Why not find mass increase in a simple way?

In summary: The relativistic momentum is not given by the same formula as the classical momentum - that is where the gamma factor and the increase in the radius comes from.
  • #36
alba said:
I make no bones of whatever you wish me to call it, since may be very soon it will change. Since your objection is only to words, any terms suits me fine.
Good, then I think the only substantive issue is that ##p\ne mv##, but it seems like you understand that now also.

alba said:
Now, after so many posts, can you please at last show me what is the 'correct' way in which you determine the radius , step by step, and show me why my way is not simpler and better than yours?
I don't know your formula so I can't comment on it, but whatever it is just replace any occurences of "relativistic mass" with "total energy" and make sure that you don't substitute mv for momentum. The complexity would be identical.

I believe that the correct formula is ##r=p/qB## where ##p## is the momentum (use the correct relativistic formula, not mv), ##q## is the charge, and ##B## is the magnetic field.
 
Last edited:
  • Like
Likes alba
Physics news on Phys.org
  • #37
alba said:
At LHC they run protons at 7TeV = 7000 GeV ( rest mass is .93827 GeV),so they are adding the equivalent of 7000/.938 = 7461 proton rest masses (= 1/cosθ (=0.000134)) both if you please to consider it mass or energy : it is not a name or a procedure that shapes or changes reality.

Its speed will be sinθ= sqrt(1-1/7461^2) * c : v = .99 99 99 99 101*2.99*10^10 , its momentum (tanθ) will increase by 7461 times and so will the radius of its circle: in a 5.5-T MF the orbiting radius will increase from 57 cm to r = 57*7461= 4.243 Km, the actual radius of LHC ring (26.6 km).
So you're calculating ##\gamma## and saying ##\gamma = 1/\cos\theta## for some parameter ##\theta##. This allows you to hide the square root in the trig functions to find the speed ##v= \sin\theta= \sqrt{1-1/\gamma^2}## and then the momentum is ##p = m\gamma v = m(\sin\theta/\cos\theta) = m\tan\theta##. That's fine, but I don't see the advantage here.

the simple and logic way of finding the radius of the particle is to multiply the regular radius of any proton (57) by 7 T eV / .938 GeV, that is 57*7461 cm.,you haven't yet shown how you figure that out.
The radius of curvature is given by (both relativistically and non-relativistically) ##r = \frac{p}{qB}## where ##p## is the momentum of the particle. The difference between the two momenta ##p_{rel} = m\gamma v## and ##p_{non} = mv## is just a factor of ##\gamma##, so as soon as you find ##\gamma = E/(mc^2)##, you know the factor by which ##r## increases between the relativistic and non-relativistic cases. There's no need for the stuff you did before.

Typically, the information you start with is the energy of the particle and its mass, and what you want is the momentum. Calculating ##p = \sqrt{(E/c)^2-(mc)^2}## and then plugging the result into ##r = \frac{p}{qB}## is pretty straightforward. There's no need to find the speed of the particle, the non-relativistic momentum, etc.
 
  • Like
Likes alba
  • #38
alba said:
All right, let's make something clear :
rest mass is equivalent to energy
toenergy of any kind bound to massive particles is equivalent to mass, it applies r thermal energy, KE, gluons etc...is that right?
Again the relationship (in natural units) is ##m^2=E^2-p^2##. So for a point particle you cannot increase E without increasing p. For multiple particle systems it is possible to increase E without increasing p using internal degrees of freedom, such as rotation.
 
  • Like
Likes alba
  • #39
Dale said:
I believe that the correct formula is ##r=p/qB## where ##p## is the momentum (use the correct relativistic formula, not mv), ##q## is the charge, and ##B## is the magnetic field.

Yes, but you have to be careful with the units when calculating. Taking my electron from post #13, its momentum in energy units is pc = 1422 keV = 2.275 x 10-13 J. Dividing by c gives p = 7.583 x 10-22 kg·m/s. Put it in a magnetic field of 1 mT = 0.001 T.

In SI units, $$r = \frac {p}{qB} = \frac {7.583 \times 10^{-22}~\rm{kg \cdot m/s}} {(1.60 \times 10^{-19}~\rm{C})(0.001~\rm{T})} = 4.74~\rm{m}.$$ In "eV units", the unit of q is the magnitude of the electron charge, e, so $$r = \frac {p}{qB} = \frac {pc}{qBc} = \frac {1422 \times 10^3~\rm{eV}} {(1~\rm{e})(0.001~\rm{T})(3.00 \times 10^8~\rm{m/s})} = 4.74~\rm{m}.$$ Or you can think of p as having units of keV/c, so $$p = \frac{1422 \times 10^3~\rm{eV}}{3.00 \times 10^8~\rm{m/s}}$$ and you can use the original form of the equation. $$r = \frac {p}{qB} = \frac {\left( \frac{1422 \times 10^3~\rm{eV}}{3.00 \times 10^8~\rm{m/s}} \right)} {(1~\rm{e})(0.001~\rm{T})} = 4.74~\rm{m}.$$ A factor of c has to come in somewhere, if you use "eV units" for momentum.
 
Last edited:
  • Like
Likes alba
  • #40
jtbell said:
Yes, but you have to be careful with the units when calculating. Taking my electron from post #13, its momentum in energy units is pc = 1422 keV = 2.275 x 10-13 J.
Doesn't the particle physics use "eV units" for everything? So B = 1 mT = 0.6925 eV^2 and r = 4.74 m = 2.402 10^7 1/eV. I must have something wrong because I get
$$r=\frac{p}{q \; B} = \frac{1422 \; keV}{1 \; 0.6925 \; eV^2} = 2.05 \; 10^6 \; 1/eV = 0.405 \; m$$
 
  • Like
Likes alba
  • #41
I don't remember anybody using eV2 for magnetic field strength, but that was 35-40 years ago. Maybe things are different now.
 
  • Like
Likes alba
<h2>1. Why is finding mass increase important in science?</h2><p>Finding mass increase is important in science because it allows us to understand the behavior and properties of matter. It is a fundamental concept in physics and chemistry and is essential for studying various phenomena such as chemical reactions, energy transfer, and gravitational interactions.</p><h2>2. What is the most common way to find mass increase?</h2><p>The most common way to find mass increase is by using a balance or scale. This involves comparing the weight of an object before and after a change, such as a chemical reaction or physical process, to determine the change in mass.</p><h2>3. Why is finding mass increase not always a simple process?</h2><p>Finding mass increase is not always a simple process because it depends on the accuracy and precision of the measuring instrument used. Additionally, some changes in mass may be too small to be detected by traditional methods, requiring more advanced techniques such as spectroscopy or nuclear reactions.</p><h2>4. Can mass increase be found in living organisms?</h2><p>Yes, mass increase can be found in living organisms through processes such as growth, metabolism, and reproduction. However, measuring the mass increase in living organisms can be more complex and may require specialized equipment and techniques.</p><h2>5. How does finding mass increase contribute to scientific advancements?</h2><p>Finding mass increase is crucial for making accurate predictions and calculations in various scientific fields. It allows us to understand and manipulate matter on a molecular level, leading to advancements in fields such as medicine, materials science, and environmental science.</p>

1. Why is finding mass increase important in science?

Finding mass increase is important in science because it allows us to understand the behavior and properties of matter. It is a fundamental concept in physics and chemistry and is essential for studying various phenomena such as chemical reactions, energy transfer, and gravitational interactions.

2. What is the most common way to find mass increase?

The most common way to find mass increase is by using a balance or scale. This involves comparing the weight of an object before and after a change, such as a chemical reaction or physical process, to determine the change in mass.

3. Why is finding mass increase not always a simple process?

Finding mass increase is not always a simple process because it depends on the accuracy and precision of the measuring instrument used. Additionally, some changes in mass may be too small to be detected by traditional methods, requiring more advanced techniques such as spectroscopy or nuclear reactions.

4. Can mass increase be found in living organisms?

Yes, mass increase can be found in living organisms through processes such as growth, metabolism, and reproduction. However, measuring the mass increase in living organisms can be more complex and may require specialized equipment and techniques.

5. How does finding mass increase contribute to scientific advancements?

Finding mass increase is crucial for making accurate predictions and calculations in various scientific fields. It allows us to understand and manipulate matter on a molecular level, leading to advancements in fields such as medicine, materials science, and environmental science.

Similar threads

  • Other Physics Topics
Replies
14
Views
2K
  • Special and General Relativity
2
Replies
55
Views
3K
  • Other Physics Topics
Replies
5
Views
726
  • Special and General Relativity
Replies
11
Views
1K
  • Other Physics Topics
Replies
3
Views
3K
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
159
Replies
15
Views
5K
  • Other Physics Topics
Replies
11
Views
3K
Replies
2
Views
2K
Back
Top