Mixing Newton's law with Adiabatic Process

[TonyCross]

Homework Statement

Given a fixed force applied to a mass, what effect would the introduction of a gas compression component make?

Relevant Equations

Newton's F=ma
Ke = 1/2 m v2
combined gas laws
p * V = n * R * T
p(V) = n * R * T / V = A / V

I have attached an image showing the perimeters of the problem.
I have included what I think is the solution, could someone please take a look and tell me if I am on the correct path, in the solution I am taking Joules as a common term to attempt to solve the question. The gas I have used is N.
Thanks in advance.

 

[TonyCross]

I forgot to give my final answer by using the figures in my example.

reverse Ke Formula v = sqrt Ke/1/2m
v= sqrt 335.04/500 = .8186 m/s

 

[BvU]

Hi,

I see some serious problems, even with your A scenario. Check the dimensions: $a = {F\over m}\$ yields $a = 1$ m/s² (not m/s) !
And the kinetic energy is not 500 J, but time dependent.

Scenario B (if I interpret it correctly) more or less gives the same result: after a very short time, the net effect is that the mass is pushed with a force of 1000 N.

$\$

 

[Steve4Physics]

Hi. In addition to @BvU’s comments...

I’m guessing that you haven’t accurately/completely stated the original question (word-for-word). This is essential.

And for information:
- you have used the wrong value for cross-sectional area when using P = F/A;
- ‘joules’ should be lower case, though its symbol (J) is upper case.

 

[TonyCross]

Hi,

I see some serious problems, even with your A scenario. Check the dimensions: $a = {F\over m}\$ yields $a = 1$ m/s² (not m/s) !
And the kinetic energy is not 500 J, but time dependent.

Scenario B (if I interpret it correctly) more or less gives the same result: after a very short time, the net effect is that the mass is pushed with a force of 1000 N.

$\$

Hi, Thanks very much for replying, in Scenairo B if there is energy lost due to the heating event why would the resultant Kinetic energy be the same, would this not violate the conservation of energy law? i.e A is 1 m/s²
then B would also be 1 m/s². Yes the kinetic energy is time dependent let's suppose that the event is one second.
If one Scenario has heat and the other does not how can the net effect be the same?

 

[TonyCross]

Hi. In addition to @BvU’s comments...

I’m guessing that you haven’t accurately/completely stated the original question (word-for-word). This is essential.

And for information:
- you have used the wrong value for cross-sectional area when using P = F/A;
- ‘joules’ should be lower case, though its symbol (J) is upper case.

Ah yes I can see my mistake in the cross-sectional area, thanks

 

[Steve4Physics]

Without knowing the exact original homework question, we can't help much.

Does the original homework require a calculation? Or only a descriptive answer?

Here are a couple of questions to think about:

If a total force of 1000N is applied to a 1000kg system, what happens to the centre of mass of the system?

In Scenario B, how does the system's centre of mass change over time?

 

[BvU]

If one Scenario has heat and the other does not how can the net effect be the same?

The work done is not the same: force F has to be exerted over a longer distance in scenario B (not only to heat up the gas, it also does compression work !)

I wonder what the composer of this exercise had in mind when putting this together. Imho this is not a good exercise: too confusing.

 

[TonyCross]

Without knowing the exact original homework question, we can't help much.

Does the original homework require a calculation? Or only a descriptive answer?

Here are a couple of questions to think about:

If a total force of 1000N is applied to a 1000kg system, what happens to the centre of mass of the system?

In Scenario B, how does the system's centre of mass change over time?

Hi Steve,
Thanks for your comment,
I suppose that in case A the force is applied to the centre of mass causing a displacement in -x only in case B the centre of mass may alter slightly as the piston is compressed but I imagine this would not have any effect on the vector displacement.
I guess the whole idea of the question is does the heating event in case B, have any effect on the resultant kinetic energy of the mass, with respect to case A?
This is the question all the rest is imagined.

 

[Steve4Physics]

Hi Steve,
Thanks for your comment,
I suppose that in case A the force is applied to the centre of mass causing a displacement in -x only in case B the centre of mass may alter slightly as the piston is compressed but I imagine this would not have any effect on the vector displacement.
I guess the whole idea of the question is does the heating event in case B, have any effect on the resultant kinetic energy of the mass, with respect to case A?

The acceleration of the centre of mass of the system would be the same in both scenarios. But because the gas gets compressed over some finite (unknown) time period, the block's acceleration is initially less than the whole system's acceleration because the system is changing shape.

My instinct tells says this...

Oscillations will occur, with the gas acting just like a spring. After some time, a steady-state will be reached - the block's acceleration will oscillate around 1m/s² and the gas+piston's acceleration willoscillate in the opposite sense around 1m/s².

This is a a difficult problem to quantitatively analyse and depends on things like the mass of gas and piston.

However, I will note (again) that you haven't told us the exact, original homework question. So we can't tell if you are 'barking up the wrong tree'!

 

[TonyCross]

The acceleration of the centre of mass of the system would be the same in both scenarios. But because the gas gets compressed over some finite (unknown) time period, the block's acceleration is initially less than the whole system's acceleration because the system is changing shape.

My instinct tells says this...

Oscillations will occur, with the gas acting just like a spring. After some time, a steady-state will be reached - the block's acceleration will oscillate around 1m/s² and the gas+piston's acceleration willoscillate in the opposite sense around 1m/s².

This is a a difficult problem to quantitatively analyse and depends on things like the mass of gas and piston.

However, I will note (again) that you haven't told us the exact, original homework question. So we can't tell if you are 'barking up the wrong tree'!

The original question was "Given a fixed force applied to a mass, what effect would the introduction of a gas compression component make? "
Thanks very much for your answer, much appreciated.

 

[TonyCross]

The work done is not the same: force F has to be exerted over a longer distance in scenario B (not only to heat up the gas, it also does compression work !)

I wonder what the composer of this exercise had in mind when putting this together. Imho this is not a good exercise: too confusing.

Thanks for your input.