[PHYSICS] Two questions whose solutions i dont understand

[Afif_D]

Here are two questions . I cant understand how they have been solved. Can anyone explain to me pls.

[mfb]

The solutions have several steps, at which step do you have problems?

For 1, consider an infinitely small change in theta (or, mathematical, the derivative): The energy must not change, so the derivative is 0.
Moving the left fluid up (left side of the first hint) costs the same energy as moving the other fluid down (right side) gives.
The other lines are just steps to get an expression theta=... based on that.

For 2: The diagonal springs are treated as effective springs with a different constant k', based on the force they apply when the mass goes up/down.

[Afif_D]

I think i am an idiot as i cant understand anything about this..

1.Could you detail me about how it is done with using mathematical symbols etc.

2.How does the (cos45)^2 term come in?

I dont understand..

Its better you show me all the steps. Sorry if its a pain for you. But i need it

[Gigano]

2.How does the (cos45)^2 term come in?

Caution: I am a biologist with limited knowledge of physics, so I may be totally wrong. I intuitively think the term comes into play by combining the force vector from the two springs that are at a 135 degree angle to the downward springs. Combining those two vectors ultimately simplifies the whole system to just two springs, each exerting a force in opposite directions.

[Charlie!]

2.How does the (cos45)^2 term come in?

Caution: I am a biologist with limited knowledge of physics, so I may be totally wrong. I intuitively think the term comes into play by combining the force vector from the two springs that are at a 135 degree angle to the downward springs. Combining those two vectors ultimately simplifies the whole system to just two springs, each exerting a force in opposite directions.

So basically, when each spring is compressed, it exerts a force back. How much do the springs at an angle get compressed when you displace the particle straight up? What is the component of the force the springs exert along the vertical direction?

[Afif_D]

Yea it is cos 45 . Why is it squared??

[mfb]

One cos comes from the lower compression, and another from the angle of the spring force.

[Afif_D]

Y U NO work it out in details?

[sigsfried]

Because it is your homework. What do you learn from any of us doing it for you?

[yurell]

You know F = k x
What proportion of k is pushing the mass back down? What proportion of x is stretching / compressing the springs?

[Sizik]

Because it is your homework. What do you learn from any of us doing it for you?

He learns the thought processes you go through in order to solve the problems. It's not like he's going to pass it off as his own work.

[starslayer]

If it is homework/coursework, Afif_D, have you already talked with your professor/teacher about these problems? If not, why not? They should be your first recourse for any questions you have; that's what they're there for. If you have already asked them about these problems, what about their explanations was unsatisfactory? Note that just giving you the exact detailed solution hardly ever lets you learn much. Trying to work it out for yourself with some hints is usually much better for gaining actual understanding.

[Afif_D]

If it is homework/coursework, Afif_D, have you already talked with your professor/teacher about these problems? If not, why not? They should be your first recourse for any questions you have; that's what they're there for. If you have already asked them about these problems, what about their explanations was unsatisfactory? Note that just giving you the exact detailed solution hardly ever lets you learn much. Trying to work it out for yourself with some hints is usually much better for gaining actual understanding.

Coz our school is closed. I have been trying to figure out how these two things come up

[Afif_D]

Its not a homework.Not a goddamn homework . Trust me

[sigsfried]

Ok. Let's work through the first one.

Can you write an expression for the total energy of the system?

[yurell]

Its not a homework.Not a goddamn homework . Trust me

Did my advice help you? I got caught on where the cos² came from too, and I think the problem is that once you write F = k_x y = 2k cos(45) y, you are treating the two springs as a single vertical one.
The thing is, when the particle moves y in the vertical direction, how much of that is compressing the springs?

[starslayer]

Coz our school is closed. I have been trying to figure out how these two things come up

They come up because physics-literate forums see this kind of thing all the time. Some people will just post their homework and ask for the answer, without mentioning that it's homework. Since you say this isn't homework, great. It still doesn't mean that presenting you with the solution in its entirety would be all that helpful to you for understanding the principles behind the solutions. Hints like the ones given are much better for that, especially since you already know what the answers are and can easily check your work.

[Dopefish]

To be fair, in this case the solution is basicly provided along with the problem with essentially all the work (although I can't seem to display it all), making it more likely to be review material rather then any form of homework, it's just the justification for each step that's missing.

The cos^2 bit is sneaky, but if you think of it as two seperate cos's (one nestled with the x, and one with the overall force) it works out I believe. I haven't looked at it too closely though since the full thing is cut off for me.

[starslayer]

To be fair, in this case the solution is basicly provided along with the problem with essentially all the work (although I can't seem to display it all), making it more likely to be review material rather then any form of homework, it's just the justification for each step that's missing.

The cos^2 bit is sneaky, but if you think of it as two seperate cos's (one nestled with the x, and one with the overall force) it works out I believe. I haven't looked at it too closely though since the full thing is cut off for me.

Point taken, however, the most the important parts of the solution aren't. For example, the first problem is all about getting the first expression (I haven't figured it out yet, but I haven't thought about it all that hard), and the rest is gravy.

To view the whole problem, right click the image and select "view image."

[Afif_D]

So how to write the energy of system??