# Questions tagged [homework-and-exercises]

Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.

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### How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$ ?

This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell Show, by explicit calculation, that $(1/2,1/2)$ is the Lorentz Vector. I see that the ...
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### How long would it take me to travel to a distant star?

Suppose I wanted to travel to one of the recently discovered potentially Earth-like planets such as Kepler 186f that is 490 light years away. Assuming I had a powerful rocket and enough fuel, how long ...
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### Toppling of a cylinder on a block

A uniform cylinder rests on a cart.The height and diameter is given.coefficient of static friction is given.How can i find the minimum acceleration of block such that the block topples? Morever what ...
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### Is it possible to produce gravitational waves artificially?

Why don't they make a ball with irregularities, say the size of a tennis ball, then spin it very rapidly, so it would produce gravitational waves like a spinning star with irregularities on it? Is ...
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### Harmonic oscillator coherent state expectation values

I'm looking to calculate the expected values of a coherent state (of a harmonic oscillator) evolving in time. I know that the $x$ and $p$ expectation values are as in classical motion, but I'm ...
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### Why is $R\cos{a} = mg$ in circular motion compared and not $R = mg\cos{a}$?

Normally, if an object of mass $m$ is inclined to the horizontal at an angle $b$, we set the reaction force of the object on the inclined plane as $R = mg\cos{b}$ (if we resolve the force of gravity ...
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### Shape of a string/chain/cable/rope/wire?

The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall) and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc ...
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### Time taken for object in space to fall to earth

The Problem For a small mass a distance $R_i$ away from the center of the Earth, how long would it take for the object to fall to the surface of the Earth, assuming that the only force acting upon the ...
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### Quadratic drag projectile motion

I have calculated formulas with 1 dimensional trajectory motion (free-fall) including quadratic drag, and have created the following equations. These equations of motion are not of much use on its ...
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### Tangential acceleration in circular motion?

A lot of my problems have objects moving in circular paths with tangential and normal components of acceleration. If the tangential component is non-zero though, the speed is changing so the radius ...
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### Eigenvalues and eigenfunctions of the exponential potential $V(x)=\exp(|x|)$

For $a$ being positive what are the quantisation conditions for an exponential potential? $$- \frac{d^{2}}{dx^{2}}y(x)+ ae^{|x|}y(x)=E_{n}y(x)$$ with boundary conditions $$y(0)=0=y(\infty)$$ I ...
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### What would be the effective resistance of the ladder of resistors having n steps

I'm a tutor. This is a high school level problem. In high school, every one have might have solved a problem of effective resistance of a ladder of resistors having infinite steps. Now the problem is ...
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### Integrating radial free fall in Newtonian gravity [duplicate]

I thought this would be a simple question, but I'm having trouble figuring it out. Not a homework assignment btw. I am a physics student and am just genuinely interested in physics problems involving ...
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### Motion of a rod struck at one end

Imagine a strong metal rod of uniform density and thickness floating in a weightless environment. Imagine it lies on an X-Y plane, with one end (A) lying at 0,0, and the other end (B) at 0,1. Then it ...
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### Tricky conceptual question: ball sliding and rolling down incline [closed]

We all are familiar with the classic ball rolling down the incline exercise in rotational dynamics. Here is quite a tricky conceptual problem: You have an incline of fixed height, but the angle of ...
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How much time would it take for a traveler (in traveler's perspective) to reach a star at distance $d$, if it accelerates at 9.8 m/s² (for a comfortable travel)? I understand that $V = V_0 + a\times ... 3answers 3k views ### Tension in an Atwoods machine conceptual? Assuming$T_1$is the force that acts on box$1$and$T_2$is the force that acts on box$2$. Exactly what causes the Tension? Why does$T_1 = T_2$? The problem is we are told to memorize that$T_1 =...
I am preparing for my quals and stumbled across the following problem, and although it only requires undergraduate-level physics, I feel I can't piece everything together. "A rocket of mass $m_0$ is ...