## Equations for Final Exam

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## Angular Momentum Example

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## Chapter 10 Equations Categories: Uncategorized

## Point particle example

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## Chapter 9 Equations Categories: Uncategorized

## Work Energy Problem From Class

I told you I would post a solution to this problem.  Here it is.

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## Work-Energy with Springs

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## The Moon Problem

Here are a BUNCH of solutions to the moon problem – where an object starts above the moon and falls.  Actually, there are six videos.  Have fun.

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## Chapter 7 Equations Categories: Uncategorized

## An Object Falling on the Moon

Here are some of the links from class today.

First, the problem was a 100 kg object starting from rest a distance of 2R from the moon (where R is the radius of the moon).  How fast was the object moving when it hit the ground.

• Method 1: Use the momentum principle.  We don’t know time and the force isn’t constant.  However, you could calculate the starting and ending force and just use the average force.  Then use this average force as though it was constant.  This would then be a problem just like a ball falling near the surface of the Earth (which we did the other day).
• Method 2: Use the momentum principle.  In this case, we used the momentum principle for a short time step of 1 seconds.  This means that we have a BUNCH of time intervals to calculate – so I did it in python.  Here is the code.
• Method 3: Use the work energy principle.  Again, it’s not trivial to calculate the work since the force isn’t constant.  I can “cheat” by just using a displacement of 1 meter—however, this means I need to do a BUNCH of steps again.  Here is my recipe:
• Calculate the force.
• Use this force to find the work done (over a small distance step).
• Use this work to update the kinetic energy.
• Update the position and repeat.
• In the end of method 3, you can use this kinetic energy to find the final velocity.  Here is the code.
• Method 4: Use the work energy principle.  Instead of using a small distance step, I can take the limit as the step size goes to zero.  This makes it an integral for the work done by gravity.
• Method 5: Since the integral of work doesn’t depend on the starting or ending position, I can instead use a system consisting of the moon plus the mass.  This means there is no work done on the system but there is a change in gravitational potential energy.

In the end, everything was awesome.

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