# Questions tagged [distance]

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### 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 (...
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### 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 ...
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### 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 $T_2$ ...
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### 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 $S'$ ...
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 ...
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### 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 ...
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 ...
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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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|$ ...
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### 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 ...
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### 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 ...
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### 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....
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### 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:...
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### 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 ...
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### 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 ...
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 ...
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### 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 ...