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Author Topic: What is the solution to a particle sliding down a hemispherical surface?  (Read 1824 times)

Offline Roju

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The problem is displayed in the picture which is attached, as well as the start of the solution. I follow the solutions reasoning except for the very first equation which the rest is based on.

Why do they solve conservation of momentum as mv_x=MV_x instead of m(v_x-V_x)=MV_x?

My thought process is that the particles net velocity is the velocity of the particle horisontally Down the hemisphere, minus the hemispheres velocity to the left. Therefore the momentum of the particle is the velocity sum times the mass: m*(v_x-V_x).

I've been looking for this for over two hours. If anyone can spot the mistake in my reasoning it would be greatly appreciated.
« Last Edit: 29/01/2016 20:56:49 by chris »


 

Offline alysdexia

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Relative to rest, not relative to the bowl, otherwise you'd set V_x = 0.
 

Offline Roju

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Yes, isn't the horisontal momentum of the particle relative to rest equal to m (v_x-V_x)?
 

Offline alysdexia

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It already defines the initial velocity as v_x.
 

Offline Roju

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It already defines the initial velocity as v_x.

But the problem arises when they og further With the Equation. Because to form Equation 2 they use that the total horisontal velocity of the particle is v_x+V_x. This implies that the v_x is not allready the sum of the different horisontal Components.
See the Attached picture
 

Offline alysdexia

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V_x implicitly comes from a_y.
 

Offline Roju

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I still do not understand. If you see exactly what i am missing, can you please explain in a more comprehensive way? Instead of just 1 liners which don't give me much understanding.
 

Offline alysdexia

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Conservation of momentum relies on the initial conditions whereas the problem itself relies on the final conditions when the velocities can be added up.
 

Offline Roju

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I don't understnad. v_x is close to zero to start With, and then it accelerates as the particle moves Down the hemisphere due to the reaction force from the surface. I dont understand what this "initial velocity" you are talking about is.
 

Offline Space Flow

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Roju, excuse my ignorance if this sounds totally stupid but seeing as they don't specify an initial velocity, and the two are the same mass, and everything is frictionless, it seems to me the only velocity that should appear is on the y axis. The x axis has to cancel out and be zero + the slight nudge.
That being the case and everything else balanced, the point of separation should be when the point particle contacts the frictionless surface directly below where it starts from.

Just saying...
 

Offline Roju

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I have figured it out. Thanks for all the input.
 

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