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Instantaneous Force and Impulse

An object of ...

Question

An object of mass $m_{1}$ moving with speed v collides with another object of mass $m_{2}$ at rest and stick to it. Find the impulse to the second object.

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Solution

From conservation of momentum of the system-

$(m_{1} + m_{2}) v_{o} = m_{1} v + m_{2} \times 0$

$⟹ v_{o} = \frac{m_{1} v}{m_{1} + m_{2}}$

The impulse imparted to second object is equal to change is momentum is -

$J = m_{2} v_{o} = \frac{m_{2} m_{1} v}{m_{1} + m_{2}}$

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