Revision Note 7: Momentum and Collisions

Momentum:

p = mv

What is important is change in momentum,

F∆t = ∆p = m∆v

Impulse:

F∆t is called the impulse, which is equal to change in momentum.

Use calculus when force varies (generally with time):

Center of mass:

For n different masses, the center of mass (x,y) is:

Problem Solving Tips:

Tip 7.1:

For solving momentum problems, first resolve momentum into two orthogonal axes. Then:

p_i,x = p_f,x

p_i,y = p_f,y

The above apply to all types of momentum problems.

The issue is with the number of unknowns and number of equations. There are now three types:

(a) Apply the principle of conservation of momentum only. Some parts of the final momentum are given – maybe the angle or the magnitude – to provide the extra equations to enable solution.

(b) Completely Elastic. No energy lost.  In this case we have the extra equation:

KE_i = KE_f

Or if springs are involved:

KE_i + PE_i = KE_f + PE_f

(c ) Completely inelastic. No, not all energy is lost, but some definitely is lost. The definition of a completely inelastic collision is that the two objects stick together after collision, so their final velocities are the same:

v_1,f = v_2,f

Broken down into two components:

v_x,1,f = v_x,2,f

v_y,1,f = v_y,2,f