Physics lab problem. Ambiguous directions. What are they asking?

In summary: It doesn't matter which variable goes on the x-axis as long as you are consistent with your labeling and the graph is readable. The relationship between A and B will be the same regardless of which variable is on which axis.
  • #1
tony873004
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We took timings in lab of a pendulum.

Activity 1: release the pendulum from 10 degrees. Time how long it takes to do 10 oscillations.

Activity 3, shorten the length of the string to 2/3 original, then to 1/3 original and time 10 oscillations from a 10 degree release point.

Conclusion:
Using your data from activities 1 and 3, compute ln(T/1s), ln(L/1cm), for each length and their worst-case uncertainties. Describe your reasoning in detail and show all calculations.

Plot a graph of ln(T/(1s)) vs ln(L/(1cm)) and determine its slope. Discuss how you use uncertainty in the data to determine worst-case uncertainty in the slope. Is your slope consistent with the expected value of n=1/2? Explain your reasoning carefully.




What does this mean?

It never tells us what the formulas ln(T/(1s)) and ln(L/(1cm)) mean. So how can I expect that the slopes of their graphs will equal 1/2? How can I draw any conclusions when I don't know why I'm applying that formula?

Also, what's the point of dividing T by 1? It's just going to give me T? And why do they want me to divide L by 1? It's just going to give me L.
 
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  • #2
Division is being performed in order to graph numerical functions,i.e.mathematical objects,which should have no physical dimansion.

I don't know why they asked you to logarithmate,the formula is not an exponential,not even in the general case.

Daniel.
 
  • #3
*** bump! ***
I still don't get it.
 
  • #4
tony873004 said:
We took timings in lab of a pendulum.

Activity 1: release the pendulum from 10 degrees. Time how long it takes to do 10 oscillations.

Activity 3, shorten the length of the string to 2/3 original, then to 1/3 original and time 10 oscillations from a 10 degree release point.

Conclusion:
Using your data from activities 1 and 3, compute ln(T/1s), ln(L/1cm), for each length and their worst-case uncertainties. Describe your reasoning in detail and show all calculations.

Plot a graph of ln(T/(1s)) vs ln(L/(1cm)) and determine its slope. Discuss how you use uncertainty in the data to determine worst-case uncertainty in the slope. Is your slope consistent with the expected value of n=1/2? Explain your reasoning carefully.




What does this mean?

It never tells us what the formulas ln(T/(1s)) and ln(L/(1cm)) mean. So how can I expect that the slopes of their graphs will equal 1/2? How can I draw any conclusions when I don't know why I'm applying that formula?

Also, what's the point of dividing T by 1? It's just going to give me T? And why do they want me to divide L by 1? It's just going to give me L.

tony873004 said:
*** bump! ***
I still don't get it.
dextercioby gave you the reason for the division. You are not dividing by 1 in either case. You are dividing the time by a time (1s) and the length by a length (1cm) in order to achieve dimensionless quantities. If you did not do that, you would wind up taking logarithms of quantities that involved dimensions. The arguments of functions like logs and exponentials and trig functions must always be dimensionless.

Now why plot logarithms? Maybe you have to be old to know this. Before everyone had a whiz-bang electronic calculator in their pocket that could do all sorts of regression analyses, graphs were often drawn on log-log paper to figure out the power in a relationship, and on semi-log paper to figure out the multiplying factor in an exponential relationship.

Suppose you suspect that the period of oscillation is proportional to some power of the length of a pendulum. How would you write such a relationship? You could write

[tex] T = aL^n[/tex]

where a would have to have dimensions of [tex]time/length^n[/tex] If you divide the equation by 1 sec you get

[tex] \frac{T}{sec} = a/sec L^n[/tex]

If you multiply the right hand side by

[tex] \frac{cm^n}{cm^n}[/tex]

you get

[tex] \left[\frac{T}{sec}\right] = \left[a\frac{cm^n}{sec}\right] \left[\frac{L}{1cm}\right]^n[/tex]

You now have a dimensionless equation. Take the log of both sides

[tex] ln\left[\frac{T}{sec}\right] = ln\left[a\frac{cm^n}{sec}\right] + n \ ln \left[\frac{L}{1cm}\right][/tex]

You now have a linear equation whose slope is the power and whose intercept is the log of the dimensionless constant. You can get both of those things from your log-log graph.
 
  • #5
Thanks, Dan. I think I got it now.

Another question: If I'm asked to plot a graph of A vs. B, does it matter which goes on the x axis. Would it be A, or does it matter?
 

Related to Physics lab problem. Ambiguous directions. What are they asking?

1. What is an ambiguous direction in a physics lab problem?

An ambiguous direction in a physics lab problem is a statement or instruction that is unclear or has multiple interpretations. It may be missing crucial information or contain vague terms that can lead to confusion.

2. How do I know if a physics lab problem has an ambiguous direction?

An ambiguous direction can be identified by carefully reading and analyzing the problem. Look for any unclear terms or instructions that could be interpreted in different ways. If you are unsure about the meaning of a direction, it is likely ambiguous.

3. Why are ambiguous directions a problem in physics lab?

Ambiguous directions can cause confusion and lead to incorrect results in a physics lab. Inaccurate data can affect the overall validity of the experiment and make it difficult to draw conclusions or make predictions based on the results.

4. How can I resolve an ambiguous direction in a physics lab problem?

If you encounter an ambiguous direction in a physics lab problem, it is important to clarify it before proceeding with the experiment. You can ask your instructor for clarification or discuss it with your lab partners to come to a consensus on the interpretation.

5. What can I do to avoid creating ambiguous directions in my own physics lab problems?

To avoid creating ambiguous directions in your own physics lab problems, be clear and specific in your instructions. Avoid using vague terms and make sure all necessary information is provided. It can also be helpful to test the problem with others to identify any potential areas of confusion.

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