Question

When we move we have a certain velocity. Newton had said that mass remains constant but if one derivates the equation dp/dt u get $m\frac{dv}{dt}+v\frac{dm}{dt}$ people say mass is constant but by Special relativity M=m/sq.rt $(1-\frac{v^2}{c^2})$ could you please explain this and also please explain if our mass changes and when we come back to rest what is that extra mass converted into?

Answer 1

# Classical physics (physics of cycle objects)
$\Rightarrow$ When the object is moving at a speed much much lesser than the speed of light, then the mass of the body remains constant and all of Newton's law will be followed by that object.

# Quantum physics (physics of small particles photons, electrons)
$\Rightarrow$ When the particles are moving at the speed of light, laws of classical physics fails. We cannot use simple equations of motion to define the motion of the small particles.
$\Rightarrow$ Theory of relativity states that mass is also a form of energy. We can transform mass into every, $E=m{c}^2$ speed of light change in mass of the object
When particles are moving close to speed of light, their mass is given by :
$M=\frac{M}{1-\frac{v^2}{C^2}}$ Speed which is close to speed of light
$\Rightarrow$ You can see mass of the particle becomes infinite if they move with speed of light
$M=\frac{M}{\sqrt{1-\frac{\text{/}{c}^2}{\text{/}{c}^2}}}=\frac{M}{\sqrt{1-1}}=\infty$
$\Rightarrow$ Change is the mass of the object can be found by conservation of energy.
The difference is mass gives the amount of energy produced when mass is converted into energy.
$E=\Delta m{c}^2$
change is mass