Finding blast radius from TNT energy using log-log plot

[williamcarter]

Homework Statement

I would really appreciate if you could give me some hints regarding what exactly to do at iv)[/B]
iv)

Given formulas:

Homework Equations

f(y)=(ro*R^5/E*t^2)

The Attempt at a Solution

we know that f(y)=0.75
1ton TNT=4.184*10^9 J
ro=1.003kg/m^3

We have the above formula:f(y)=(ro*R^5/E*t^2)
we have almost everything, but I do not know exactly how to approach this problem and what exactly to do with that table.I was thinking of doing the slope,[/B]

 

[gneill]

The image attachment is missing.

 

[williamcarter]

The image attachment is missing.

Ow,my bad, I will fix it, I don't know why it didn't upload maybe because format.

 

[Chestermiller]

There are several possibilities:
1. Plot $R^5$ vs $t^2$ and determine the slope.

2. Take the log of both sides of the equation: $5 \log R = \log \frac{Ef}{\rho}+2 \log t$ or $$\log R = 0.2\log \frac{Ef}{\rho}+0.4 \log t$$
Use your graphics package (say Excel) to plot logR vs log t. The slope should be 0.4. Have your graphics package determine the equation of the best straight line. Find the value of R at 1 sec.

3. Calculate $R^5/t^2$ for all four data points, and take the average.

I would always choose item 2.

 

[williamcarter]

There are several possibilities:
1. Plot $R^5$ vs $t^2$ and determine the slope.

2. Take the log of both sides of the equation: $5 \log R = \log \frac{Ef}{\rho}+2 \log t$ or $$\log R = 0.2\log \frac{Ef}{\rho}+0.4 \log t$$
Use your graphics package (say Excel) to plot logR vs log t. The slope should be 0.4. Have your graphics package determine the equation of the best straight line. Find the value of R at 1 sec.

3. Calculate $R^5/t^2$ for all four data points, and take the average.

I would always choose item 2.

Thank you, much appreciated !