pendulum help

[drbeck]

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i'm going over AAMC test 9 Question 26 of the Physical science section. it pertains to a passage about water sloshing up and down the sides of a lake, pool, etc. like a pendulum. question 26 asks to pick a graph that shows the velocity at each point (each extreme height and middle level of equilibrium). the answer and explanation shows a graph where velocity is at a max at each extreme height (if you can imagine water sloshing to one side like a pendulum swings to one side) and the velocity is lowest at the middle level.

I THOUGHT WITH SPRINGS AND PENDULUMS POTENTIAL ENERGY IS HIGHEST THE FURTHEST FROM EQUILIBRIUM AND TURNS INTO KINETIC (HIGH VELOCITY) AS IT NEARS EQUILIBRIUM POINT AND THAT'S WHY THEY OSCILLATE! SHOULDN'T THE ANSWER SHOW A GRAPH WITH VELOCITY HIGHEST IN THE MIDDLE EQILIBRIUM LEVEL? I DON'T THINK IT WOULD KEEP OSCILLATING IF THAT WEREN'T THE CASE. I WONDER IF I'M MISSING SOMETHING HERE. THERE'S NOT MUCH MORE TO THE PASSAGE THAN THAT THOUGH. IT'S SHORT AND JUST EXPLAINS SLOSHING AND GIVES AN EQUATION FOR FREQUENCY THAT IS DEPENDENT ON GRAVITY, HEIGHT OF LIQUID AND LENGTH OF A TANK HOLDING THE LIQUID.

 

[drbeck]

i just reread the explanation and it says the SPEED must be greatest at the ends and zero in the middle. i have a feeling that this makes a difference, but i'm still not sure on this question. The question asks to pick the right VELOCITY profile. hmmfff. i don't get it.

 

[bluemonkey]

I think I remember this problem. Essentially the center of the lake is a node where there is no oscillation and as you get further from the center, you are further and further on the pendulum. Actually, the problem is more like two pendulums, one going in each direction from the center, one to the right and one to the left. As you get further along the length of the pendulum, the velocity is higher and higher with respect to SHM. So you should see the largest velocity vectors at the greatest distance from the center and then smaller and smaller vectors as you get closer to the center. Additionally, since the system is in SHM, the vectors on either side of the center should be pointing in opposite directions.

 

[HawkeyePostOp]

You should not compare this to a pendulum just because they have H and L in an equation for fundamental frequency. This system does not lend itself easily to being modeled that way, so just use wave equations and deduction.

If state II of figure 1 has just undergone state I before and not state III, the velocity and speed profile looks like it should be answer choice B. (I have the exam but not the answers.)

 

[drbeck]

that definitely helps to see it as two pendulums...almost like one comes down and hits the other so the velocity is in opposite directions in the middle...

BUT i still don't understand why velocity is highest at the extreme sides. those are changing direction also and are momentarily still.

 

[drbeck]

the answer is (B). i didn't think of it as a pendulum because of the equation. it just looks like the motion of a pendulum, swaying to a height on one side from equilibrium. if i shouldn't look at it like a pendulum, how should i look at it?

 

[HawkeyePostOp]

the answer is (B). if i shouldn't look at it like a pendulum, how should i look at it?

hehe water sloshing around on a planet that chooses to ignore most of applied physics.

Look at it frame by frame. The system goes from frame I to frame II in a given segment of time. If we pretend that the particles of water on the surface stay in roughly the same place relative to each other, we can draw displacement vectors from frame I to frame II. These are distances. But since these distances were covered in the same span of time, they are also proportional to velocity and speed. And since acceleration and deceleration in this system happen only above and below the waterline, this velocity is maxed out when the surface parallel to the ground.