# What is Mass: Definition and 1000 Discussions

Mass is both a property of a physical body and a measure of its resistance to acceleration (rate of change of velocity with respect to time) when a net force is applied. An object's mass also determines the strength of its gravitational attraction to other bodies.
The SI base unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that (along with gravity) determines the strength of this force.

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1. ### I What would a calculus author have to say on ##\int r^2dm##?

So I've been searching around for rigorous explanations for things like ##dx## in physics, I'm not looking to fully commit myself to reading the relevant literature at the moment but just want to know what I'll have to do in order to understand. Perhaps I'll make a separate thread about that...
2. ### Potential Energy Problem: Pulling a Chain up onto a Table

So, the first thing that came to mind when I was trying to figure out how to set this up is that it will be a dU problem. After trying to figure out how to set it up to no avail, I took a look at how they solved it in the solutions manual. It's making absolutely no sense to me... They state...
3. ### How can I identify the molecular fomula, based on an m/z of 350.7897?

TL;DR Summary: I have the aforementioned m/z and a mass spec graph, my lecturer completely glossed over how to find the molecular formula so I'm stumped. I have a mass spec with 4 peaks and the m/z value, how can I find the molecular formula.
4. ### I What temperature would 1 keV neutrinos have today?

Suppose there was a 4th generation of neutrino (X, say) with mass m ~ 1 keV. The other three neutrino generations decouple at T ~ 1 MeV and are not heated during ##e^{\pm}## annihilation (whereas the plasma is heated, leading to a bookwork ##T_{\nu}/T_{\gamma}## factor due to conservation of...
5. ### Finding a formula for displacement of a mass on a spring using v.

I have tried to answer this using the relevant equations I am provided on my formula sheet, however I get stuck pretty close to the end. I start with 1/2mv^2=1/2kx^2 at the equilibrium position, and kx=mg, x=mg/k. This gets me to v^2=mg^2/k, but I don't know where to go from there. The potential...
6. ### B How Much Mass Required to Demonstrate Gravity?

If one were to demonstrate gravity independent of earth's constant gravity, how could it be done? Assuming this would need to be done in space, what minimum proportions of mass would be required to demonstrate gravitational pull to a human's naked eye?
7. ### what the relation between the amplitude magnitude and mass at resonance?

should I be expecting a higher amplitude at resonance for a mass that's heavier to an extent form another where each is attached to a spring vertically , I assumed that's true since the heavier mass will stretch the spring more meaning when moving like a sin or cos wave the amplitude...
8. ### I Determining stellar mass independent of its gravity

What are the independent and accurate ways of determining stellar mass apart from its gravitational effect?
9. ### B Mass defect and electron transition

According to STR: E=MC^2. When an electron and proton are independent( without influence of any kind of fields, especially electrostatic fields )their rest masses are Me and Mp. When they combine to form Hydrogen atoms they emit photons. So, some energy loss in the form of photons. So, now...

I can't possibly be the first to notice this numerical coincidence, but my search skills are inadequate to find information about it, and I was hoping others could point me toward papers on the subject. Neutron mass, mN: 939565420.52 (54) Proton mass, mP: 938272088.16 (29)...
11. ### B Energy required to bring 1 kg 1000 meter above the surface of the Earth

How can i calculate the Energy required to bring 1 kg 1000 meter above the surface of the earth ?
12. ### A Variation of CMFR mass density ##\rho## along a world line

Dirac ("GTR" p. 47) makes an interesting observation immediately after obtaining Einstein's field equations with the simple energy-momentum tensor ##T^{\mu\nu}=\rho v^\mu v^\nu##. (##v^\mu## is the four-velocity.) First, the conservation of matter ##\left( \rho v^\mu \sqrt{-g}...
13. ### Drag Forces and Terminal Velocity

Teacher says Im wrong on both these questions. I have consulted with other teachers and they say im correct. What do you guys think? 3. As mass increases, so does terminal velocity. 5. Fnet = FDrag - Fg ma = FDrag - mg FDrag = 79(8) + 79(10) FDrag = 632 + 790 = 1422 N Teacher Comments 5...
14. ### B I wonder about a particle's energy when mass is obtained or lost

According to Einstein's formula, energy is generated when mass is obtained or lost. What does losing or gaining mass mean for an atom or particle valence? It's simply because of the formula I don't want this kind of answer I want. What does it mean for an atom or particle to lose or gain mass...
15. ### B Percentage of known energy in the Universe

It is said that the universe is made up of approximately 4.9% ordinary matter, 26.8% dark matter and 69.3% dark energy. Why isn't ordinary energy included in this "pie"? I suppose it is included within ordinary matter, but could it be calculated what % are particles with mass and what % is pure...
16. ### I Can there be slowly-falling accretion disks in black holes?

Black holes accrete mass around them and it falls gradually up to the even horizon where mass is trapped by the black hole forever. However, the rate of mass falling from the accretion disk to the black hole ranges from being very fast to very long-lived, depending on various conditions...
17. ### Relativistic 2 -> 2 scattering with all equal masses

Stuck on (c), part (i). Any ideas about what is the most elegant way to prove it, maybe using Mandelstam variables since this exercise is supposed to be about them?
18. ### A How the mass term of the Hamiltonian for a scalar fields transform?

The Hamiltonian for a scalar field contains the term $$\int d^3x m^2 \phi(x) \phi(x)$$, does it changs to the following form? $$\int d^3x' {m'}^2 \phi'(x') \phi'(x')=\int d^3x' \gamma^2{m}^2 \phi(x) \phi(x)$$? As it is well known for a scalar field: $$\phi'(x')=\phi(x)$$ .
19. ### Vertical Mass Spring System | Analyzing work

Is there a typo in this question? Supposing there was no friction, the block would fall until the force of the spring was equal to ##mg = 2 * 9.8 = 19.6##, taking the upward y direction as positive. Since ##F_{spring} = -200y## and ##19.6 = -200(-0.098)##, the block would fall 9.8 cm. It's not...
20. ### Wave function of infinite potential well

Hi guys i have this exercise: A particle of mass m, confined in the segment -a/2 < x < a/2 by a one-dimensional infinite potential well, is in a state represented by the wave function: 1. Determine the constant N from the normalization condition. To do this, I have to integral the square...
21. ### Why does mass not affect sliding speed down an inclined plane?

I think that both kids experience the same acceleration (irrespective of mass) since the only force pushing them downwards is acceleration due to gravity, which is the same for both of them. Thus, since they start sliding down the hill at the same time (assumption), and are accelerating at the...
22. ### B Is the Higgs Boson the Only Source of Mass?

This is meant for our younger readers who have only seen popular accounts of where mass comes from. They often say it comes from the Higgs boson, which is sort of true. But it is deeper than that. Sabine has given a deeper popular account in the following video: As an aside, forget this...
23. ### I Mass in an expanding or static spherical distribution of matter

In a spherical distribution of matter - such as with clusters of galaxies - how to calculate how much mass there should be for it to not expand with the expanding universe - in other word, for it to be a bound, static system?
24. ### Problem Related to Photons with Mass

Before boost we have Then using the Lorentz boost: I want to calculate: I tried multiplying the matrices together but I never get the stated answer which should be:
25. ### B "If a black hole has more mass then the event horizon shrinks" ???

The title is a direct quote of this video by Dr. Becky Smethurst, an astrophysicist specializing in black hole research. This is a mistake, right? Supermassive black holes, for example, don't have tiny radii, compared to stellar mass BHs. Then there's the equation she presents seconds later...
26. ### I Do objects of different mass but same size/shape accelerate the same?

Hi. I remember having learnt in school that if you'd like to verify that bodies of different mass accelerate the same in free fall, but don't have a vacuum available, the bodies should be of same size and shape (e.g. spheres). This made sense to me back then because drag should be the same...
27. ### Is the Final Velocity of a Fly Impacted by an Elephant's Mass?

My solution was that the final velocity of the fly is equal to the mass of the elephant divided by the mass of the fly, and then multiplies by the delta in the elephant's velocity. My teacher said it was the wrong answer and that the calculations are presumably pretty long
28. ### Scarf modelled as a pulley system / F=ma exercise

My teacher gave the above answer as a solution. However, I am not convinced that the proportion is really $$\frac{m_1}{m_1+m2}$$. If m2 << m1the proportion would be really big, right? But intuition tells me that it should be the opposite. Furthermore, if m2 >> m1, then one would expect the...
29. ### I Explanation of parallel axis theorem

For a rotating system with mass m this theorem says that if it rotates about an axis distance x from but parallel to the axis through it's natural mass center (CM), then I moment of inertia is $$I=I_{CM}+mx^2$$ My thinking is if one move the axis x distance away from the axis through it's CM...
30. ### Speed of a mass falling into a star given the mass and radius of the star

I tried the square root of ((2)(6.67*10^-11)(3.90E+30))/(5.70E+7) I got 1.55*10^-5 and that is wrong. Maybe I am using the wrong equation but this is the one of professor gave me and I don't know what I am doing wrong :-(
31. ### B How quickly does the Earth feel the effects of a halved Sun's mass?

I have a doubt about gravitation. Suppose the mass of the Sun halves in an instant, after how long does the Earth ''notice'' it? That is, does the gravitational force also decrease instantaneously? Instinctively I would say yes, but I don't understand why it should be so. If, for example, we...
32. ### B Speed of separation of two masses

Hello. Let's say we have two masses, each moving in 90 percentage of light speed in opposite direction. Then what will be the speed of the one mass according to an observer in the other mass?
33. ### How much impact mass does a boxing strike need to compensate for slower speed?

I'm trying to wrap my head around the mass vs speed equation of mechanical power. If you double mass, you double power. If you double speed, you quadruple power... Fine, but what does that tell us about the relative importance when things aren't doubled? Let's say boxing Agent 1: has 3%...
34. ### I Can you increase the mass of a closed system with information?

Let's assume that there is a closed box, with mass M. There are some random quantum processes inside it, say radioactive decay. Let's assume that we can manipulate the decay from the outside somehow, thus 'putting information' into the box. Can that affect its mass?
35. ### A Higgs boson and its decay width

hi, I noticed that with higher mass decay width also go higher - but for higgs boson its mass is higher that W and Z boson but its decay width is lower , why?
36. ### B Would a solid neutron mass be stable?

not asking about neutron stars, where gravity holds neutrons together, rather would the strong force hold individual neutrons together in a solid mass, preventing their decay if one could somehow put them together in a lab?
37. ### I What was the four-momentum meant to include?

Hello, was the four-momentum of relativity, Pν, supposed to include all mass and energy contributions from every field i.e. electromagnetic, strong, gravitational... Or is it just the momentum of what was known in Einstein's time?
38. ### I Without degeneracy, when would Solar cores collapse?

I believe I know the answer to this question, but it is still very informative to ask: Would iron stellar cores still collapse when they reached some mass without degeneracy (by which I mean, if electrons were not indistinguishable, so did not obey the Pauli exclusion principle on such large...
39. ### Same Charge, Same Mass? | Subatomic Particles

I converted 3.1eV into J, substituted into E = mc^2. Since the energy is the same, I got the same answer for both: 5.52*10^-36 kg. This doesn't seem quite right- I doubt that a photon and an electron have the same mass. So, when two particles have the same charge, does that mean they have the...
40. ### I Mass measurement of galaxies with non-gravitational means

What are the non-gravitational ways of determining mass of galaxies, and how accurate are they?
41. ### B How will object's velocity change when a frictional force increases?

Let's say that the mass of the objest is suddenly bigger, so when I want to maintain the constant movement, my force must increase as well. But will the velocity have the same magnitude? I think that the velocity will be smaller, so if I want to have the same initial velocity, I must apply an...
42. ### B Force transition through spring

We put object on weight ang get a mass. What would that mass be if we put a spring between object and weigt, so that the spring woul shrink to half its original size?
43. ### I Higgs Field & GR: Are They Related or Not?

Since these two pillars of science have mass as a common core, are they related, essentially the same or not?
44. ### B Things giving rise to static and dynamic coefficients of friction?

Topography of both the object and the surface. Mass/inertia. Moisture, but that can probably fall under topography. I suppose atmospheric pressure, maybe. Or wind. Magnetism. Any others?
45. ### Finding acceleration of the pulley block system

What is the initial acceleration of mass 5M .The pulleys are ideal and the string inextensible. My attempt- 2Mg-T=2Ma (for 2M) T=Ma (for M) Solving we get T=2Mg/3 T-N=5MA (for 5M) N=2MA (for 2M) Solving we get A=2g/21 but the given ans. is 2g/23
46. ### I Belle II Measurement Makes World Average Tau Mass Match Koide's Rule

Belle II Collaboration, "Measurement of the τ-lepton mass with the Belle~II experiment" arXiv:2305.19116 (May 30, 2023). Combining the uncertainties in quadrature, the newly measured tau quark mass is 1777.09 ± 0.136 MeV/c^2. This is a big improvement over the previous Belle II tau lepton mass...
47. ### Explanation for Newton II giving negative mass in my Physics lab results please

I am trying to verify Newton II. The setup I am using is, Where ##m_1 = 0.887 kg## is a cart and ##m_2 = 0.02016 kg## is a small hanging mass. There is a force sensor on ##m_1## to measure the force acting on it from the string and the acceleration of the cart. To verify Newton's Second Law...
48. ### How can I calculate the cumulative mass of a disk using disk mass density?

I want to find the cumulative mass m(r) of a mass disk. I have the mass density in terms of r, it is an exponential function: ρ(r)=ρ0*e^(-r/h) A double integral in polar coordinates should do, but im not sure about the solution I get.
49. ### Heat added to system increases mass

According to this, The heat added to the system is proportional to the mass. Does someone please know how that highlighted statement is so? I think it is because the heat increases the internal energy of a system and internal energy is the sum of the translational, rotational, and vibrational...
50. ### A Is M_{Pl} the Planck mass or the reduced Planck mass?

What is the value of M_{Pl} used in the Planck (CMB) collaboration's observation papers, such as the one referenced in this link: https://arxiv.org/pdf/1807.06211.pdf. Specifically, I am wondering if it refers to the Planck mass or the reduced Planck mass?