Is there a physics argument, based on scaling, that leads to the conclusion that an elephant and a human could jump about same height?  Could this be extended to any two creatures with different masses?
122034
The following question was put on hold:   It reminded me of an exercise (24a) on that exact topic in Arnold's "Mathematical Methods of Classical Mechanics". The solution he gives goes like that:     For a jump of height h one needs energy proportional to $L^3h$, and the work accomplished by muscular strength $F$ is proportional to $FL$. The force $F$ is proportional to $L^2$ (since the strength of the bones is proportional to their section). Therefore, $L^3h$~$L^2L$, i.e. the height of a jump does not depend on the size of the animal. In fact, a jerboa and a kangaroo can jump to approximately the same height.   The comments of the above question tended to dismiss that argument. What's wrong with it?  Addendum: It seems obvious that not all animals jump exactly to the same height, given their different physiologies/shapes. Some of them can't jump at all.  The question is to be understood in the following spirit: if we plotted jumping height vs animal size for a lot of different species, would there be a correlation? I don't mean there is no spread; I totally expect a big spread due to the other factors involved.  Second addendum: Some interesting points have been raised in comments and answers. I will accept an answer that incorporates: the domain of validity of Arnold's argument (or explain why it is never valid), the effect of air drag on very small jumpers and the impossibility of very large animals.   Bonus points for documenting the yet elusive jumping elephant and plotting jumping height vs size for different species ;)
781
It has been a while since I've thought about physics, however, I remember something about how if you are on a train with no windows that is going perfectly straight and is perfectly smooth, there is no experiment that you could perform to prove that you are in motion or at rest. So I have a couple of questions related to this.   Is this still held to be true? I was just wondering if anything in physics has come to light since I learned about this (about 10 years ago) that would allow an observer on the train to tell if they are moving. If this is true, why couldn't you accelerate a particle in different directions to a certain mass and measure how much energy it took to get it up to that mass. If you were moving in any direction, wouldn't you measure less energy in your direction of travel? Would having an outside observer affect the aforementioned experiment in any way?
28410
Why is force = mass $\times$ acceleration? I have searched in many sites but didn't actually get at it. Simply I want to know that if a mass in space moves (gains velocity thus further accelerates), how can I think, postulate and further believe that force = multiplication  of mass and its acceleration ?
66450
Imagine there are two observers $A$ and $B$ and a particle $P$.  $A$ and $B$ are at about the same point, $P$ is some distance away.  From $A$'s point of view, $P$ has velocity $V$ and $B$ has velocity $-V$.            P----&gt;            A      &lt;----B   Suppose $A$ and $B$ have the same rest mass $m$ and $P$ has rest mass $m_P$.  It seems to me that $A$ will observe a gravitational force between $P$ and $A$ of $F_a$ and between $P$ and $B$ of $F_b$ with $F_a\neq F_b$ because the relativistic masses of $A$ and $B$ are different.  However, B will observe forces $F_a'$ and $F_b'$ and it seems to me that $F_a' \neq F_a$ and $F_b' \neq F_b$ because $A$ and $B$ observe different relativistic masses for everything involved.  I've tried demonstrating $F_a=F_a'$ on paper and gotten into a tangle. Intuitively, I think this equality is false and expect the difference to be resolved elsewhere.  I have a qualitative understanding of general relativity, but can't handle tensors etc. Can this be explained with high-school maths?
119117
And that even their physical appearances are exactly the same? This seems very counterintuitive and goes against many people's personal experiences and observations when they were kids. But i have comes across claims that prior to puberty, there are no differences in size, strength, speed or even physical appearance. How true is this?
9192
In Ant-Man, it's (briefly) explained that the Pym particle reduces the distance between molecules, allowing a person to shrink while retaining his mass and strength.  Much of the movie is consistent with this explanation. For example:   While ant-sized, Ant-Man falls from the edge of bathtub onto a tile floor, cracking the tile as though with the weight of a full sized human. He falls from a rooftop onto a car, denting the roof. He punches full sized humans, and they respond as though hit by a real punch. Another character, while tiny, is hit by a speeding toy train. The train is knocked aside as though it hit a full sized human.   But then there are things that appear totally inconsistent with "mass stays the same":   Ant-Man is constantly running and climbing around on surfaces (air vents, ant tunnels, etc.) that couldn't possibly support the weight of a 200 lb man on a footprint the size of an ant. The toy train, when expanded to the size of a real train, is heavy enough to rip through a wall and crush a police car.     Hank Pym carries a shrunken tank in his pocket on a keychain. It obviously doesn't weigh as much as a tank, but it does when expanded to full size.  Another character, while tiny, gets swatted with a (normal sized) table tennis paddle, and goes flying like an insect.   Obviously the out-of-universe explanation is that mass behaves in whatever way is most convenient at the moment because it's just for fun.  But I'm curious: is there any in-universe explanation, either hinted at in the film itself or in the comic books, as to why mass is conserved sometimes but not always?
89148
What is the distance a creature or player can travel if they have multiple types of movement?  For example, the  has a 40 ft walking speed, a 40 ft climbing speed, and an 80 ft flying speed. Can it move a total of 160 ft in a round using each of those fully, or is there another way this is calculated?
52222
I was thinking about Flash, the superhero, or the little boy in the Incredibles.   There is  that doesn't answer a lot. Especially, I don't think surface tension would help a lot for a human to run over water, I think one would have to build on the inertial effect of the water.  There is one empirical approach based on figuring out the speed at which bare-footed water skiing is done, but I wasn't able to find a decent number. Still the difference may be that a hypothetical runner would have to propulse herself over the water, which may or may not make the thing more difficult.  Hence, I raise the question here.
2611
We all know that in an idealised world all objects accelerate at the same rate when dropped regardless of their mass.  We also know that in reality (or more accurately, in air) a lead feather falls much faster than a duck's feather with exactly the same dimensions/structure etc.  A loose explanation is that the increased mass of the lead feather somehow defeats the air resistance more effectively than the duck's feather.  Is there a more formal mathematical explanation for why one falls faster than the other?
90598
Greetings StackExchange!  We were having a conversation with a peer about stupid ways of interpreting theories. We would go to and fro with an interpretations, but we would always find a way to disprove them. There was one, however, that we couldn't refute:  Gravity on a plane in a bidimensional space can be interpreted as the acceleration of spacetime towards an object.   We tried to invalidate in saying that the inertial mass and gravitational mass would be different, thus violating GR, but after some thought this couldn't be. The gravitational mass would accelerate spacetime towards it. If that object we were to be pushed, the pulling of spacetime would make it difficult for it to move.   We know for a fact this can't be true, and we would greatly appreciate any refutation of this thought. I can clarify if needed, or do a sketch. I apologise in advance as I'm not a native speaker.
66525
I did a weird activity and now I am trying to figure out the physics behind it:  While sitting on a chair I kept my feet above the ground and tried to move the chair forward. I was able to. Initially, I thought that perhaps the center of mass won't be changing as I was pushed backwards. But I moved the chair for a while and saw that it had moved a considerable distance and I was still sitting on the chair. Hence the center of mass did change for sure. According to Newton's second law, there must be an external force acting on the system(me and the chair). But I am not able to figure out what force is it. I have a feeling that it is somewhere related to the fact that the system is not completely isolated but I am not sure how.     Note: I am not in contact with the ground or any other object close to me. I have lifted my feet and have my hands on my lap.
86311
: Earth weighs about 13,170,000,000,000,000,000,000,000 pounds (or   5,974,000,000,000,000,000,000,000 kilograms). Since Earth is too big   to be placed on a scale, scientists use mathematics and the laws of   gravity to figure out Earth's weight.   So, this seems to be a constant. But I guess it doesn't consider the things that are on the earth, the trees, buildings, people, animals, water etc...  So, are all the above mentioned things' mass is too small or negligible to be left off?
7634
Similar to my old question about  are there any limits to the animal forms an Animagus can be?     We know that the animal form can be much smaller than human (cat, rat, beetle) so I don't think size is a factor.   I'm not aware of any Animagus who transforms into a magical creature (e.g. unicorn or phoenix) so maybe those aren't possible.   Ultimately, what I'd like to know is whether there could be a T-Rex Animagus... (prompted by )
51531
(This is not homework; a friend shared with me this puzzler and neither of us can figure it out.) Suppose you are in a plane traveling at velocity $v_1$ relative to the ground. The flight attendent pushes a cart of mass, say, $m$, accelerating it from rest to $v_2$, relative to the plane (so relative to the ground, its velocity goes from $v_1$ to $v_1+v_2$). From your perspective, the work done is then $$W = \Delta E = \dfrac{1}{2}mv_2^2$$ but from the perspective of the ground, the work done is $$W = \Delta E = \dfrac{1}{2}m(v_1+v_2)^2 - \dfrac{1}{2}mv_1^2 = \dfrac{1}{2}mv_2^2 + mv_1v_2.$$ Why are these quantities unequal?  I've seen some similar problems, like a body colliding with a wall in different reference frames, but I don't have the physics experience to tell if that question is analogous to this one. So, my apologies if this is a duplicate. :)
45215
Arthropods have 6 or more limbs and arthropods with 6 limbs appear to move faster than arthropods with 8 limbs so I wonder whether this might have something to do with fast and efficient locomotion. But, this is just a guess. I wonder what the official explanation is, if it exists.
104656
So, according to Einstein's theory of general relativity, gravity is not a force instead it is a consequence of objects with mass deforming spacetime, right? And so, according to him, there is no difference between standing on a platform accelerating upwards at 9.81 m/s^2 and standing on Earth, right? But, there is a difference. At least, I think it's a valid difference. If you drop two apples from a high altitude on Earth, not only will they accelerate downwards at 9.81m/s^2 but they will also slightly move towards each other because the Earth is a sphere and gravity acts radially inwards pulling the two apples closer to each other. But if you drop the apples from the same height above the accelerating platform, the apples will only appear to accelerate downwards at 9.81 m/s^2 but will not move towards each other like they would on Earth. Why is this true? Is this even a valid difference? If it isn't, why isn't it?
37385
In the comments to this , it was hinted that proving that the force acting on a charge at a vertical distance from a uniformly charged plane is independent of that distance can be done by recalling the scale invariance symmetry. Can someone explain that to me?