Why can I have a pillow fight with my friends but not a hammer fight? There are a number of factors that I can think of:


*

*The larger mass of the hammer would cause more force to be applied due to
F=MA.

*The larger surface area of the pillow would spread out the force of the impact, applying less pressure at any given point.

*Air resistance due to the pillow's larger surface area seems like it would also reduce the acceleration of the pillow, which would affect the force due to F=MA. Or perhaps it would just reduce the speed the pillow could be swung at, which would lower the pillow's momentum (does that matter?)

*The pillow is more compressible, which I believe should absorb some of the energy of the impact.


So the question is two-fold:


*

*Are there other factors which I've missed?

*What is the relative importance of the factors in determining the overall harm that a pillow versus a hammer would cause?


Note: Don't hit people with hammers. Question for fun only ;)
 A: According to Newton, $$\vec{F} = m \frac{d \vec{v}}{d t},$$ which implies that when two objects collide and have the same momentum difference before and after collision, the forces exerted depend on the duration of impact. The duration is higher for a soft object, which makes the force smaller than the hard object and this is the reason that we use hammers instead of pillows of similar momentum to hit nails, also the reason that the steering wheel of a car does not replace an airbag, if you want to increase the chances of remaining alive after an accident. This conclusion stands regardless of conservation of energy, because it applies even in the case of inelastic collisions.
A: Similar to auxsvr's answer, but more general, and often the way you'll find it in intro physics textbooks:
Newton's 2nd law in its most general form is $$F=\dot{p}$$, where p is the momentum. If you write it in terms of finite differentials, you get $\Delta p = F \Delta t$ (this is more general because it includes the possibility of the mass changing too, like a rocket).
So, if the pillow and the hammer have the same $p$, but the pillow compresses so it takes longer to go from $p$ to $0$, the $F$ is smaller. The hammer loses all its $p$ almost immediately, so $F$ is huge (as a secondary effect, the pillow is spread out all over your face, whereas the hammer's head is very small and thus concentrated in one spot).
Don't let me stop you from having fun though!
