How Does Small y and d Affect the Difference Between r2 and r1 in Physics?

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In summary, to expand this experiment, one could vary the independent variable, increase the sample size, or add more control variables. Some potential variables that could be manipulated include time, temperature, pressure, concentration, and pH. To ensure the validity of the results, it is important to use proper experimental design, control potential confounding variables, replicate the experiment, and analyze the data using statistical methods. Expanding the scope of the experiment can involve increasing participant diversity, conducting the experiment in different settings or environments, or collaborating with other scientists. The results of the experiment can be used to inform future studies by identifying potential areas for further research, confirming or contradicting existing theories, and developing new hypotheses. Thorough analysis and interpretation of the results is
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A9876
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Homework Statement



r1 = √(L2+(y-0.5d)2)
r2 = √(L2+(y+0.5d)2)
Show that in the limit that both y and d are <<L r2 - r1 = yd/L

Homework Equations


The Attempt at a Solution



r2 - r1 =(√(L2+(y+0.5d)2)) - (√(L2+(y-0.5d)2))

Nevermind, I've figured it out but can't seem to be able to delete this post :s
 
Last edited:
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  • #2
I'd have tried substituting x=[(y-0.5d)/L]2 and used the binomial approximation.
Oh you figured it out - rather than delete the post - how about posting your result: that way others who get stuck can benefit.
 

1. How would I expand this experiment?

To expand this experiment, you could vary the independent variable, increase the sample size, or add more control variables. This will allow for a more comprehensive understanding of the phenomenon being studied.

2. What are some potential variables I could manipulate?

Some potential variables that could be manipulated in an experiment include time, temperature, pressure, concentration, and pH. It is important to carefully consider which variables are relevant to the research question and to only manipulate one variable at a time to ensure accurate results.

3. How can I ensure the validity of my results when expanding the experiment?

To ensure the validity of your results, it is important to use proper experimental design and control any potential confounding variables. Additionally, replicating the experiment multiple times and analyzing the data using statistical methods can help validate the results.

4. What are some ways to expand the scope of the experiment?

Expanding the scope of an experiment can involve increasing the diversity of participants, conducting the experiment in different settings or environments, or exploring the research question from multiple perspectives. Collaboration with other scientists can also help expand the scope of an experiment.

5. How can I use the results of this experiment to inform future studies?

The results of an experiment can be used to inform future studies by identifying potential areas for further research, confirming or contradicting existing theories, and providing a foundation for developing new hypotheses. It is important to thoroughly analyze and interpret the results to draw meaningful conclusions for future studies.

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