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If mosquito and train each travelling in a straight line towards each other with the same velocity, collide with each other head-on, then which object would under the exercion of a greater force?

Now since,

$\mathit {m_{mosquito}} \lt \mathit {m_{train}}$ and $\therefore$ $\dot p_{mosquito} \gt \dot p_{train}$

Now here, we get $F_{mosquito} \gt F_{train}$, but isn't both train and mosquito exert the same force on each other according to 3rd law of motion?

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  • $\begingroup$ Why do you think that "$\dot p_{mosquito} \gt \dot p_{train}$"? $\endgroup$
    – user258881
    Jun 9, 2020 at 12:32
  • $\begingroup$ @FakeMod Wouldn't the change in $v_{mosquito}$ be infinite since, $m_{train}$ is greater and they both possess the same velocity initially making $\dot p_{train}$ larger compared to $\dot p_{mosquito}$? $\endgroup$
    – mnuizhre
    Jun 9, 2020 at 12:38
  • $\begingroup$ No, the greater mass of the train can be simply compensated by a greater change in the mosquito's velocity. That change need not be infinite at all. $\endgroup$
    – user258881
    Jun 9, 2020 at 12:39

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$m_1<m_2$ does not imply $|\dot p_1|>|\dot p_2|$. Changes in momentum also depend on changes in velocity. Indeed, since there are no external forces here, we will have $$\dot p_\text{mosquito}=-\dot p_\text{train}$$

as, by Newton's third law, the forces on each object will be equal and opposite. Then you can say that since $m_\text{mosquito}<m_\text{train}$ then this must mean that $|\dot v_\text{mosquito}|>|\dot v_\text{train}|$

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