Collision between moving walls

  • Context: Undergrad 
  • Thread starter Thread starter Buffu
  • Start date Start date
  • Tags Tags
    Collision Mechanics
Click For Summary

Discussion Overview

The discussion revolves around a problem involving the collision of a ball with moving walls, focusing on the implications of constant velocity, time of collision, and the relationship between the ball's motion and the walls' motion. Participants explore various approaches to understanding the mechanics of the situation, including the potential use of thermodynamics and elastic collisions.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions the validity of the solution stating that ##\Delta T = 2x/v##, suggesting that if the time of collision decreases, the distance should also approach zero, leading to a contradiction.
  • Another participant challenges the assumption of constant velocity, indicating that the speed of the ball increases with each bounce, which may affect the calculations.
  • Some participants propose that the approximation of ##\Delta T = 2x/v## holds under the condition that the wall's velocity is much smaller than the ball's velocity.
  • There is a suggestion that the acceleration of the ball could be derived using an ideal gas model under adiabatic compression, although this raises questions about the necessary parameters like temperature and pressure.
  • Participants discuss the simplicity of treating the problem as an elastic collision scenario, with some expressing a preference for mechanics over thermodynamics in solving the problem.

Areas of Agreement / Disagreement

Participants express differing views on the constancy of the ball's velocity and the implications for the time of collision. There is no consensus on the best approach to solve the problem, with some favoring mechanical methods while others consider thermodynamic perspectives.

Contextual Notes

There are unresolved assumptions regarding the relationship between the velocities of the ball and the walls, as well as the conditions under which the approximations hold. The discussion also highlights the complexity of deriving acceleration without specific parameters.

Buffu
Messages
851
Reaction score
147
https://www.physicsforums.com/attachments/upload_2017-6-17_4-22-26-png.205585/?temp_hash=f9f8d75085046fd530ad1071794d65c1

I have problem with the solution given of the (b) part of the question.
The given solution is :
upload_2017-6-17_4-23-44.png


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 ?
 
Physics news on Phys.org
The value of what should be zero? And why do you expect velocity to be constant?
 
jbriggs444 said:
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.
 
Buffu said:
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.
 
jbriggs444 said:
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 ?
 
Buffu said:
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.
 
jbriggs444 said:
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.
 
Buffu said:
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.
 
  • Like
Likes   Reactions: Buffu
jbriggs444 said:
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 ?
 
  • #10
Buffu said:
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.
 
  • #11
jbriggs444 said:
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 :((.
 
  • #12
Buffu said:
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.
 
  • #13
sophiecentaur said:
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 ?
 
  • #14
Buffu said:
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.
 

Similar threads

Vertical Wall approaching Man - Impulse and Momentum Conservation
  • · Replies 10 ·
Replies
10
Views
1K
High School Collision time interval of a gas molecule with wall of container
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How to Calculate force exerted on a falling body?
  • · Replies 12 ·
Replies
12
Views
3K
Ambiguous question on momentum and how it works...
  • · Replies 13 ·
Replies
13
Views
1K
Impulse and perfectly inelastic collision between 2 points
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad How will the two balls move after the collision?
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Kinetic theory of gases: rebound speed and force questions
  • · Replies 2 ·
Replies
2
Views
3K
High School Does Normal force always HAVE to be perpendicular to plane ?
  • · Replies 24 ·
Replies
24
Views
4K
Undergrad Trajectory collision calculation
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How can angular displacement be larger than 2pi?
  • · Replies 20 ·
Replies
20
Views
3K