This Problem is Killing me and I don't know why!

  • #1
3,003
6

Homework Statement


It's 2.31


Photo10.jpg


Here is what I am thinking so far:

At V2 the system is at equilibrium, so p2 equals p_atm since the spring exerts no force.

So p2 is known.

I now need p1. I am not sure where to go from here. I have V1, V2 and p2.
I think that spring-force/area is part of p1...

Can someone give me a hint? :smile: Just a hint....
 

Answers and Replies

  • #2
116
0
The work done by the piston on the air is

[tex]\int[/tex] P dV

You could write a linear equation for P as a fcn of V with the info you have, but of course geometrically this is just the area under the graph of P vs V, which in this case is trapezoidal in shape. Sketch the P-V trapezoid, calculate its area (watch the units), and you gave the work.
 
  • #3
3,003
6
That sounds reasonable! But, let's look at it for a moment w/out the p-V diagram, I am confused as to how to right out [itex]\int pdV[/itex] What kind of compression is this considered? p is not constant, nor is V. I am just confused as to how to incorporate the spring force?
 
  • #4
116
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It says the spring force varies (decreases) linearly as the volume. You have two sets of (P,V) graph points, so you could write an equation of the form P = mV + c and use that to calculate the integral.
 
  • #5
3,003
6
I wish I followed you. What is P=mV+c ? It say that the spring force varies linearly, not the pressure...:confused:
 
  • #6
3,003
6
Are you saying that p can be written as a function of volume since ot is just the sum of p_atm and F_spring/area?

That is that [tex]p(V)=F/A+p_{atm}[/tex] so I have to find out what F is...

So I need to write F_spring as a function of V somehow....
 
Last edited:
  • #7
116
0
We know the following:

The spring force varies linearly from 9.00 kN to 0 kN. I'm writng this in kN for convenience, since kN / m^2 is kPa. Since the area of the piston is constant, and P = F / A, the pressure varies linearly also (as volume decreases) and so we can write a function P(V) = mV + c.

Now, when V = 0.003 m^3, F = 9.0 kN and P = (9.0 kN / 0.018 m^2) + 100 kPa = 600 kPa

When V = 0.002 m^3, F = 0.0 kN and P = (0.0 kN / 0.018 m^2) + 100 kPa = 100 kPa

Now using the two points (P,V) = (600,0.003), (100,0.002), we can find m and c for our function P(V).
 

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