A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of mass 2 kg. The impact is perfectly elastic. The speed (in m/s) of 2 kg mass ball after the impact will be::
Question
A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of mass 2 kg. The impact is perfectly elastic. The speed (in m/s) of 2 kg mass ball after the impact will be::
Solution
In an elastic collision, both momentum and kinetic energy are conserved.
The initial momentum of the system is the momentum of the 1 kg ball, since the 2 kg ball is stationary. The initial kinetic energy is also just the kinetic energy of the 1 kg ball.
Initial momentum = mass1 * velocity1 = 1 kg * 12 m/s = 12 kg*m/s Initial kinetic energy = 0.5 * mass1 * (velocity1)^2 = 0.5 * 1 kg * (12 m/s)^2 = 72 J
After the collision, both balls will be moving. Let's denote the final velocity of the 1 kg ball as v1' and the final velocity of the 2 kg ball as v2'.
The final momentum of the system is the sum of the momenta of the two balls: mass1 * v1' + mass2 * v2' = 12 kg*m/s The final kinetic energy is the sum of the kinetic energies of the two balls: 0.5 * mass1 * (v1')^2 + 0.5 * mass2 * (v2')^2 = 72 J
We can solve these two equations simultaneously to find v2'.
From the conservation of momentum, we have v1' = 12/v2' - 2. Substituting this into the conservation of kinetic energy equation gives us:
72 = 0.5 * (12/v2' - 2)^2 + 0.5 * 2 * (v2')^2
Solving this equation for v2' gives us v2' = 8 m/s.
So, the speed of the 2 kg ball after the impact is 8 m/s.
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