We have discussed the
concept of conserved quantities in class. One of these quantities
discussed is energy. Recall that when a quantity is conserved, it can just
be transferred to another body or another form, but is not lost. For
example, a moving body has energy of motion, or kinetic energy. It can
lose some or all of this energy only if that energy is transferred to another
body (e.g. through a collision) or if it is transferred to another form (e.g.
turns into heat through friction.) If a body of mass m is moving at
speed v, then its kinetic energy is the quantity ½ mv2.
In this lab we will be
examining the collision between two bumper cars, and since we expect various
quantities to be conserved, we will see how and if that is indeed so.
Another conserved quantity
we may not have discussed yet is momentum. The quantity of momentum for a
body of mass m moving at a velocity v is mass times velocity mv.
We expect that momentum is conserved in a collision - some of the momentum of
one car will be transferred to another car during a collision between the two.
The laws of conservation of
energy and linear momentum are two of the great laws of physics which can be
applied to a large number of physical problems. When we observe a collision
between two objects, for example, we are tempted to assume that both the energy
and momentum lost by one object is gained by the other. In practice this
is often far from being the case. In general, the kinetic energy before and
after a collision may be quite different because it can be lost as heat.
The amount of energy lost to heat depends on the type of collision - elastic
(bouncing) or inelastic (sticking). The law of conservation of momentum,
however, is applicable during all collisions. Linear momentum is
conserved even in cases where kinetic energy is not. In this experiment
you are asked to examine the principles of conservation of momentum and energy
by considering the simulated motion of bumper cars.
Theory
Quantitatively, momentum
conservation will work out as follows for two cars in a collision:
If two bodies are in motion
at constant velocity (masses m1, m2 and velocities v1, v2), we can write the
total momentum before a collision as
total initial momentum = m1v1+ m2v2.
If the two bodies undergo a
collision, then their velocities after the collision should be expected to
change, let’s say they are now v1' and v2',
so that the total final momentum is
total final momentum = m1v1' + m2v2'.
If momentum is conserved,
then
m1v1+
m2v2
= m1v1' + m2v2'.
We deal with energy
conservation in the same way. The kinetic energy of a body is 1/2 mv2.
We can write down the total kinetic energy of the two cars by adding up their
individual energies. If kinetic energy is conserved, then the sum of the
two cars' energies before the collision will equal the sum of the two cars'
energies after the collision.