. Therefore, calculate the slope of the line to find the value of b.
Remember to consider the uncertainties while interpreting the slope value.