the first step makes sense: ln[(x^2+1)(x-1)]=ln(x^2+1)+ln(x-1)
but then you continued: ln(x^2+1)=ln(x^2)+ln(1)
You can't do that, but you can do something else to the x^2+1...
Do you mean you need to reproduce the theoretical calculations present which involve a step function? I'm not exactly clear on what you're trying to do.
This is a really cool question. I was stumped for a few minutes before I started thinking about what additional effects are present when the capillary tube is vertical that were not there before. Do you remember in which direction pressure acts?
one of the key differences in your choices are the numbers 12 and 24. What do they represent, and which one is relevant in the case of a full rotation of the hour hand?
Yes, that is what I meant, except that I used the second derivative of temperature. I know there's a major difference, is your first derivative just a typo or is there something I missed?
By assuming that T(x) << T(outer) I can get a temperature of approximately 175K. Thanks for all of your...
Perhaps I'm not approaching the problem the same way you are:
\alpha = \kappa / c_p \rho
C = \epsilon \sigma A * T(outer)^4 / (m*c_p)
--> this is the delta T as contributed from external radiation, adjusted for the mass (which will have the inner and outer diameters in the...
you're right, there should be a constant in front of the second derivative of temperature wrt x:
\alpha d^2 T(x)/dx^2 = C - \epsilon \sigma A*T(x)^4
However, I'm changing the problem into a 1D heat conduction problem because I want to solve the simpler version first. In...
Homework Statement
Let's say you have a 3m long copper pipe, 3mm in thickness with a diameter of 170mm. You fix one end at 1K and insulate it to prevent conduction or convection between the air and the pipe itself. There is still radiation. Assume that the inside of the pipe has no effect...
I don't understand where you're getting your angles from, unless one of the masses is also on a ramp? Can you describe the geometry of the setup a little better?
three hints:
-in which axis is "range" measured?
-what forces do you have acting in this axis?
-based on these forces, formulate your acceleration and displacement equations.
delta PE is just your change in gravitational potential energy, delta KE is your change in kinetic energy. Does this formula seem different than the one you used?