I have a system that looks like this:
The top part is a piston, whereas the bottom is a displacer.
I have looked at the Isothermal case for this system in a separate thread (https://www.physicsforums.com/showthread.php?t=553165)
But in short, the result was that the pressure of the system...
I'm hoping to start a simple heat transfer model. It's basically a cylinder filled with air at a temperature T=300K. The bottom wall of the cylinder, made of steel, is heated (and kept at the constant temperature of T=400K). The side walls and top for the moment are treated as adiabatic (since I...
If I have a string with a lump on the end and is being swung in a circle with a continuous angular velocity then I know that:
F= m\frac{v^2}{r}
or using angular velocity,
F= m r \omega^2
But, is there a tangential force acting at the point of mass in its instantaneous direction, and if...
Hi tiny-tim,
τ, the torque is a function of θ. I guess I should avoid using f at all?
I've changed it to this now:
The trapezoidal rule, which says:
\displaystyle\int^{b}_{a}f(x) dx\approx(b-a)\frac{f(a)+f(b)}{2}
Applied to the work integration...
or would this be more appropriate?
W=\displaystyle\int^{\theta_{2\pi}}_{\theta_{0}} \tau d\theta\approx \frac{\pi}{360}\displaystyle\sum\limits_{\theta=0}^{359} (f(\theta)+f(\theta+1))
How could I adjust this to follow the same formatting as above...
Thank you for the replies.
Is this better now?
W=\displaystyle\int^{\theta_{2\pi}}_{\theta_{0}} \tau d\theta\approx \frac{h}{2}\displaystyle\sum\limits_{k=0}^{359} (f(\frac{k\pi}{180})+f(\frac{(k+1)\pi}{180}))
How can I make this mathematically correct? I hope you see what I'm trying to do?...
If you have a graph where:
W=\displaystyle\int^{\theta_{2\pi}}_{\theta_{0}} \tau d\theta
Then the estimated area with the trapesium rule:
\displaystyle\int^{\theta_{2\pi}}_{\theta_{0}} \tau...
Sorry, I should add why I'm asking this. I have the following diagram:
Where f_g is the combustion force, f_j is the inertial force and f is the resultant force. I'm trying to work out what's providing the force to overcome the acceleration around 650 to 90 degrees.
I'm struggling to apply F=ma to the motion of a slider crank, more specifically the piston. I want to find out how much force is nessesary to keep the piston in motion. Essentially, in the mechanism there is acceleration and deceleration, does that mean only at some points in the cycle there is...
Thank you both for your replies :smile:
I've worked it through algebraically with both your methods and I see how it works now :)
I should've started the problem algebraically in the first place, instead of jumping in there with the numbers.
It's really helped with my project, so thank...
Ok, bbbeard, so using your equation:
P = \frac{MR}{V_{1}/T_{1} + V_{2}/T_{2}}
With:
V1 = 0.75 m^3
V2 = 0.25 m^3
T1 = 300 k
T2 = 900 k
M = 1kg
R = 287 J/Kgk
Which gives an answer for P of 103,320 Pa
Whereas following klimatos logic, my T would be 0.75*300 + 0.25*900 = 450...
Sorry for my ambiguity, I guess I didn't explain it very well.
Imagine a sealed cylinder, with a total volume of 1 m^3. The bottom half of the cylinder is being kept at a temperature of 300k. The top half is kept at a temperature of 900k.
Now, there is a circular disc (of negligable...
I'm attempting to construct a very simplified mathmatical model of a stirling engine. I'm assuming that in one space hot gas exists at a temperature of 800k and in another the gas exists at its cold temperature of 300K.
The gas is shuttled back from each space via displacer, which does so by...
Not a homework question, but here seems the most revelant place for this kind of maths.
I have a problem similar to a slider crank but not quite.
http://imageshack.us/photo/my-images/851/sw1b.png/
Fixed points are A and B, all others are free to pivot. The beam labeled 20 is rotating...