# Since force is related to a change in momentum and not necessarily just to a change in velocity, what would be an example where only the mass of a body changes but not its velocity when subjected to a force?

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Since force is related to a change in momentum and not necessarily just to a change in velocity, what would be an example where only the mass of a body changes but not its velocity when subjected to a force?

In: Physics

Totally prepared to get this wrong but would this be like a rocket or helicopter hovering? Using fuel to stay in the same place?

My first thought was particle accelerators where the particles are close to the universal speed limit and will therefore not go any faster no matter how much acceleration you give them but will instead increase in mass. However /u/LordSpazpatty is completely right with the hovering rocket example as well as the mass is reduced due to fuel being burned by the engines requiring less force to keep the same acceleration.

Chip a piece off a stationary rock. The force of the chisel does not put the rock into motion. It fractures the mass instead.

You don’t have the extremes in the real world.

At newtonian speeds, the change in mass will be negligible. As you approach C, the increase of speed will be negligible.

A spherically symmetric explosion where the outer layer of the body is ejected?

Momentum is something that exists in mass. If you apply a force, it inherently *must* change an object’s velocity (however slightly) and does not change its mass.

To increase the momentum of an object, you must decrease the momentum of another object, as momentum is a conserved quantity. Note that momentum is a vector, and so a “decrease” could just as well mean an increase in the opposite direction. The force ‘moves’ momentum between the two objects.

The force could, instead, move mass between the two objects, but the scenario is a bit odd, since the new mass isn’t necessarily the same object but simply travels alongside the object.

For example, imagine a very fast aircraft flying over enemy territory. So fast that it keeps pace with bullets. The enemy fires upon the aircraft, but the bullets can only match speeds with it and will not damage it. The bullets are now traveling with the aircraft, and with some mid-flight gluing they could become a part of it. In this case, the force of firing the bullet is pumping mass to the object without changing its velocity.

Rockets. Or anything that burns fuel to stay at a constant speed.

Rockets need to fight the force of gravity so they burn fuel for force.
Obviously it doesn’t always happen like that but I’ve seen textbooks that give this example. .

If we use a rocket as an example, this situation would mean the thrust of the rocket (which is achieved by ejecting mass) equals its weight (the external force acting on the rocket), therefore there’s no acceleration (the rocket may be hovering or moving at a constant velocity). It just describes how the forces are balanced, it doesn’t mean the external force is causing the mass to change. In the absence of the external force (no gravity) the rocket can still eject mass and accelerate.