Recent content by Awatarn

I have two coupled ordinary differential equations: \displaystyle \frac{dx}{dt} = f(y) x \displaystyle \frac{dy}{dt} = s(x) y To solve these equations, we generally use explicit method, but these equations are stiff equations. Therefore semi-implicit method might be a better choice. I'm...

I'm tying to solve a stochastic differential equation of stock price. The equation is dX = X(\mu dt + \sigma dW) where \mu, \sigma are constants and greater than zero. It is easy to show analytically that the expectation value to the solution is E[X(t)] = E[X(0)] e^{\mu t} Then I solved...

Solving problem is not that hard. You may use the cosine law and the sine law, but it might be lots of algebra. For me, I would like to write components of force in x and y direction. The force in each component must be canceled ( forces are balance) So you have two unknown variables ( F3 and...

Almost correct except r in your equation r is a distance from the charge you are considering. So each r on the left side and right side of your equation should not be equal. One should be include the distance between two point charges.

Correct, good work

It's would be nice if you use LaTex. You might check your answer by using Mathematica. It's really useful program.

Never heard that Check it at http://en.wikipedia.org/wiki/Selection_rule

Your logic looks good. The first thing that I'm aware is your Xf equation. the initial velocity in x direction should have v_i cos(\theta) And an acceleration in that direction is zero.

Your method is correct. I check your answer, but I got the initial speed is 48.8 m/s.

There are more than one way to tackle this problem. First of all, you should find wave equation in string (without point mass). This equation will give you a general wave equation. Second, consider motion of the point mass by using Newton's equation. There are three force relevant to the mass...

That looks good. You can check your answer in limiting case. When mass of the rope goes to zero, your answer gives the same result as massless rope.

I try to answer your questions:

You need to convert the unit of mass to kg to make a consistent. It may be easily for you to convert every unit into SI unit which mean [mass] = kg, [Force] = N = kg s^2 / m I'm not sure about your experiment so I can't answer your second question.

An electron has no substructure. Unlike other composite system you cannot split it.

You're correct. The electron repels each other because of the same charge but attracts because of the gravitational force. Both kinds of force obeys the square law (force is proportional to \frac{1}{r^2}). Two things repelling or attracting depending on charge and mass of themselves.