Does extremely small mass accelerate faster under a given force?

[Sundown444]

I have a question about inertia (as in mass and Newton's first law) being extremely small. Now, say the inertia of an object is, say, 0.00000000000000000000005 kilograms, or something like that. Would a light, weak force exerted on the object accelerate the object to high speeds, or would it work any differently from that?

 

[Ibix]

I don't think this question is answerable as written. What do you mean by inertia in this context? And what units are you quoting your number in?

 

[Sundown444]

I don't think this question is answerable as written. What do you mean by inertia in this context? And what units are you quoting your number in?

For the number, it is kilograms. For inertia, it is the tendency to resist change in motion, whether speeding up, slowing down or changing direction. Newton's first law, to be exact.

Sorry I forgot those details.

 

[Ibix]

Ok - so you are using "inertia" to mean "mass". Fine. In that case, $F=ma$ is the only important thing (until we get to relativistic velocity, anyway). If $m$ is very small then $F/m$ will typically be large and so will $a$.

Exactly what happens depends on how the force is being applied. It might reduce with velocity (like a ship being blown by the wind) or remain constant (like a rocket).

 

[Sundown444]

Ok - so you are using "inertia" to mean "mass". Fine. In that case, $F=ma$ is the only important thing (until we get to relativistic velocity, anyway). If $m$ is very small then $F/m$ will typically be large and so will $a$.

Exactly what happens depends on how the force is being applied. It might reduce with velocity (like a ship being blown by the wind) or remain constant (like a rocket).

So you're saying both the acceleration and the force will be very large?

 

[Ibix]

So you're saying both the acceleration and the force will be very large?

No. You didn't specify your force, but I had the impression that it wasn't meant to be tiny. I may have inferred incorrectly.

The acceleration will be $F/m$. If $F$ is very small then the acceleration will be small. But for a given force, a smaller mass will accelerate faster.

 

[Sundown444]

No. You didn't specify your force, but I had the impression that it wasn't meant to be tiny. I may have inferred incorrectly.

The acceleration will be $F/m$. If $F$ is very small then the acceleration will be small. But for a given force, a smaller mass will accelerate faster.

Okay, so I used a calculator, and I put 500 Newtons over 0.000000000000005 Kilograms and the result I got was 100000000000000000 Meters per second squared. Would that be considered accurate, in that the force here is small and the acceleration is big if the mass or inertia is that small?

 

[russ_watters]

Okay, so I used a calculator, and I put 500 Newtons over 0.000000000000005 Kilograms and the result I got was 100000000000000000 Meters per second squared. Would that be considered accurate, in that the force here is small and the acceleration is big if the mass or inertia is that small?

Yes.

 

[Sundown444]

Yes.

So small forces can produce large accelerations if there are infinitesimal masses (or inertia) in reality, then?

 

[russ_watters]

So small forces can produce large accelerations if there are infinitesimal masses (or inertia) in reality, then?

Yes; a=f/m. The equation works the same for an ant and an aircraft carrier.

 

[Sundown444]

Yes; a=f/m. The equation works the same for an ant and an aircraft carrier.

Okay, thanks!

 

[Ibix]

Okay, so I used a calculator, and I put 500 Newtons over 0.000000000000005 Kilograms and the result I got was 100000000000000000 Meters per second squared. Would that be considered accurate, in that the force here is small and the acceleration is big if the mass or inertia is that small?

With these numbers you will be up to relativistic velocities in less than a nanosecond, and would need to think about relativity theory rather than Newton's laws. But, with that caveat, you are correct. There's nothing special about small masses.