52 votes
Accepted

Why does work depend on distance?

You have to put in the distance on which the force acts. If you release the force, there will be no work done since there is no force acting on the body.
EuklidAlexandria's user avatar
52 votes
Accepted

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

Work is the dot product of a vector force and a vector displacement, hence a scalar. Knowing just the scalar distance isn’t enough to calculate work. That distance might be in the same direction as ...
Bob Jacobsen's user avatar
  • 14.4k
50 votes

Why does work depend on distance?

Often it is important to know if a given formula is a simplification of a more general equation and, when you encounter a conceptual problem, check the general formula. In this case it is a ...
Dale's user avatar
  • 94.6k
48 votes
Accepted

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

The general-relativistic corrections are too small to matter. The Schwarzchild metric has dimensionless corrections of order $GM/rc^2$. Here $G$ is the Newton's gravitational constant, $M$ the mass ...
G. Smith's user avatar
  • 51.3k
47 votes
Accepted

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

The key point of this question is that it intuitively seems like conservation of energy is not working right. A rocket is powered by a chemical reaction that releases chemical energy at a constant ...
Dale's user avatar
  • 94.6k
43 votes

Why do objects appear smaller when viewed from a distance?

It's all about the angles made by the object when light from it enters the eye. Consider this crude doodle of an eye looking at two identically sized trees. The light entering the eye from the ...
cobaltduck's user avatar
40 votes
Accepted

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

The distance light travels in a given period is the same for every observer. That's the whole point of relativity. You can figure out for yourself almost all the effects predicted by relativity if ...
Marco Ocram's user avatar
  • 25.4k
30 votes

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

The general definition of work is $$W=\int\mathbf F\cdot\text d\mathbf x$$ Which essentially says, "Add up all of the dot products between the vector force $\mathbf F$ and the vector displacement $\...
BioPhysicist's user avatar
  • 55.8k
30 votes

When we say 'Andromeda galaxy is 2 500 000 light years away from us' do we mean 'now' or in a far past?

The light that we see from the Andromeda galaxy was emitted 2.5 million years ago. During those 2.5 million years the Andromeda galaxy may have moved one or two thousand light years closer to us. ...
gandalf61's user avatar
  • 47.6k
28 votes

Why do objects appear smaller when viewed from a distance?

It is because light travels in more-or-less straight rays. Let's assume for simplicity that your eye is like a pinhole camera; it has a pinhole in front and a screen at the back. Then an image forms ...
user21820's user avatar
  • 2,863
28 votes

Inverse square rule for strong forces

Most of the forces induced by a point particle follows the 1/r^2 rule No, it's the forces mediated by point particles with no mass and charge that follow the the 1/r^2 rule. then why does strong ...
Maury Markowitz's user avatar
28 votes
Accepted

The difference between comoving and proper distances in defining the observable universe

Let's start with some general notions. The Cosmological Principle postulates that at each location in the universe one can define a hypothetical observer to whom the universe appears isotropic and ...
Pulsar's user avatar
  • 14.5k
24 votes
Accepted

Does the mass of a bicycle directly affect stopping distance?

The answer is a little more nuanced than a simple yes or no, but for most cyclists stopping distance will increase with mass. Allow me to explain how: We can use the work-energy theorem to write down ...
cms's user avatar
  • 3,820
24 votes
Accepted

How far can a shout travel?

Gabriel Golfetti's answer assumes no dissipation. In reality, atmospheric attenuation is quite important for this calculation. According to Engineering Acoustics/Outdoor Sound Propagation: Attenuation ...
probably_someone's user avatar
18 votes

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

No. There is no proof of this. What we do know is that the models that result from assuming it allow us to correctly predict the outcome of all experiments to date. Therefore, it is accepted for the ...
Dale's user avatar
  • 94.6k
17 votes

When was today's radar measurement of the Earth-Sun distance made and by who?

There never has been a direct measurement of the distance between the Earth and the Sun. The best we can do is measure the distance between the Earth and the other planets, and from that infer the ...
David Hammen's user avatar
  • 41.1k
17 votes

When we say 'Andromeda galaxy is 2 500 000 light years away from us' do we mean 'now' or in a far past?

This is a more complicated question than you might think because in relativity there is no unique definition of time and therefore no unique definition of now. You have probably heard of time dilation,...
John Rennie's user avatar
13 votes

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

Your question seems to be: the reals as defined by mathematicians are characterized by a highly asbtract algebraic structure, so why should it have anything to do with distances? Well the point of ...
Gold's user avatar
  • 35.1k
13 votes
Accepted

If two reference frames are not moving with respect to each other, do we take into account their distance apart to determine simultaneity of events?

The lighting strikes are simultaneous in your scenario. The observer may not observe the flash hitting their eyeballs/detectors at the same time, but when they work out conceptually when the ...
Cort Ammon's user avatar
  • 45.6k
13 votes

What is the "true" distance an object travels based on relative speeds?

To specify the distance an object has travelled, you need to also specify its position relative to some initial reference point. In the context of your question, there is no "true distance" ...
joseph h's user avatar
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12 votes
Accepted

Regarding distance laws of gravity from “A Brief History of Time” and why the Earth doesn't fall into the Sun

As you say in your question the gravitational force is proportional to $1/r^2$ so we can write it as: $$ F \propto \frac{1}{r^n} \tag{1} $$ where $n = 2$. When Hawking talks about gravity decreasing ...
John Rennie's user avatar
12 votes

What is the "true" distance an object travels based on relative speeds?

There is a "true" distance in relativity, but it involves both space and time. The true distance an object travels in spacetime between two points is called the "proper time", and ...
Eric Smith's user avatar
  • 7,760
11 votes

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

The Pythagorean distance formula doesn't hold for arbitrary shapes, thanks to the negative sign in the metric. It's also pretty easy to say that boosts obey hyperbolic angle addition rules rather ...
Zo the Relativist's user avatar
10 votes

How far can a shout travel?

To answer this, we need to estimate the level of sound that a shout creates near its source. Since I have no idea what that value is, I googled it: around 88dB at 0.3m away (https://www....
Gabriel Golfetti's user avatar
10 votes

Why does work depend on distance?

If I'm in a vacuum, and I push a block with a force of 1N, it will move forwards infinitely and accelerate the block ie change the block's velocity and hence change the kinetic energy of the block. ...
Farcher's user avatar
  • 93.8k
9 votes
Accepted

What is "velocity distance" in astrophysics?

It is used because of uncertainty in the Hubble constant. The relationship between recession velocity and distance is given by $v=H_{0}d$ Where $H_{0}$ is the Hubble constant. Since that isn't ...
PhillS's user avatar
  • 2,394
9 votes

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

A light-year is exactly 9,460,730,472,580,800 meters, the distance light travels in one Julian Earth year. Time dilation is irrelevant to its definition.
G. Smith's user avatar
  • 51.3k
9 votes

Difference between distance and norm

First, it's important to note that "displacement vectors" - which one might interpret as beginning at one spacetime point and ending at another - are a generally untenable concept if the ...
J. Murray's user avatar
  • 67.6k
9 votes

Does work done by a non-conservative force involve distance rather than displacement?

Both conservative and nonconservative forces do work as the path integral $\int _L \vec F \cdot d\vec s$. If force and path are antiparallel (as for friction*) and force is constant in magnitude along ...
g s's user avatar
  • 12.7k
9 votes

Why decreasing the distance between a parallel plate capacitor increases the electric field? Wouldn't it remain the same? $\sigma/\epsilon_0 $?

Two possibilities. 1 Charged capacitor not connected to anything else. Charge,$q$, and hence charge density, $\sigma = q/A$, cannot change. Electric field $E = \sigma/\epsilon_0 = V/d$ does not change....
Farcher's user avatar
  • 93.8k

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