# Which body would have a greater force exerted on it?

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?

• Why do you think that "$\dot p_{mosquito} \gt \dot p_{train}$"?
– user258881
Jun 9, 2020 at 12:32
• @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 $\dot p_{mosquito}$? Jun 9, 2020 at 12:38
• 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.
– user258881
Jun 9, 2020 at 12:39

$$m_1 does not imply $$|\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} then this must mean that $$|\dot v_\text{mosquito}|>|\dot v_\text{train}|$$