Questions tagged [distance]

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12
votes
4answers
3k views

If work is a scalar measurement, why do we sometimes represent it as the product of force (a vector) and distance (scalar)?

Consider an object being pushed 3/4 of the distance around a circular track. The work done on the object would be the distance of 3/4 the track’s circumference times the force applied to the object (...
-2
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2answers
50 views

Taking a frictionless object to a full stop given initial velocity and stopping distance [closed]

I am working on a simplistic simulation program where at some times I have to take an object to a full stop, while only knowing it's velocity and the distance in which it has to stop. Though, I want ...
1
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2answers
49 views

Why does calculating relative velocity with vectors yield diferrent results than with distances?

Suppose two points are situated at the origin of xy coordinate system. Two points start moving at the same time. Point $T_1$ starts moving towards north with velocity $v_1 = 2.7m/s$ while point $T_2$ ...
0
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1answer
19 views

About comparing distances between different frames of reference, and meter sticks

If a frame of reference $S'$ is moving with respect to a frame of reference $S$ with a velocity $v$ (along the $x$ axis of $S$), then an event $(x,t)$ in $S$ is viewed as an event $(x',t')$ in $S'$ ...
4
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0answers
71 views

Why is the metric used in physics a squared norm? [duplicate]

The length metrics used in physics are usually a squared norm, like the following: $$ds^2 = g_{\mu \nu} \, dx^{\mu} \, dx^{\nu}. \tag{1}$$ What other kinds of continuous metrics could we define? Why ...
0
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2answers
46 views

Finding the distance travelled by a fly in a room from one lower corner to the diagonally opposite one [closed]

A room has a length of 4 meters, width of 5 meters and height of 3 meters. A fly is on one of the corners and walks to the diagonally opposite one. What is the length of the shortest possible ...
0
votes
3answers
117 views

What is the distance from an object at which the gravitational force is exactly zero?

It is clear that the gravitational pull diminishes with increasing distance, but I can't find the answer to whether there is a point where it becomes "exactly zero". Is there such distance? Is it ...
3
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3answers
233 views

What's the proper distance from the event horizon to the singularity?

How far away is the event horizon of a (Schwarzschild) black hole away from the central singularity for a radially infalling observer starting with $v=0$ somewhere outside the black hole? After ...
2
votes
2answers
144 views

Distances in general relativity

Three dimensional distance doesn't exist in general relativity because the integration of $ d \vec l $ depends on the integration path. Well, maybe there is no mininum but it must be a maximum lower ...
0
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1answer
26 views

Graph of distance travelled in $n$th second with time

I was asked to graph the distance travelled in $n$th second by an object with time, taking the object to be at rest initially, and accelerating with a constant acceleration of $1 \, \text{m}/\text{s}^...
1
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2answers
49 views

Viewing LEDs at great distance

Say I put a satellite in orbit with several LEDs on the outside: red, yellow, blue, white and green. Could I see them from the ground with consumer-grade binoculars or telescopes? If I can see them, ...
-2
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2answers
96 views

Moon is receding from Earth approximately 4cm per year [closed]

According to the theory of relativity the universe is styled as a fabric which is depressed by a large mass and a moon, still following a straight path ever 'curves inward' toward the large mass. Now ...
0
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0answers
14 views

How do we determine the $H_0$ from standard rulers and standard candles

I am doing a research project about hubble tension. Even if I have some ideas about how we messure the $H_0$ by using the standard candles, i dont have much knowledge about it. I suppose we are ...
0
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1answer
44 views

How to find distance travelled when the change in the force of gravity is not negligible? [duplicate]

Usually when on Earth we can use as an approximation: g = a = 9.18 $\frac{m}{s^2}$ s = vi + 1/2 a$t^{2}$ However, how would I determine the distance traveled in situations where the the ...
0
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1answer
40 views

Distance in seconds between moving vehicles

If two cars are moving in the same direction. let’s say ego car is in the front and another follower car. the speed, location in x, y coordinates of both cars are given. How to calculates the ...
30
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6answers
6k views

Is a light year a different distance if measured from a moving object?

The speed of light is absolute, but time is relative. So would a light-year for us on earth be a different distance from a light-year on a different uniformly moving object? Why or why not?
2
votes
1answer
85 views

Horizon problem: Angular size of the causality patches on the CMB surface

I'm having difficulties in calculating the angular size of the causally connected regions on the cosmic microwave background (CMB), as seen from Earth today. I read in several documents that this ...
0
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1answer
46 views

Confusion on co-moving distance and the Big Bang

I'm at sea. From the wiki. entry https://en.wikipedia.org/wiki/Comoving_and_proper_distances : “..Most textbooks and research papers define the comoving distance between comoving observers to be a ...
0
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1answer
29 views

Formula for blurring out a grid of holes

Place a camera lens with focal length f_l mm and camera sensor size w mm and h mm behind an ...
7
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7answers
1k views

What is the difference between position, displacement, and distance traveled?

Suppose the question is somewhat like this: If $v=8-4t$ and the position at time $t= 0\ \rm s$ is $2\ \rm m$, find the distance traveled, displacement, and final position at $t=3\...
0
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0answers
37 views

Distance of two indistinguishable particles

Consider: The wavefunction of a two-particle system (both Fermions and Bosons possible): $$ \psi_\pm(x_1,x_2) = \sqrt{\frac{1}{2}}[\psi_n(x_1)\psi_m(x_2) \mp \psi_m(x_1)\psi_n(x_2)] $$ And a ...
0
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1answer
22 views

Voltage calculation at any point between two plates at different voltage

I have two plates (actually they are electrical connectors on a board) and I try to find the way of getting the $V$ value at any point between two plates, $A$ and $B$. A is at $V_o$ (in my case it is ...
0
votes
1answer
29 views

Doubt in this displacement-time graph

According to a book, this is a graph of "a ball resting on a smooth floor is kicked which rebounds from a wall with reduced speed. It then moves to the opposite wall, which stops it." My Question ...
15
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11answers
1k views

Is there a proof that the set of real numbers can exactly represent distances? [duplicate]

Mathematicians define real numbers in an abstract way - as an 'ordered field' with 'the least upper bound property'. In physics, we use real numbers to represent distances. For us to be able to do ...
4
votes
3answers
134 views

What is the best way to conceptualise a 'division' [closed]

This may seem like a strange question, but my question is more along the lines of trying to figure out how people were able to 'discover' the formulas which have shaped our understanding of the ...
1
vote
1answer
97 views

How can someone calculate distance between Earth and Moon using a laser?

I have a book stating: When astronauts of the Apollo missions visited the moon, they placed a mirror on its surface, facing the earth. Then scientists on the earth sent a strong laser beam, which ...
4
votes
0answers
127 views

Thought experiment - Universe that follows $f \propto \frac{1}{r}$ law [closed]

In our universe, due to reasons usually attributed to the 3D geometry of it, the forces of nature seem to mostly be $\propto \frac{1}{r^2}$, inversely proportional to the distance of the source of the ...
2
votes
4answers
218 views

Different expressions for distance & displacement : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r|$

I came across these expressions in my book. And the book says that all these are different from each other. The expressions are : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r|$ ...
2
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0answers
58 views

How did Henry Kater measure distances down one part in $10^5$?

Wikipedia says that in 1817, Henry Kater was able to measure distances accurately enough to get at least five significant figures in a measurement of $g,$ suggesting that he could measure a distances ...
1
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1answer
227 views

Apparent frequency as function of distance

So the Doppler effect says that the frequency of sound changes due to relative motion of source and observer. My question is if there any expression that tells how the apparent frequency changes in ...
1
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1answer
107 views

How far away are distant objects really?

I've done some research on this site and others and I'm having a bit of trouble. References: Why is the observable universe so big? Does the speed of light change? https://www.skyandtelescope....
1
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3answers
1k views

How exactly is conformal time, $\eta$, calculated?

As I understand it, Conformal Time is basically the comoving distance divided by the speed of light. $$\eta=\int_0^t\frac {dt'}{a(t')}$$ I can make the connection between the scale factor and redshift:...
1
vote
1answer
55 views

How large would the Moon have to be such that I could not see it in its entirety from earth? [closed]

The [^circumference of the] moon can be seen in its entirety from Earth [^during a full moon] taking up a very small portion of the visible sky. The Moon is ~1/4 the diameter of the Earth. If for the ...
1
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2answers
110 views

Paradox are all 4D distances zero?

The 4 dimension distance from the origin of a point is $\sqrt{x^2+y^2+z^2-t^2}$. Which means the 4 dimensional distance on the light-cone is zero. Take a point A and a point B in the future at ...
1
vote
2answers
133 views

Proper distance in cosmology

If considering two galaxies $\mathcal{A}$ and $\mathcal{B}$ being separated by $d$ ($d$ being the comoving distance) and light is emmited from $\mathcal{A}$ at time $t_1$ and that light is received to ...
2
votes
4answers
531 views

Understanding the difference between timelike and spacelike separations

From Woodhouse's General Relativity: If $A$ is the origin and $B$ is a nearby event with coordinates $dt, dx, dy, dz$, then, $$ds^2 = dt^2 - dx^2 - dy^2 - dz^2$$ is the same in all local inertial ...
3
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2answers
95 views

Why work definition involves displacement?

$$W=\left\Vert\vec{F}\right\Vert \left\Vert\Delta\vec{r}\right\Vert \cos{\theta}$$ A greater magnitude force will have a greater influence than a smaller magnitude one when they have the same $\theta \...
35
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2answers
4k views

Why isn't the GPS location calculated from the Schwarzschild metric?

The GPS uses the flat space light propagation formula to calculate the distance from the source (the satellite) to the receiver (observer on Earth): $$ d=c \cdot \Delta t$$ where $c$ is the speed of ...
2
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3answers
78 views

Can length contraction help the moving observer reach a star system 'faster'? [duplicate]

Would an observer moving with close to the speed of light ($\sim 99\%$) towards a star system that's $20$ light years away perceive the distance as being less than $20$ light-years? If yes, how much ...
0
votes
1answer
77 views

Calculating the distance between two masses with respect to gravitational force [duplicate]

Call them $m_1,m_2$. They are compressed to their center of masses, if you wish. If the initial distance at $t=0$ is $d$, is there a formula or an efficient way to calculate the distance between them ...
9
votes
4answers
2k views

Are any of Euclid's 5 postulates false in Minkowski spacetime?

I often hear that Minkowski spacetime is non-euclidean. Euclidean geometry is characterized by Euclid's five postulates being true. Which of those postulates are untrue in Minkowski spacetime (if any),...
0
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4answers
239 views

Why is Work equal to Force * distance? [duplicate]

I totally get the mathematical part, but I cannot imagine how this works. I apply a force to a ball. Why does the distance over which it moves matter to me? Sure, if I calculate the kinetic Energy of ...
0
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1answer
92 views

Shortening of distances in Relativity Theory

I am studying relativity theory and I have understood why distances become shorter from the perspective of someone who is travelling close to the speed of light. However, later on I read that the ...
0
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1answer
122 views

Compare 2d metric to metric on sphere-puzzling result

I calculated the infinitisimal distance squared $(\mathrm{d}s)^2$ in 3d polar coordinates and 3d cartesian coordinates in an example to show that they were identical. I chose $P(r,\theta,\phi)$ as ...
1
vote
2answers
205 views

Are distance and displacement always frame independent?

I'm aware that distance and displacement, both are independent of reference frames, when the two frames are stationary wrt each other. Because the actual distance (or the shortest distance) between ...
5
votes
2answers
196 views

'Ambiguity' of dual vectors $\{dx^i\}$ in cotangent space in general relativity

The metric tensor is defined as: $$g = g_{ij}dx^i \otimes dx^j,$$ where I used the summation convention. We often omit the tensor product sign $\otimes$ and just write this as: $$g = g_{ij}dx^idx^...
28
votes
3answers
3k views

Why is the work done by a rocket engine greater at higher speeds? [duplicate]

From this comment by orlp: If I strap a rocket booster to a rocket in space and fire it for one second, then the work provided is much higher when the rocket is flying fast compared to when the ...
-1
votes
2answers
118 views

Is the astronomical magnitude identical to the distance? [closed]

Why do astrophysicists use Magnitude rather than the actual distance to calculate intergalactic parameters? The magnitude is the relative brightness and has no units, the typical distance requires the ...
24
votes
9answers
6k views

Why does work depend on distance?

So the formula for work is$$ \left[\text{work}\right] ~=~ \left[\text{force}\right] \, \times \, \left[\text{distance}\right] \,. $$ I'm trying to get an understanding of how this represents energy. ...
0
votes
2answers
856 views

Given Max Speed, Max Acceleration and Jerk - How do I calculate time?

I'm developing some python code that controls an end effector moving in a two-dimensional plane (XY). It moves through a list of points sequentially and I'd like to estimate the time it will take as ...

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