Re: Will a rubber bullet or an aluminium bullet knock a block of wood over?

The question: "Will a rubber bullet or an aluminium bullet knock a block of wood over? They Are the Same Size Weight And Shape From The Same Distance And Speed."

Although not stated, it seems that the intent of this question is to ask whether or not either a rubber or aluminum bullet will knock over a block of wood as well as a lead bullet. But even if regular (lead) bullets are not included in the question, the general principles of collisions will hold. One of the pieces of information needed to begin to answer the question is the "coefficient of restitution", which I will hereinafter abbreviate as "C.O.R.".wi

Begin by reading through the material at the following four great web sites:

at hyperphysics: elastic collisions

at hyperphysics: inelastic collisions

more on coefficent of restitution

yet more on C.O.R.

A table of some approximate values of C.O.R.:

If two colliding materials have different Cs.O.R. the individual Cs.O.R. are multiplied to obtain an approximate mutual C.O.R. If we are discussing a wood block with a C.O.R. = 0.5 with rubber bullet having a C.O.R. = 0.6, and an aluminum bullet having a C.O.R. = 0.4, then the effective collisional Cs.O.R. will be 0.3 for the block and rubber bullet, but 0.2 for the block and aluminum bullet. However, if either of the bullets embeds itself into the block then the C.O.R. of the two is zero! In that case the collision is totally inelastic.

One of the major lessons to be taken from all the above information is that the C.O.R. is defined as the ratio of the separation velocities to the approach velocities, of the two colliding bodies. If v_1o is the initial velocity of the first mass, v_2o is the initial velocity of the second mass (Which, in our case, is zero!), v₁' is the final velocity of the first mass, and v₂' is the final velocity of the second mass, then the C.O.R. is
C.O.R. = (v₂' - v₁') / (-v_2o + v_1o)
with velocities positive if to the right and negative if to the left. (You will see different signs for this formula in different places, depending on the sign convention.)

There is a really cool applet for playing with different masses, velocities, and Cs.O.R. here.
Let's plug in some reasonable values:
bullet mass = 13 g (about 200 grains) = 0.013 kg
block mass = 2 kg (slightly less than a pound)
bullet velocity = 100 m/s (about 300 f.p.s.)
block's initial velocity = 0
for rubber bullet, combined C.O.R. = 0.3
for aluminum bullet, combined C.O.R. = 0.2
(If we assume the bullet penetrates and embeds itself into the block, the C.O.R. = 0)

Results of using the applet:

Because I have no idea of the actual masses of your block and bullets, and I do not know the actual velocity of the bullets, you will have to put in your values and determine what the applet predicts! By the way, if the bullet passes through the block then the C.O.R. can be negative! In fact, using a "C.O.R." for the case of a penetrating bullet really isn't quite right, although it does work out okay. Also, if you can find some actual values for the C.O.R. for aluminum you will have to adjust the combined C.O.R. and see what happens.

John Link, MadSci Physicist