proof of in elastic collision kinetic energy (before)> ketice energy (after)?
i need proof of this formula
- WoodsmanLv 76 years agoBest Answer
The easiest way is probably to choose an inertial reference frame where one of the masses appears to be at rest. Let's say m2 is "at rest": then
½*m1*(v1)² <?> ½*(m1+m2)*u²
We can always conserve momentum:
m1*v1 = (m1+m2)*u
v1 = u*(m1+m2)/m1
Plug that into the energy statement and divide out the ½:
m1*u²*(m1+m2)²/m1² <?> (m1+m2)*u² → simplify, including u² cancels:
(m1+m2)² / m1 <?> (m1+m2) → divide by m1+m2
(m1+m2) / m1 <?> 1
Clearly, (m1+m2) / m1 > 1,
so the LHS > RHS
and initial KE > final KE.