# B Can force change mass keeping velocity const

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1. Mar 14, 2016

### hackhard

can a resultant external force on a body change its mass but keep velocity of its centre of mass constant ? Is it practically possible -
$\vec{F}_{ext}=\vec{v}_{com}\frac{\mathrm{d} M}{\mathrm{d} t}$
where F is nonzero

Last edited: Mar 14, 2016
2. Mar 14, 2016

### A.T.

If the mass is increasing by picking up stuff of different velocity, a force is required to keep velocity constant.

3. Mar 14, 2016

### hackhard

no body isnt picking up things. mass increases due to relativistic speed

4. Mar 14, 2016

### jbriggs444

Then you would be wise to rewrite the equation since an object's [invariant] mass does not increase due to relativistic speed.

5. Mar 14, 2016

### A.T.

You said the velocity is constant.

6. Mar 14, 2016

### Staff: Mentor

7. Mar 14, 2016

### A.T.

Regardless of that, even "relativistic mass" doesn't increase when velocity is constant.

8. Mar 14, 2016

### DrStupid

A resultant external force and constant velocity of the center of mass without mass exchange? I'm afraid that's impossible.

9. Mar 14, 2016

### hackhard

i just needed to know that

10. Mar 20, 2016

### pervect

Staff Emeritus
If the net force on a body is nonzero, it must accelerate, therefore the velocity of its center of mass will not be constant if a net force is present.

It is possible to have a pair of opposing forces acting on different parts of a distributed body (which is not a single particle). If this pair of forces is doing net work on the body, the body will gain energy without gaining momentum, which implies that both its relativistic and invariant mass of the body will increase. Note that the energy needs to be stored somewhere, for instance by heating the body (which is due to internal vibrations of its molecules). Usually there is some limit on how much energy a realistic body can absorb in this manner - for instance, if you imagine that the pair of forces is turning a wheel agains some brake drums, the wheel and brakes will heat up, and eventually they'll fail.