Collision between moving walls

[Buffu]

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I have problem with the solution given of the (b) part of the question.
The given solution is :

I did not understand why the value of $\Delta T = 2x/v$ even when $\Delta T \to 0$ ?
Since if the time taken for collision reduces so does the distance between the wall and the ball and since velocity is constant. The value should be $0$. No ?

 

[jbriggs444]

The value of what should be zero? And why do you expect velocity to be constant?

 

[Buffu]

The value of what should be zero? And why do you expect velocity to be constant?

Oh sorry, I mean the value of $dv/dt$ should be infinite.
I expect the value to be constat because it is given in the question that the ball moves with a constant velocity.

 

[jbriggs444]

Oh sorry, I mean the value of $dv/dt$ should be infinite.
I expect the value to be constat because it is given in the question that the ball moves with a constant velocity.

As I read the question, no such thing is given. The speed increases with each bounce.

 

[Buffu]

As I read the question, no such thing is given. The speed increases with each bounce.

If v was not constant then how does we got $\Delta T = 2x/v$ in the first place ?

 

[jbriggs444]

If v was not constant then how does we got $\Delta T = 2x/v$ in the first place ?

Because V << v and because v is increasing, it is a good approximation that gets better and better.

 

[Buffu]

Because V << v and because v is increasing, it is a good approximation that gets better and better.

I am sorry, I did not follow how does velocity of wall has to do anything with the velocity of ball ? Can you elaborate on it please.

 

[jbriggs444]

I am sorry, I did not follow how does velocity of wall has to do anything with the velocity of ball ? Can you elaborate on it please.

The velocity of the ball changes at each bounce from a moving wall. How much it changes depends on V.

Also, how much x changes during a round trip depends on V.

 

[Buffu]

The velocity of the ball changes at each bounce from a moving wall. How much it changes depends on V.

Also, how much x changes during a round trip depends on V.

I can buy that explanation.
If I wanted to find accelaration of ball without doing all this. Is it possible ?

 

[jbriggs444]

I can buy that explanation.
If I wanted to find accelaration of ball without doing all this. Is it possible ?

I suspect that treating the ball as an ideal gas under adiabatic compression would work.

 

[Buffu]

I suspect that treating the ball as an ideal gas under adiabatic compression would work.

I intended to ask if there is some more mathematically accurate way to do this using mechanics.

Since you have mentioned, how should I go doing that ? I thought I will differentiate adiabatic work done but I don't know temperature, pressure and thing like that :((.

 

[sophiecentaur]

If I wanted to find accelaration of ball without doing all this.

All what? It's a simple elastic collision situation at each bounce. This is the sort of situation that is built on in deriving the simple theory for the Gas Equations so I think it would be much easier to keep to simple Mechanics, rather than getting into thermodynamics.

 

[Buffu]

All what? It's a simple elastic collision situation at each bounce. This is the sort of situation that is built on in deriving the simple theory for the Gas Equations so I think it would be much easier to keep to simple Mechanics, rather than getting into thermodynamics.

I also don't like to use thermodynamics. But I want to know if there is a different way to solve this question using mechanics ?

 

[sophiecentaur]

I also don't like to use thermodynamics. But I want to know if there is a different way to solve this question using mechanics ?

As I said before, the gas laws can be derived using exactly the same idea of elastic collisions against the walls of a box. What more could you ask for? See this link and do some more searching. The Web is seething with information about the.