Sample Write-up
Physics 99999, Lab 3
September 34, 2008
Joe Student
Lab Partners:
Julie Etudiant, Atru Schola
Purpose:
We are asked to determine the speed of a 0.22 caliber bullet as accurately as
possible.
This could be useful in forensic investigations, where the speed of the
bullet may determine how much damage is done, or gun design, where the
objective may be to reach a given muzzle velocity, for example.
Background
:
The measurement of velocity can usually be reduced to a measurement of the
time required to pass between two known points: v=d/t, assuming that the
velocity is constant (a good approximation in this case).
However, given the
extreme speed of the bullet, this was not practical in this case. We guess that the
bullet's speed is about 100m/s, which means it would only take .2s to cross the
lab if the lab is about 20 meters long. The photogates only have a timing
resolution of about 40ms, so, this would lead to something like a 30% error on
the velocity.
Instead, we chose to create a collision, so that the momentum of the
bullet was transferred to that of a stationary object.
We chose a heavy object so
that its velocity was much smaller than that of the bullet, making it much easier to
measure.
So, the underlying principle we used was conservation of momentum.
This was a totally inelastic collision, since the bullet was imbedded in the object
after the collision.
So, our equation is:
pi = pf;
mV = (m+M)v
where m is the mass of the bullet, V is the bullet's initial velocity, which we wish
to measure, M is the mass of our target object, and v is the final combined
velocity.