# Should force impact moving objects less than ones at rest?

1. Mar 29, 2010

### Apteronotus

I'm sure I'm not thinking of this the right way. I'm hoping someone can see the error in my logic.

Should a force have less of an impact on a moving object than one which is at rest?

An object which is in motion has a momentum given by p=mv. A force F acting (say in the opposite direction) on this object need to overcome the object's momentum.

The same force acting on an object at rest needs not overcome any momentum (thought I guess the object here has inertia).

So wouldnt it make sense for the force to have more of an effect on the object which was at rest than one which was in motion? (By 'effect' I suppose I mean difference between initial and final velocities vf-vi)

If this is not the case, then does it mean inertia and momentum are the same thing?

2. Mar 30, 2010

### Stonebridge

A meaningful "effect" would be a change in the object's momentum when considering forces. It doesn't matter whether the object is moving or not; the (resultant) force will change its momentum. If the object is at rest it will start to move and gain momentum, if it is already moving, it might move faster and gain momentum, or be slowed down and lose some. (It might even just change direction)
Either way, what the force has done is to change the object's momentum. (By an amount = force times time)

3. Mar 30, 2010

### sganesh88

At non-relativistic speeds, the acceleration of a body under the influence of force F remains the same irrespective of its speed. a= F/m. No speed component here.
Inertia is the nature of any particle- To remain at rest or uniform motion if no force acts on it. Momentum is a quantity. You can attribute a value to it. Because of inertia (First law), momentum "happens" to remain constant if there's no external force.

4. Mar 30, 2010

### Apteronotus

Thanks for your replies. I have some lingering issues...

But a change in an objects momentum is equivalent to a change in its velocity since
$$p=mv$$

What happens if the force is applied for a very short period of time, say its given by
$$F(t)=F\delta(t)$$

where $$\delta(t)$$ is the Kronecker delta function.

How does this change the momentum?

5. Mar 30, 2010

### EvilKermit

v = a*t + vo

If the force is applied for only a short time, then the momentum change is based on that above. .

Actually momentum can be thought of the integral of force in change in time, although the term impulse is used instead of momentum.