# Aamc 9 #26, 29

#### johnmhh

I know this question has been posted before in the forum but I would really appreciate if if someone could explain to me why would the velocity be maximum at the ends if this is a harmonic motion. I thought that, like the case in springs maximal kinetic energy is at x=0. Any help would be appreciated.

Also question number 29 when they ask about which work is greater in magnitude, lifting the block from position A to B or moving it from B to A. Isn't the former one gonna require more work since the Tension force exerted by you through the pulley needs to overcome the gravitational force to lift the mass and therefore the work done here will be greater.

Thank you very much for any help in advance.
Good luck to everyone studying.

#### chiddler

5+ Year Member
I know this question has been posted before in the forum but I would really appreciate if if someone could explain to me why would the velocity be maximum at the ends if this is a harmonic motion. I thought that, like the case in springs maximal kinetic energy is at x=0. Any help would be appreciated.

Also question number 29 when they ask about which work is greater in magnitude, lifting the block from position A to B or moving it from B to A. Isn't the former one gonna require more work since the Tension force exerted by you through the pulley needs to overcome the gravitational force to lift the mass and therefore the work done here will be greater.

Thank you very much for any help in advance.
Good luck to everyone studying.
regarding number 26, just intuit it. how does a wave move?

regarding #29, as mass moves up, gravity does work. as mass moves down, you have to do work.

please correct me if i'm wrong - this is how i thought of it.

#### MedPR

Removed
regarding number 26, just intuit it. how does a wave move?

regarding #29, as mass moves up, gravity does work. as mass moves down, you have to do work.

please correct me if i'm wrong - this is how i thought of it.
Wouldn't it be opposite for #29?

5+ Year Member
yes oops!

OP
J

#### johnmhh

Thanks for the replies.
For number 29, I though it was the pullyy doing the work AGAINST THE GRAVITY and it has to be greater in order to lift the mass, that's what i am not getting.
As for number 26, I am sorry but I have no idea what you mean here. I am thinking of it like I am thinking of spring oscillations when the max. kinetic energy is at x=0 not at max. amplitude.

Thanks for the help though

#### chiddler

5+ Year Member
hope this helps.

i think easier to think about 29 in terms of energy rather than W=Fd work.

didn't do anything special for 26, i just thought would be easier to see if superimposed.

hypothalamus13
OP
J

#### johnmhh

Thank you so much for caring to answer my questions. I don't mean to bother you any further but I still don't understand. Even if I think about number 29 in terms of energy not Fd, wouldn't lifting the block be requiring more energy than its weight in order to lift it
As for number 26, I am sorry but I don't understand the drawing and most of all I want to understand why can't we treat this like a regular oscillation problem that we encounter for instance with springs.
I really do prefer detailed explanations but you don't have to answer to any of this if you don't want to.
Thanks again for your time and I do appreciate any further help if possible.

#### chiddler

5+ Year Member
Thank you so much for caring to answer my questions. I don't mean to bother you any further but I still don't understand. Even if I think about number 29 in terms of energy not Fd, wouldn't lifting the block be requiring more energy than its weight in order to lift it
As for number 26, I am sorry but I don't understand the drawing and most of all I want to understand why can't we treat this like a regular oscillation problem that we encounter for instance with springs.
I really do prefer detailed explanations but you don't have to answer to any of this if you don't want to.
Thanks again for your time and I do appreciate any further help if possible.
#29: Prove that to me. How much work is involved in moving a 5 kg object 10 meters upwards? How much work downwards? (meaning try to illustrate this with equations and numbers)

#26: It is an oscillation problem with frequency and period and all that fun stuff. But that doesn't really change anything. Can you explain in what ways you want to compare it to a spring?

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OP
J

#### johnmhh

I am so sorry it took me forever to reply. But what I am confused about is that I keep thinking that the wave generated here is similar to that of a spring. At high amplitude (highest potential energy) the speed or kinetic energy is zero and as you approach the equilibrium point, the potential energy is zero (because there is no amplitude or amplitude is zero) and therefore maximum kinetic energy and speed is greatest there.
I now understand the other problem that I asked about. Thanks a lot

#### gentlebeast

I think this question is too ambiguous. I had trouble interpreting it too.
I would say it asks the energy involved in both process is the same in magnitude. It did not ask the work done by object or by force on rope, so we cannot determine positive or negative work.

#### LianaStan

Bump.

I was hoping someone could provide a satisfactory answer for AAMC Practice #9, Question #26.

The question states that a wave sloshing in a tank has the highest velocity at the end points where amplitude of the water wave is highest. Like the OP, intuition would seem to dictate the motion would follow that of a harmonic oscillator, where the highest velocity is when the tank of water lies in the equilibrium position. However, the correct answer is contrary to this. Any good explanations for why this is the case?

#### Saint Fu

10+ Year Member
5+ Year Member
Pick a point on the left side, a point on at the center, and a point on the right side of the fluid. As II goes to III, how are these points going to change position?

Alternatively, if you want to think about it in terms of an oscillator, do something similar. Pick a couple points along the surface of the fluid. How does the gravitational potential at each point on the surface change as you move from left to right in I? What, then, would the maximum kinetic energy of each corresponding point in II look like? You are correct that the highest velocity occurs in the equilibrium position, and the correct answer is actually consistent with this.

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#### LianaStan

Pick a point on the left side, a point on at the center, and a point on the right side of the fluid. As II goes to III, how are these points going to change position?
If the question was asking for the position, not the velocity, then it would be clear then that the answer would be the diagram with longer arrows at the ends.

Alternatively, if you want to think about it in terms of an oscillator, do something similar. Pick a couple points along the surface of the fluid. How does the gravitational potential at each point on the surface change as you move from left to right in I? What, then, would the maximum kinetic energy of each corresponding point in II look like? You are correct that the highest velocity occurs in the equilibrium position, and the correct answer is actually consistent with this
I see the mistake I made. I was thinking of it in terms of right to left oscillation whereas the correct way is to look at it in terms of infinitely small oscillators oscillating in the up and down plane across the water-air interface.

Thanks for the help!