# AP Physics C Take Home Quarterly

1. Apr 9, 2007

### Sammnyah

I used this forum to get a lot of help with the first problem on my quarterly, but there are still 2 more problems and nobody in my class knows how to do them. I was hoping somebody here would. Here are the problems

1. A particle of mass m moves in a conservative force field described by the potential energy function U(r) = a(r/b +b/r), where a and b are positive constants and r is teh distance from the origin. The graph of U(r) has the following shape.

a. In terms of the constants a and b, determine the following.
i. The position ro (the 0 is subscript) at which the potential energy is a minimum
ii. The minimum potential energy Uo (also subscript)

b. Sketch the net force on the particle as a function of r on the graph below, considering a force directed away from the origin to be positive, and a force directed toward the origin to be negative.

The particle is released from rest at r = ro/2
c. In terms of Uo and m, determine the speed of the particle when it is at r=ro.

d. Write the equation or equations that could be used to determine where, if ever, the particle will again come to rest. It is not necessary to solve for this position.

e. Briefly and qualitatively describe the motion of the particle over a long period of time.

The first graph is like a swoosh. On the right it has Uo and U and on the bottom it shows r, 2r, 3r, and 4r. Dashed lines connect to meet at a point from Uo and r to get to the lowest point of the swoosh. The graph it says to draw on is just F on the y axis and r on the x axis.

2. Two stars, A and B are in circular orbits of radii ra and rb, respectively, about their common center of mass at point P, as shown above. Each star has the same period of revolution T.
Determine expressions for the following three quantities in terms of ra, rb, T, and fundamental constants.
a. The centripetal acceleration of star A
b. The mass Mb of star B
c. The mass Ma of star A

Determine expressions for the following two quantities in terms of Ma, Mb, ra, rb, T, and fundamental constants.
d. The moment of inertia of teh two-star system about its center of mass.
e. The angular momentum of the system about the center of mass.

The picture is 2 circles, one inside the other. B is on the outer circle to the right, rb is on the inner circle to the right, P is in the center, A is on the inner circle to the left, and ra is between P and A.

I know it's a lot. I'm sorry I just really really need help. If you know how to do any part of either of these questions, help would be REALLY appreciated!

2. Apr 9, 2007

### Mindscrape

Isn't this cheating, or are you allowed to get outside help? Seems like cheating to me.

Also your description of the graph is not very good. You would have to draw it. Remember that F = ma = -dU/dt.

Again, for the stars, if you really can get help, you will have to scan the drawing or figure out a way to convey it graphically.

Last edited: Apr 9, 2007
3. Apr 9, 2007

### Sammnyah

No, it's not cheating. Everybody else did it together, but they all copied off of each other so none of them can help me. I've seriously asked the 7 smartest people in the class to help me and they all said they copied off somebody else. I, however, don't want to copy. I want to learn how to do it. Copying is cheating. Learning isn't.

4. Apr 9, 2007

### cristo

Staff Emeritus
And then please show some work, and some efforts at attempting the question, especially since you've said that this is an exam! These forums are to provide help; not pass your test for you! I'd be happy to give small hints or check your solutions, but there's no way I'm going to help you cheat on your exam and do it for you!!

5. Apr 9, 2007

### Sammnyah

And all the points in the star problem are on a line drawn straight across the middle horizontally.

6. Apr 9, 2007

### Sammnyah

And as I've already said, I don't want the test passed for me. I don't understand how to begin these problems and I'd like to learn how to do them. If somebody could at least get me in the right direction and not accuse me of cheating, that would be excellent.

7. Apr 9, 2007

### Sammnyah

Also, yes, we are allowed to get outside help. That's why it's take home. There are a lot of problems with the way the class is set up and the tests really actually need to be take home for anybody to pass them at all.

8. Apr 9, 2007

### cristo

Staff Emeritus
I'll quote from the guidelines, https://www.physicsforums.com/showthread.php?t=5374 which you agreed to on joining the forum:

The reasons for asking you to show your work are twofold; firstly, it shows us that you're not expecting us to do the work for you, but secondly, it enables us to judge our responses to your questions. For example, for the first part of question 1, you have a function and are asked to find a minimum of this function. I would say that you should look at the derivative of the function, but I dont know whether you have come across calculus yet.

So, again, I'll ask-- what have you tried? What do you know about the subject? Have you looked at the relevant chapters in your textbook? You say that nobody in your class can do them, but surely you must have made some attempts. It doesn't matter whether they are incorrect; it's somewhere to start at least!

Also, as an aside, I've never understood take home tests. I'm sure that they are meant so that you can spend as much time as you need, and use as many books as you can, not so that you friends or anyone else can do it for you. After all, if it were, then it wouldn't be examining you would it?

Last edited: Apr 9, 2007
9. Apr 9, 2007

### Sammnyah

Okay, I haven't really tried anything because as I said, the structure of the class is messed up. Most of the people in the class are seniors who already took a year of physics and calculus, but they randomly threw in people like me, who are in pre-calculus and haven't taken physics yet. Our teacher doesn't seem to understand this, and tests us all the same. Long story short, I don't know what to do at all, so I haven't really tried anything. I know I have to take the derivative of the function to find the maximum and the minimum, but I don't know how to do the derivative of anything with more than one variable, and I need that to do the rest of the problem.

This take home test is so that we can all work together and pass it. I know the term "work together" sounds like cheating, but really, with all the problems with the way the course is set up, we really need people to show us how to do it. I've been trying to get people from my class who did it already to show me how to do it but they all copied. I've spent the last 6 hours trying to learn this material. He gave us this test so we can learn from the people who know how to do it. I joined this forum because nobody from my class could help me and I was hoping somebody who knew what they were doing could teach me how to do it.

10. Apr 9, 2007

### Sammnyah

Is the derivative of U(r)= a(r/b + b/r) U'(r)= a(1/br + br)? I know you have to do something with the rs... but that doesn't seem right. The multiple variables are really confusing.

11. Apr 9, 2007

### cristo

Staff Emeritus
The derivative of rn=nrn-1. So, firstly you need to write each term as a power of r. Now, the derivative of a sum of terms is equal to the sum of the derivatives of each term, so this means you can differentiate each term one by one, then add up what you get.