Recent content by Macykc2

Homework Statement I need to evaluate the following integral using the antiderivative: $$\int log^2(z) \, dz$$ I don't know how to make a subscript for the integral sign, there should be a "c" on the bottom part. C is any contour from ##π## to ##i##, not crossing the non-positive x-axis...

Homework Statement Discuss the motion of a particle in a central inverse-square-law force field for a superimposed force whose magnitude is inversely proportional to the cube of the distance from the particle to the force center, that is: F(r) = -k/r2 - λ/r3 and k,λ>0 Show that the motion is...

Also I should add this isn't the final solution to the problem, it's just the step I'm having trouble understanding.

Alright so the cartesian coordinate system is chosen with the y-axis parallel to the magnetic field. If q is the charge on the particle, v it's velocity, "a" it's acceleration, and B the Earth's magnetic field, then: v=x'i + y'j + z'k a = x''i + y''j + z''k B = Boj The magnetic force F=qv X B =...

No sadly, I'll just type it out, give me a few mins

Here are the pics straight from the book, I thought this would be easier than typing it out, hopefully they turn out fine.

Homework Statement Consider a charged particle entering a region of uniform magnetic field B - for example the Earth's field. Determine it's subsequent motion when the y-axis is parallel with the magnetic field Homework Equations F=qv x B = ma vector components of velocity, acceleration, and...

I also just noticed a very crucial mistake, this whole time I've been writing eβv as e-βv, so I need to re-do everything...

I figured that's what i had to do, I took a look at it after I posted and tried some other things including that, and although I do get results it's once again hard to see if it makes sense, as they do not specify what alpha and beta are. Also I will try in the future to just use this site...

Homework Statement A boat with initial speed vo is launched on a lake. The Boat is slowed by the water by a force F=-αeβv. Find an expression for the speed v(t), and find the time and distance for the boat to stop. Homework Equations Drag force F=-αeβv alpha and beta are not specified as to...

Alright I've figured out that part, and I've also solved for θ', then I put that equation into r' and ended up with ##r'=\frac{v[1+cos\theta - sin\theta]}{\sqrt{1+2cos\theta}}## Now you say I'm supposed to differentiate with respect to t, dv/dt would make acceleration, but differentiating the...

My confusion is with the last sentence, I was able to get to, ##k\theta'(-sin\theta)\hat{r}+k(1+cos\theta)\theta'\hat{\theta}##, but I'm not sure of the reasoning behind the next part where he mentions it's a constant magnitude and concludes the second equation.

I was going to create a whole new thread with reference to this post, but I guess I should check if this will bump it. My question lies in posts 2 and 3, I understand where we get the velocity function in terms of cylindrical cords, but I'm missing the bridge between the v2 part, why is it...

Hello everyone, I'm a 3rd year math major physics minor, and if everything goes well I'll be getting my masters and PhD in Physics, but I have yet to determine which branch. I'm here to hopefully get some pointers, I'm in a mechanics class right now and it is very intense, the math is easy but...