Wolfram Alpha:
Search by keyword:
Astronomy
Chemistry
Classical Mechanics
Classical Physics
Climate Change
Cosmology
Finance and Accounting
Game Theory
General Relativity
Group Theory
Lagrangian and Hamiltonian Mechanics
Macroeconomics
Mathematics
Microeconomics
Nuclear Physics
Particle Physics
Probability and Statistics
Programming and Computer Science
Quantum Computing
Quantum Field Theory
Quantum Mechanics
Semiconductor Reliability
Solid State Electronics
Special Relativity
Statistical Mechanics
String Theory
Superconductivity
Supersymmetry (SUSY) and Grand Unified Theory (GUT)
The Standard Model
Topology
Units, Constants and Useful Formulas
Center of Mass Frame
--------------------
We can always choose a frame of reference where the center of
mass is stationary. Under these circumstances Σp = 0. Consider,
the following inelastic collision between 2 masses moving in the
same direction.
Before:
->v1 ->v2
m1 m2
After (masses stick together):
->v3
m1 + m2
In the laboratory frame:
Momentum: m1v1 + m2v2 = (m1 + m2)v3
Energy: (1/2)m1v12 + (1/2)m2v22 = (1/2)(m1 + m2)v32
In the COM frame:
Momentum: m1(v1 - v3) + m2(v2 - v3) = 0
Energy: (1/2)m1(v1 - v3)2 + (1/2)m2(v2 - v3)2 = (1/2)(m1 + m2)v32
Add some numbers
m1 = 1, v1 = 4
m2 = 2, v2 = 2
Laboratory frame:
Momentum: 1*4 + 2*2 = 3*v3
=> v3 = 8/3 = 2.67
Energy: (1/2)*1*16 + (1/2)*2*4 ≠ (1/2)*3*64/9
=> 1.35 units of energy lost in collision.
COM frame:
Momentum: 1*(4 - 2.67) + 2*(2 - 2.67)
=> 0
Energy: (1/2)*1*(4 - 2.67)2 + (1/2)*2*(2 - 2.67)2
=> 1.35 units of energy lost in collision.