A body of mass M𝑀 moving with a speed u𝑢 has a head-on elastic collision with a body of mass m𝑚 originally at rest. If M>>m𝑀>>𝑚, the speed of the body of mass m𝑚 after collision will be nearlyAumM
Question
A body of mass M𝑀 moving with a speed u𝑢 has a head-on elastic collision with a body of mass m𝑚 originally at rest. If M>>m𝑀>>𝑚, the speed of the body of mass m𝑚 after collision will be nearlyAumM
Solution
In an elastic collision, both momentum and kinetic energy are conserved.
The initial momentum of the system is given by the momentum of the moving body, which is Mu (since the other body is at rest). The final momentum of the system is the sum of the momenta of both bodies.
Let's denote the final velocities of the bodies as v1 and v2 for the bodies of mass M and m respectively.
So, we have:
- Conservation of momentum: Mu = Mv1 + mv2
Since M >> m, Mv1 is much larger than mv2. Therefore, we can approximate the equation as Mu ≈ Mv1, which gives us v1 ≈ u.
- Conservation of kinetic energy: 1/2Mu^2 = 1/2Mv1^2 + 1/2mv2^2
Substituting v1 ≈ u into the equation, we get 1/2Mu^2 ≈ 1/2Mu^2 + 1/2mv2^2. Simplifying, we find that v2 ≈ 2u.
So, the speed of the body of mass m after the collision will be nearly 2u.
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