Chapter 4 - UCSB HEP

WORK AND ENERGY
the momentum and energy of each particle change due to the
interaction forces. Finally, long after the collision, (c), the particles
are again free and move along straight lines with new directions
and velocities. Experimentally, we usually know the initial
velocities vl and Y,; often one particle is initially at rest in a target
and is bombarded by particles of known energy. The experiment
might consist of measuring the final velocities vi and vi with suitable
particle detectors.
Since external forces are usually negligible, the total momentum
is conserved and we have
For a two body collision, this becomes
Equation (4.29) is equivalent to th ree scalar eq rrations. We have,
however, six unknowns, the components of v', and vi. The energy
equation provides an additional relation between the velocities, as
we now show.
v
Before
After
/
Elastic and Inelastic Coliisions
Consider a collisian on a linear air track between two riders of
equal mass which interact via good coil springs. Suppose that
initially rider 1 has speed v as shown and rider 2 is at rest. After
the collision, I is at rest and 2 moves to'the right with speed v.
It is clear that momentum has been conserved and that the total
kinetic energy of the two bodies, Mv2J2, is the same before and
after the collision. A collision in which the total kinetic energy is
unchanged is called an elastic collision. A collision is elastic if the
interaction forces are conservative, !ike the spring force in our
exa rn ple.