I am in my 4th year (3 semesters left including the current one), taking mechanics, E&M, quantum mechanics, and a lab course. For each of the three main courses, we get one problem set per week that's around 5-8 questions. In addition to that there's a lab report due every 1-2 weeks.
It really...
This is a random problem I am trying to figure out. The context doesn't matter.
I wish to define a function z(x, y) based on the following limits:
1. lim z (x→∞) = 0
2. lim z (x→0) = y
3. lim z (y→∞) = ∞
4. lim z (y→0) = 0
This is a somewhat vague question that stems from the entries in a directional cosine matrix and I believe the answer will either be much simpler or much more complicated than I expect.
So consider the transformation of an arbitrary vector, v, in ℝ2 from one frame f = {x1 , x2} to a primed...
I am looking at an explanation of the gradient operator acting on a scalar function ## \phi ##. This is what is written:
In the steps 1.112 and 1.113 it is written that ## \frac {\partial x'_k} {\partial x'_i} ## is equivalent to the Kronecker delta. It makes sense to me that if i=k, then...
1. Homework Statement
Integrate by changing to polar coordinates:
## \int_{0}^6 \int_{0}^\sqrt{36-x^2} tan^{-1} \left( \frac y x \right) \, dy \, dx ##
2. Homework Equations
## x = r \cos \left( \theta \right) ##
## y = r \sin \left( \theta \right) ##
3. The Attempt at a Solution
So this...
I assume this is a simple summation of the normal components of the vector fields at the given points multiplied by dA which in this case would be 1/4.
This is not being accepted as the correct answer. Not sure where I am going wrong. My textbook doesn't discuss estimating surface integrals...
1. Homework Statement
Given this diagram, the problem is to find an expression for β/ΘE in terms of X/ΘE and Y/ΘE.
2. Homework Equations
β = Θ – α(Θ)
Dsβ = DsΘ – Dlsα'(Θ)
3. The Attempt at a Solution
I really only need help starting this problem. In my textbook and every document I can...
2-3 hours is just on the one homework assignment that is due each week. That does not count time spent studying for the weekly quizzes or just reviewing lecture material. And also the same question in my reply above is really what I was looking for. Thanks.
Sorry I didn't mean to sound like I'm not interested in learning the harder problems but I am in multivariable calculus, advanced statistics, and principles of astrophysics as well and I don't just have time to be delving into subjects I don't think I will be tested on. Believe me I would love...
I am currently in Honors Physics 3 which is the third introductory course of my physics degree program and covers modern physics beginning with special relativity. So far we have covered Lorentz transformations and velocity additions, relativistic energy and momentum, blackbody radiation, photon...
The problem is to find the general term ##a_n## (not the partial sum) of the infinite series with a starting point n=1
$$a_n = \frac {8} {1^2 + 1} + \frac {1} {2^2 + 1} + \frac {8} {3^2 + 1} + \frac {1} {4^2 + 1} + \text {...}$$
The denominator is easy, just ##n^2 + 1## but I can't think of...
Thanks, so just to be clear that would mean that I should express the change in volume and the uncertainty in the change in volume to the nearest thousandth of a centimeter because they were measured to that degree of accuracy in the question, right?
1. Homework Statement
A car engine moves a piston with a circular cross section of 7.500 ± 0.005cm diameter a distance of
3.250 ± 0.001cm to compress the gas in the cylinder.
(a) By what amount is the gas decreased in volume in cubic centimeters?
(b) Find the uncertainty in this volume.
2...
1. Homework Statement
A uniform disk of radius R=1m rotates counterclockwise with angular velocity ω=2rads/s about a fixed perpendicular axle passing through its center. The rotational inertia of the disk relative to this axis is I=9kg⋅m2. A small ball of mass m=1 is launched with speed v=4m/s...
1. Homework Statement
A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 49.0 m. Answer the following for the instant it makes an angle of 32.0° with the vertical as it falls. (Hint: Use energy considerations, not a torque.)
(a) What is...
583.1 is the distance the rock slides found by the Pythagorean Theorem √3002+5002. I tried both positive and negative with those answers. I assume the work done by friction is always negative since it is opposite the motion. and the kinetic energy should be positive because the velocity would be...
1. Homework Statement
During a rockslide, a 710 kg rock slides from rest down a hillside that is 500 m long and 300 m high. The coefficient of kinetic friction between the rock and the hill surface is 0.23...