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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.

141
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10answers
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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 ...
88
votes
5answers
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 ...
74
votes
8answers
14k 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 ...
73
votes
3answers
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 ...
67
votes
2answers
16k 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?
55
votes
15answers
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 ...
51
votes
1answer
21k 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 ...
49
votes
9answers
14k 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 ...
48
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5answers
15k 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 ...
47
votes
2answers
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 ...
40
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4answers
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 ...
40
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10answers
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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 ...
40
votes
8answers
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 ...
39
votes
7answers
8k 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 ...
37
votes
6answers
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 ...
31
votes
4answers
5k 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 °...
30
votes
2answers
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?
28
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6answers
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 ...
28
votes
3answers
5k 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 ...
27
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4answers
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 ...
27
votes
3answers
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 ...
26
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5answers
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 ...
25
votes
4answers
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 ...
25
votes
0answers
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 ...
24
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6answers
34k 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, ...
24
votes
3answers
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 ...
23
votes
18answers
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...
22
votes
5answers
10k 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 ...
22
votes
6answers
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 ...
22
votes
3answers
7k 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 ...
21
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8answers
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 ...
21
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3answers
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....
21
votes
1answer
527 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 ...
20
votes
3answers
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 ...
20
votes
3answers
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 ...
19
votes
7answers
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 ...
19
votes
5answers
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 $23$ ...
19
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3answers
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?
18
votes
7answers
18k 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 ...
18
votes
4answers
1k 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 ...
18
votes
3answers
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 ...
18
votes
3answers
2k 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 $\phi^4$ ...
18
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1answer
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 $P =9 \times 10^4 Pa$,...
17
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2answers
5k 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}{}} \...
17
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3answers
6k 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 $B$ ...
17
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4answers
3k views

Why don't humans burn up while parachuting, whereas rockets do on reentry?

I guess it has something to do with their being both a high horizontal and a vertical velocity components during re-entry. But again, wouldn that mean there is a better reentry maneuver that the one ...
17
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2answers
3k views

Increase in mass of battery of my smartphone [closed]

The charge on my smartphone was zero. I charged my phone to its maximum capacity. How much mass $\Delta m$ did my mobile gained after charging the battery? Maximum capacity of the smartphone's ...
17
votes
3answers
31k views

How do you find the uncertainty of a weighted average?

The following is taken from a practice GRE question: Two experimental techniques determine the mass of an object to be $11\pm 1\, \mathrm{kg}$ and $10\pm 2\, \mathrm{kg}$. These two ...
17
votes
1answer
864 views

How hot would tritium water be?

I realize this is kind of a silly question, but if you have tritium water, with the tritium half life of 12.5 years, I expect it would be quite hot. (note, this is not a homework question, I'm just ...
17
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3answers
15k views

“Find the net force the southern hemisphere of a uniformly charged sphere exerts on the northern hemisphere”

This is Griffiths, Introduction to Electrodynamics, 2.43, if you have the book. The problem states Find the net force that the southern hemisphere of a uniformly charged sphere exerts on the ...