Momentum and Force

†  An object’s linear momentum, p, for a particular instant is given by

     p = mv, expressed in units of kgm/s

†  Force is required for an object’s momentum to change.

     åF = ma = mDv/Dt

†  From the above definition of momentum, this can be expressed as (Newton’s original formulation)

     F_Net = Dp/Dt

Law of conservation of Momentum

†  Net momentum is conserved in collisions when no external forces are acting on the system

     m₁v₁ + m₂v₂ = m₁v’₁ + m2v’₂     where the primes represent the velocities post collision

†  When no external forces are acting on a system it is called an isolated system.

Collisions and Impulse

†  In the course of a collision, the force changes considerably over the total time interval.

†  Using the above equation, F_Net = Dp/Dt, we can cross multiply and arrive at

     FDt = Dp

†  We define the impulse, J, to be FDt

†  Note that, since the change in momentum can be calculated and is fixed, if we increase the time interval, the force is decreased

Elastic Colllisions

†  Elastic collision occur in objects that are hard enough for no thermal energy to be produced from any structural deformation.

†  Net kinetic energy is conserved in elastic collisions.

     (1/2)mv₁² + (1/2)mv₂² = (1/2)mv’₁² + (1/2)mv’₂²