Question

does mass increase in falling bodies with increase in kinetic energy.

Answer 1

I think mass does not increase is the Energy

Answer 2

well. if you need an accurate answer.. according to the theory of relativity, the mass DOES increase... but that increase is so small and minute.. ll give you the expression.. if a body is going with a velocity v then the mass of that body during that velocity is
\[{m = \frac{m(rest)}{\sqrt{1- \frac{v^2}{c^2}}}}\]

Answer 3

mass does not increase in general situations which we observe in daily lives but as @Mashy says if we are talking relativistic stuff i.e v nearly equal to c then yes it will change.

Answer 4

when there is an increase in kinetic energy in falling objects, the KE does nit effect the mass. it stays the same

Answer 5

@vjha is correct

Answer 6

Rane that appears to be good answer can you get me refrences

Answer 7

reference for wht ?

Answer 8

I coulds not find answer to my question in any book. Normally when we accelerate a mass its relativistic energy/mass increases as KE and we can use relativistic equation. . However if an object is falling at very high velocity i.e like near neutron star or black hole and acquires a high velocity: does its mass Kinetic energy increase (1/2 mv^2) or as per relativistic equation.

Answer 9

the old KE equation invalid for high speed. if you confuse what equation must be chosen you can use the relativities one. actually we can say that the KE's old equation is wrong but for low velocity case its almost same with relativities calculation.

Answer 10

as an FYI, it is no longer standard practice to say that the mass of an object increases at high velocity. Nowadays, when we say mass, we mean rest mass, which is a constant. The only reason "relativistic mass" was defined as above was to preserve the equation
p = mv

But this somewhat obscures the real physics and so "relativistic mass" has gone by the wayside.

The (relativistic) fact is that the relationship between momentum and velocity becomes nonlinear near the speed of light, so p=mv breaks down.

If you HAD to preserve that relationship, it would be much better to redefine velocity

u = v/sqrt(1-v^2/c^2)

and write

p = mu

So after all that, using standard terminology today, the answer to your question is unequivocally no.

Answer 11

And to touch on your second post, relativistically
\[E = \sqrt{ m^2 c^4 + p^2c^2} = mc^2 \sqrt{1+\frac{p^2}{m^2c^2}} \]

So since we know how the momentum changes with velocity
\[ p = \frac{mv}{\sqrt{1-v^2/c^2}} \]
We could put all that together and find
\[ E = mc^2 \sqrt{1 + \frac{v^2}{c^2-v^2} } \]

which tells you directly the relationship between velocity and energy.

If we assume that velocity is much smaller than the speed of light, then we can approximate that fraction by
\[ E = mc^2 \sqrt{1+v^2/c^2} \]
Which can be further approximated by
\[ E = mc^2 ( 1 + \frac{v^2}{2c^2}+...)\approx mc^2 + \frac{1}{2}mv^2 + ... \]

So disregarding the constant term for the rest energy, it increases as in the classical case. For high velocities, the approximations are no longer valid, so we must obviously either keep more terms in the expansion or keep the full expression.

Answer 12

I think is a constant in universe it does not change....

Answer 13

Thanks. Let me put that question in a different way. We all know that relativistic KE increases with increase in velocity when object is accelerated by a force say a rocket ship. . The question is does the exact same thing happens if object is in free fall and approaches high velocity. Remember now no force is acting on the object. The question is about an object in free fall.

Answer 14

mass does not changes

Answer 15

@Rane was correct

Answer 16

An object in free fall DOES have a force acting on it -- gravity.

Answer 17

Exactly,free fall is due to gravitational force.and KE increases if velocity is increased but i think you were earlier concerned whether mass remains constant..is that correct @whizmd?