"What one man can invent another can discover"
Arthur Conan Doyle
where we have assumed that the mass of the particle is independent of time and we define the momentum of the particle, p = mv. Momentum is a clearly a vector quantity, with units, kg.m/s (SI) or slug.ft/s (British).
Note that writing the 2nd law as
force equal to the rate of change of momentum is the form in
where P is the vector sum of all the
individual particle momenta in
Important basic principle of Science
"Total momentum of
a system remains constant,
when the net external force acting on the system is zero"
Within the system objects may collide with each
other, thus exerting forces on each other. However,
"Total momentum of system before collision = Total momentum of system after collision"
Note that since momentum is a vector quantity, this equation is actually three scalar equations, one for momentum along each of the three Cartesian axes, x,y,z.
The condition that the net external force on the system be zero appears to make momentum conservation less basic that energy conservation (since there is no such condition for energy). However, if we define the Universe as our system, then all forces are internal and universal momentum conservation is guaranteed.
Given that we can assume momentum is conserved there are two classes of collisions
o ELASTIC: Kinetic energy is conserved, KEinitial = KEfinal
o INELASTIC: Kinetic energy is not conserved.
§ If the maximum kinetic energy is lost, consistent with momentum conservation, the collision is called Completely Inelastic. This situation can be achieved when two objects stick together after colliding.
§ In inelastic collisions the “lost” kinetic energy is converted into some other form of energy – heat, sound, elastic etc.
§ The total energy in a system is always conserved, but in collisions we are usually only able to easily measure kinetic energies, which means we can apply (kinetic) energy conservation only to elastic collisions.
Remember, momentum is
a vector quantity. Thus, in three
dimensions, application of conservation of momentum will lead
to 3 equations relating the components of momentum before and
after a collision.
Momentum conservation video
Using the alternative formulation of the second law, , we can write
The impulse is defined here for a single object, during a 2 body collision the impulse on the first object will be equal and opposite to that on the second. Consideration of the impulse is most useful when the force during a collision is not constant.
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