Recent content by vuellesse

If you rotate the vectors a and b in a way such that a is aligned along the z axis, the expression for the scalar product reduces to a \cdot b=a b_z =a b cos \theta. The last passage follows the change of coordinate system (from cartesian to spherical).

I think it is correct to say that the work is equal to the object's change in kinetic energy, if by work you mean the one of the net force on the object (which includes gravity).

Actually it is time invariant, since the time reversal operator is not unitary but antiunitary, so you have to complex-conjugate the wave function besides changing the sign of the time. Of course it doesn't respect relativistic invariance.

I think that one of the mistakes you made is when you substitute the expression for v(t): you should have (ln (m/M))^2 instead of ln(m^2/M^2)=2ln(m/M)

Let's think the cylinder as if it has one base free to move. The gas inside the cylinder applies a pressure p on the base (so the force is F_in=p S, where S is the area of the base). Because of Newton's law, the base itself applies on the gas the same force (in opposite direction). Moreover...

Let's suppose T and n fixed. If you don't apply any other forces from the outside besides the atmospheric pressure, the expansion can happen only if the pressure of the perfect gas is greater than the atmospheric pressure. The work done by the gas can be correctly calculated using your formula...

Hi! Does anyone know how to solve the following integral analitically? \int^{1}_{0} dx \ e^{B x^{2}} J_{0}(i A \sqrt{1-x^{2}}), where A and B are real numbers. Thanks!