well, we tried searching up simple physics equations on google, as dr. bob222 suggested, but we found problems that were way out odf our range. we are looking for problems similar to this. --- Suzan does not remember which one of the following equations --- t=2pi �ãl/g or t=2pi �ãg/l gives a possibly correct relationship between: t(the time to make one back-and-forth swing) of a simple pendulum of length l, where g is the acceleration due to gravity. Use the dimensional analysis to help Suzan remember the possibly correct equation. Show all your work, not only the answer. ---- This was a problem on our test and we were supposed to simplify this problem into the 3 SI units, length (L), mass (M), and time (T). we don't need the answer to this problem, when we were given back our tests we already got the answers back. However our grades weren't very pleasant so for extra credit our assignment is to find 5 problems over the internet similar to this one. However, me and my friend have been searching similar problems for 3 hours and have had no luck! could you please help us! Thank you for any contributions. We'd really appreciate it. if you need more examples from our test, we would be glad to give them to you. Thanks!

Question

well, we tried searching up simple physics equations on google, as dr. bob222 suggested, but we found problems that were way out odf our range. we are looking for problems similar to this. --- Suzan does not remember which one of the following equations --- t=2pi �ãl/g or t=2pi �ãg/l gives a possibly correct relationship between: t(the time to make one back-and-forth swing) of a simple pendulum of length l, where g is the acceleration due to gravity. Use the dimensional analysis to help Suzan remember the possibly correct equation. Show all your work, not only the answer. ---- This was a problem on our test and we were supposed to simplify this problem into the 3 SI units, length (L), mass (M), and time (T). we don't need the answer to this problem, when we were given back our tests we already got the answers back. However our grades weren't very pleasant so for extra credit our assignment is to find 5 problems over the internet similar to this one. However, me and my friend have been searching similar problems for 3 hours and have had no luck! could you please help us! Thank you for any contributions. We'd really appreciate it. if you need more examples from our test, we would be glad to give them to you. Thanks!

Answer 1

The period of a pendulum is

P = 2 pi sqrt (L/g)

It does not depend upon the mass. Dimensional analysis can tell you that, but not the constant coefficiet. That's a whole differnet and liong story. A Google search of the Buckingham Pi Theorem might help you understand dimensional analysis better.

There is a slight dependence of a pendulum's period upon the angular amplitude when it is larger than about 0.2 radians. The period gets longer.

I'm not sure what kind of help you are looking for other than that.

Answer 2

I would suggest trying out the following steps to find problems similar to the one you mentioned:

1. Start by searching for physics websites or educational platforms that provide practice problems or worksheets on simple pendulum equations. Websites like Khan Academy, Physics Classroom, or OpenStax might have resources that could be helpful.

2. Once you find a suitable website, navigate to their physics section or search for keywords like "simple pendulum equations," "dimensional analysis in physics," or "pendulum time formula."

3. Look for practice problems or exercises that focus on the relationship between time (t), length (l), and acceleration due to gravity (g) in simple pendulums. It is possible that you may find problems that involve dimensional analysis to simplify the equations.

4. When you find a problem, carefully read the question and understand what it is asking for. If it aligns with what you are looking for, try to solve it step by step and use dimensional analysis to simplify the equation, just like you did in your test problem.

5. Repeat this process on different websites and platforms to find a variety of problems that test your understanding of simple pendulum equations and dimensional analysis.

Remember to keep practicing and don't get discouraged if it takes some time to find the right problems. Physics concepts can sometimes be complex, so it's crucial to familiarize yourself with various types of problems to enhance your understanding. Good luck!