# The Naked Scientists Forum

### Author Topic: What is the solution to a particle sliding down a hemispherical surface?  (Read 1669 times)

#### Roju

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• Posts: 23
##### What is the solution to a particle sliding down a hemispherical surface?
« on: 29/01/2016 20:45:17 »
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 »

#### alysdexia

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##### Re: What is the solution to a particle sliding down a hemispherical surface?
« Reply #1 on: 30/01/2016 09:13:17 »
Relative to rest, not relative to the bowl, otherwise you'd set V_x = 0.

#### Roju

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##### Re: What is the solution to a particle sliding down a hemispherical surface?
« Reply #2 on: 30/01/2016 10:03:35 »
Yes, isn't the horisontal momentum of the particle relative to rest equal to m (v_x-V_x)?

#### alysdexia

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##### Re: What is the solution to a particle sliding down a hemispherical surface?
« Reply #3 on: 30/01/2016 12:28:55 »
It already defines the initial velocity as v_x.

#### Roju

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• Posts: 23
##### Re: What is the solution to a particle sliding down a hemispherical surface?
« Reply #4 on: 30/01/2016 15:19:55 »
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

#### alysdexia

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##### Re: What is the solution to a particle sliding down a hemispherical surface?
« Reply #5 on: 30/01/2016 21:31:06 »
V_x implicitly comes from a_y.

#### Roju

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##### Re: What is the solution to a particle sliding down a hemispherical surface?
« Reply #6 on: 30/01/2016 22:11:26 »
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.

#### alysdexia

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##### Re: What is the solution to a particle sliding down a hemispherical surface?
« Reply #7 on: 30/01/2016 22:51:54 »
Conservation of momentum relies on the initial conditions whereas the problem itself relies on the final conditions when the velocities can be added up.

#### Roju

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• Posts: 23
##### Re: What is the solution to a particle sliding down a hemispherical surface?
« Reply #8 on: 30/01/2016 23:19:28 »
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.

#### Space Flow

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##### Re: What is the solution to a particle sliding down a hemispherical surface?
« Reply #9 on: 01/02/2016 07:19:11 »
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...

#### Roju

• Jr. Member
• Posts: 23
##### Re: What is the solution to a particle sliding down a hemispherical surface?
« Reply #10 on: 01/02/2016 11:17:28 »
I have figured it out. Thanks for all the input.

#### The Naked Scientists Forum

##### Re: What is the solution to a particle sliding down a hemispherical surface?
« Reply #10 on: 01/02/2016 11:17:28 »