Two objects of mass $1.5 k g$ each are moving towards each other in the same straight line. Before the collision, the velocity of each object is $2.5 m s^{- 1}$ , after which they stick together. What will the velocity of the combined object be after collision?

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Solution

Given:

Mass of the object $(m_{1}$ and $m_{2}) = 1.5 k g$

Initial velocity of the first object $(u_{1}) = 2.5 m s^{- 1}$

Initial velocity of the second object $(u_{2}) = - 2.5 m s^{- 1}$

When the two masses stick together, the resulting object has a mass of $3 k g (m_{1} + m_{2})$

Velocity of the resulting object $(v) = ?$

As per the law of conservation of momentum, the total momentum before and after the collision is equal if no external unbalanced force is applied.

Total momentum before collision $= m_{1} u_{1} + m_{2} u_{2}$

$= 1.5 (2.5) + 1.5 (- 2.5)$

$= 0$

Therefore,

Final momentum after collision $= 0$

$(m_{1} + m_{2}) v = 0 \Rightarrow v = 0 m s^{- 1}$

Hence, the combined mass after collision will come to a rest.
Thus, the final velocity will be $0 m / s$ .

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Two objects each of mass 1.5 kg are moving in the same straight line but in opposite directions. The velocity of each object is $2.5 m s^{- 1}$ before the collision during which they stick together. What will be the velocity of the combined object after the collision?