# 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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### Why is my hand not burned by the air in an oven at 200°C?

I have this problem from University Physics with Modern Physics (13th Edition): The inside of an oven is at a temperature of 200°C (392°F). You can put your hand in the oven without injury as long ...
11k views

### Does a gun exert enough gravity on the bullet it fired to stop it?

My question is set in the following situation: You have a completely empty universe without boundaries. In this universe is a single gun which holds one bullet. The gun fires the bullet and the ...
15k views

### Does a thrown ball have kinetic energy at the top of the curve?

I'm going through physics with my 5th grade child. There is a question and answer that indicates that a airborne ball at the top of the trajectory does not have kinetic energy. The diagram below ...
13k views

### How big would my telescope have to be if I wanted to see the Mars rover from my backyard?

I imagine that with a big enough telescope, I would be able to zoom in and see the Mars rover in enough detail to make out the details (like the wheels, cameras, etc.). How large would the telescope ...
17k views

### How to measure the wavelength of a laser pointer?

I'm working on something and I need to know the wavelength of the laser pointer that I'm using. Can you suggest me a way, using some optics formulae, or anything else to calculate the wavelength?
12k views

### When a balloon pops and lets a brick fall, where does the energy come from?

Let's say a scientist attaches a 1 kg brick to a large helium inflated balloon, lets the balloon go, and then it reaches an altitude of 10 000 meters before it pops, dropping the brick. The brick ...
15k views

### Are we slightly lighter during the day and slightly heavier at night, owing to the force of the Sun's gravity?

Using $g = \frac{Gm}{r^2}$, the force on a point mass located at 1 AU from the Sun ($m = 2 \cdot 10^{30} \text{ kg}$) is about ~0.006 N/kg. Does that mean that, e.g., a 70 kg person is ~42g lighter ...
22k views

### 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 ...
16k views

### Freefall into snow

In the movie Frozen, the following dialogue takes place: Anna: "It's a hundred-foot drop." Kristoff: "It's two hundred." Anna: "Okay, what if we fall?" Kristoff: "There's 20 feet of ...
7k views

### 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 ...
5k views

### How far out from the Sun is visible light still sufficient to read a book?

Recent pictures from the New Horizons spacecraft, shown below, seem to indicate that, at Pluto's distance, we are entering a twilight zone, with a distinct lack of colors, although that could be due ...
9k views

### Why do we need to know the shape of the slide to find the time to slide down it?

In my physics book after this solved example: A child of mass $m$ is initially at rest on top of a water slide at height h = 8.5m above the bottom of the slide. Assuming that the slide is ...
8k views

### “Falling upward” - how far you have to be from Earth to start falling to the Moon?

Talking about gravity with my 9 y/o she asked when do we start "falling upward" to the Moon. What is the distance at which the Moon's gravitational attraction is higher than that of the Earth and thus ...
12k views

### Which ball touches the ground first?

This is a very well known problem, but I can't find an answer in the specific case I'm looking for. Let's consider two balls : Ball 1 weighs 10 kg Ball 2 weighs 1 kg Balls have identical volumes (so ...
8k views

### Condensation of Water. Classroom Controversy

In our test there was a question that went like so: Question 4 You have a glass of iced water on an unshaded picnic table and went for a walk for 30 minutes. When you return you noticed the glass ...
6k views

### Speed of sound at temperatures below 0 °C

How can the speed of sound be calculated for temperatures below 0 °C (down to -40 °C)? Does the calculation $v=331\ \frac{m}{s} + 0.6 \frac{m}{s°C} \times T$ still hold (where T's unit is °...
3k views

### Are the units of energy the same in higher dimensions?

In 3 spatial dimensions, $$[E] = [ML^2 T^{-2}]$$ Would it change in higher dimensions? If yes, then what would be the dimensions for 4 spatial dimensions?
8k views

### Can a gym be built to supply electricity to homes? [closed]

A moving magnet induces a current in a conductor, then shouldn't we be able to generate electricity through manual labour? I was thinking about building a gym that used magnets as weights. People ...
6k views

### How many X-rays does a light bulb emit?

I read somewhere that most things1 emits all kinds of radiation, just very few of some kinds. So that made me wondering whether there is a formula to calculate how many X-rays an 100W incandescent ...
4k views

### When should you jump off a falling ladder?

If you stand on the top of a falling ladder you will hit the ground at a higher speed (and therefore presumedly sustain more injury) if you hold on to the ladder than if you jump off it. This was ...
5k views

### Does bonfire night in the UK increase temperature of the country / local area?

I am not sure if this is the right forum for the question but failing to have any better location to ask it, i have come here. In the UK we have a tradition of lighting bonfires on the 5th of ...
37k views

### How to get the position operator in the momentum representation from knowing the momentum operator in the position representation?

I know that $$\tag{1}\hat{p}~=~-i\hbar \frac{\partial}{\partial x}~.$$ How can I get $$\tag{2}\hat{x}~=~i\hbar \frac{\partial}{\partial p}~?$$ I think this simple and I'm just over thinking it, ...
18k views

### Is it possible to shoot bullets in space or would the recoil of the gun be too strong?

I've read a few articles that say that astronauts have already brought guns in space and that shooting bullets in space is possible. But won't the recoil of the gun be too strong? Law of ...
9k views

### Why doesn't a spinning object in the air fall?

Let's say I have a ball attached to a string and I'm spinning it above my head. If it's going fast enough, it doesn't fall. I know there's centripetal acceleration that's causing the ball to stay in a ...
1k views

### How to apply the Faddeev-Popov method to a simple integral

Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
20k views

### How long does it take to travel 36 light years with tolerable acceleration and deceleration?

The recent discovery of HD85512b only 36 light years from Earth has promising attributes to harbor life. Assuming we want to travel there, we cannot instantaneously jump to light speed, (StarTrek ...
573 views

### Aether existance in alternate universe made of Bose-Einstein condensate

I came across an interesting question which was shown to me by my professor, it is as follows: Investigation of an alternative Universe: This Universe contains three spatial and one time ...
12k views

### Doesn't a box holding a vacuum weigh the same as a box full of air?

This was recently brought up, and I haven't been able to conclude a solid answer. Let's say we have two identical boxes (A and B...
4k views

### Conical train wheels

I've been reading about how the conical shape of train wheels helps trains round turns without a differential. For those who are unfamiliar with the idea, the conical shape allows the wheels to shift ...
8k views

### Deriving the speed of the propagation of a change in the Electromagnetic Field from Maxwell's Equations

I've been told that, from Maxwell's equations, one can find that the propagation of change in the Electromagnetic Field travels at a speed $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ (the values of which can ...
11k views

### Is this scene from the A Team explainable by Physics?

This scene (youtube link) from the movie The A-team, the four members are in the tank and its falling from the air, they fire the canon and it slows the tank from falling for a moment before falling ...
4k views

### Will the ball come out of the well or not?

A small ball moves at a constant velocity $v$ along a horizontal surface and at point $A$ falls into a vertical well of depth $H$ and radius $r$. the velocity of the ball forms an angle $\theta$ with ...
1k views

### Shape of a rotating rope with one free-end [closed]

One end of a uniform rope (with total mass $M$) is fixed on the edge of a cylinder. The cylinder has a radius $R$ and rotates with angular velocity $\omega$. The axis is vertical in a gravitational ...
9k views

### Oh-my-god particle: How can it get through Milky way in 10 seconds?

My question is concerning wikipedia article on Oh-my-God particle, to be precise, this paragraph: This particle had so much kinetic energy it was travelling at 99.99999999999999999999951% the speed ...
9k views

### How quickly was the Earth rotating 250 million years ago?

The Earth is slowing at a rate of $4.7\times10^{-4}$ miles per second every 100 years due to tidal forces of the moon. See: http://en.wikipedia.org/wiki/Earth%27s_rotation http://imagine.gsfc.nasa....
8k views

### Why does gravity act at the center of mass?

Sorry if this is a trivial question. Why does gravity act at the center of mass? If we have a solid $E$, shouldn't gravity act on all the points $(x,y,z)$ in $E$? Why then when we do problems we ...
5k views

### How many minutes in a year?

I knew that there were $365.25$ days in a year (ish) but we only have $365$ on calendars, that's why we have February 29. I then learned in class about the sidereal and solar day; sidereal being $23$ ...
2k views

### Electromagnetism problem: where does the magnetic field come from?

Consider the following problem: Consider a plane with uniform charge density $\sigma$. Above the said plane, there is a system of conducting wires made up of an U-shaped circuit on which a linear ...
2k views

### Why can't a nucleus become a black hole?

A nucleus is very small and very dense. Its density is approximately $2.3 \times 10^{17}~\mathrm{kg/m^3}.$ So why can't a nucleus itself become a black hole?
5k views

### Does friction always oppose motion?

Recently I had the following misconceptions: Static friction always opposes the motion of body. The force of friction cannot initiate motion in a body. Now I came to know that my understanding was ...
20k views

### Why can't a single photon produce an electron-positron pair?

In reading through old course material, I found the assignment (my translation): Show that a single photon cannot produce an electron-positron pair, but needs additional matter or light quanta. My ...
2k views

### Does 60kg of fusion fuel produce as much energy as 400 kilotonnes of coal?

Several people, including Fusion for Energy have posted this infographic: To meet the energy needs of a city of 1 million people one would need: Either 250,000 tonnes of oil Or 400,000 ...
4k views

### Gravitational force when standing on an infinite disc

If a person were to stand on a flat disc of thickness 1 meter but infinite diameter, would they experience finite or infinite downward force? There is an infinite amount of mass, all of which ...
3k views

### Problem understanding the symmetry factor in a feynman diagram

I am trying to understand a $1/2$ in the symmetry factor of the "cactus" diagram that appears in the bottom of page 92 In Peskin's book. This is the diagram in question (notice that we are in $\phi^4$ ...
2k views

### Mechanics + Thermodynamics: Bouncing Ball

In preparation for an exam, I'm revisiting old exam questions. This one seems neat, but also quite complicated: A soccer ball with Radius $R=11cm$ is inflated at a pressure of $P =9 \times 10^4 Pa$,...
883 views

### Applying energy and momentum conservation to the problem of pulling a bent carpet at a constant speed

Consider this system. A long, thin, pliable carpet is laid on a floor. One end of the carpet is bent back and then pulled backwards with constant speed $v$, just above the part of the carpet ...
6k views

### How to calculate how many photons are in the universe?

The "universe" is a sphere with a radius of $10^{25}$ m the medium temperature is 3K, how many photons there are in the universe? n_\gamma = \int_{0}^{\infty} \frac{8h\pi\nu^3} {{c^3}{}} \...
8k views

### Why is the period of rotation the same for two stars orbiting the same centre?

In a binary star system, two stars $A$ and $B$ follow circular orbits, of radius $R$ and $r$ respectively, centred on their common centre of mass $O$. The mass of star $A$ is $M$, and that of star $B$ ...