# Only the best-physics(unit analysis) question

1. Sep 2, 2007

### frasifrasi

Only the best--physics(unit analysis) question

1. The problem statement, all variables and given/known data
Ok, this is under the unit analysis section:

-----------> We can express the radius of the fireball (resulting from a bomb) R in terms of t, ρ and E as R= const2x E^(1/x)t^(-y/x)ρ^(−z/x).
Verify the relationship between R and t (That is R is proportional to t^(–y/x)) by plotting log (R) vs log (t) using the information provided in the pictures.
Fit the data of log (R) vs log (t) with a straight line. What is the slope of the
fit? What does the slope mean? Can you see why we are plotting log (R) vs
log (t) instead of R vs t?

--Basically, the pictures show the fireballs of a bomb with the diameter(m) at certain times(ms):
6ms--80m
120ms--110m
53ms--180m

2. Relevant equations
- Is it me, or is the question too vague? I am trying to understand what it's asking and how I should answer.

3. The attempt at a solution

In the previous question, I have found z= 1 y= -2 and x= 5 for the values in the R=.... equation.

However, I don't know what they mean by plotting the log and fitting the data. I have tried graphing log (x) and log (x^(2/5)) but it doens't seem correct.

Thank you in advance.

Last edited: Sep 2, 2007
2. Sep 2, 2007

3. Sep 2, 2007

4. Sep 2, 2007

### Astronuc

Staff Emeritus
The times correct, particularly the second time.

6ms--80m
120ms--110m
53ms--180m

Normally when one has a function y = exp (kt), one can plot with semi-log, and the slope is the constant k.

if one has R = A tn, then ln R = ln A + n ln t