Calculating the average force of a molecule in a vessel

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SUMMARY

The discussion focuses on calculating the average force exerted by an oxygen molecule traveling at 484 m/s in a cubical vessel with a side length of 0.1 m. The average force is derived using the formula F = 2mv/t, where t is calculated as 0.2 m / 484 m/s, resulting in a time of approximately 4.13 x 10^-4 seconds. The factor of 2 in the impulse calculation accounts for the molecule's change in momentum during collisions with the wall, as it reverses direction upon impact.

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  • Understanding of basic physics concepts such as momentum and force.
  • Familiarity with the equation F = p/t for calculating force.
  • Knowledge of how to calculate time of travel using distance and speed.
  • Basic grasp of elastic collisions and impulse in physics.
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  • Study the principles of momentum conservation in elastic collisions.
  • Learn about impulse and its relation to force in physics.
  • Explore the concept of average force and its applications in different scenarios.
  • Investigate the behavior of gas molecules in confined spaces using kinetic theory.
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Students studying physics, particularly those focusing on mechanics and thermodynamics, as well as educators looking for examples of molecular behavior in confined environments.

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Homework Statement



Suppose an oxygen molecule traveling at the speed of 484 m/s bounces back and forth between opposite sides of a cubical vessel 0.1 m on a side. What is the average force the molecule exerts on one of the walls of the container?

Homework Equations


F=p/t

The Attempt at a Solution


t=0.2 m / 484 m/s = 4.13 *10^-4 seconds

In a collision v changes direction so delta p = 2*mv

(mv was calculated in a previous question so it is known)

The average force can then be calculated as:

F = 2mv / t

My question here is, how come when calculation the time, they use 0.2 m and not 0.1 as given in the assignment? Is this because the molecule moves back and forth 0.1 m during the collision?

Second question: why do they multiply a factor 2 on the impulse? Where does this come from?
 
Physics news on Phys.org
They are considering impacts on a given wall. How far does the molecule travel between successive impacts there?
Each impact, the molecule strikes the wall with velocity v, head on, and bounces back. What is the net change in velocity?
 

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