Question

two ball beraing of mass m each in opp. direction withe outh equal speed v collide head on with each other . peridict the outcomeof the collision assuming it to be perfectly elastic?

Answer 1

Answer on Question #45254, Physics, Mechanics | Kinematics | Dynamics

Question:

Two ball bearing of mass m each in opp. direction with outh equal speed v collide head on with each other. Predict the outcome of the collision assuming it to be perfectly elastic?

Answer:

The law of conservation of momentum:

$$m v - m v = m v _ {1} + m v _ {2}$$ $$0 = v _ {1} + v _ {2} \quad v _ {2} = - v _ {1}$$

The law of conservation of energy:

$$\frac {m v ^ {2}}{2} + \frac {m v ^ {2}}{2} = \frac {m v _ {1} ^ {2}}{2} + \frac {m v _ {2} ^ {2}}{2}$$ $$m v ^ {2} = \frac {v _ {1} ^ {2}}{2} + \frac {(- v _ {1}) ^ {2}}{2}$$ $$v _ {1} = \pm v$$

Therefore:

$$v _ {2} = \mp v$$

Bearings will move with the same speed in opposite directions.

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