# Small car colliding with large truck

A small car collides with a large truck. Why do both vehicles experience the same magnitude of force? Wouldn't the large vehicle experience less force than the small one?

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## 2 Answers

The two vehicles experience a force of the same magnitude due to Newton's third law:

If object $A$ exerts a force $\mathbf F_{AB}$ on object $B$, then object $B$ will exert a fore $\mathbf F_{BA}$ on object $A$ and $$\mathbf F_{BA} = -\mathbf F_{AB}$$

However, what you're probably thinking about is that motion of the car is more drastically affected by the collision. This can be explained by Newton's second law. Let's say the truck has mass $M$ and the car has mass $m$. If the magnitude of the force that both vehicles experience is $F$, then the magnitudes of their respective accelerations are $$a_\mathrm{truck} = \frac{F}{M}, \qquad a_\mathrm{car} = \frac{F}{m}$$ and combining these we get $$\frac{a_\mathrm{truck}}{a_\mathrm{car}} = \frac{m}{M}$$ So if the mass of the car is a lot less than the mass of the truck, then the acceleration of the truck is much smaller than the acceleration of the car, and if you were to watch the collision, the truck would pretty much seem like it's motion was unaffected, but the car's motion will change quite a bit.

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Thanks but how do you know the forces are the same? – user1530249 Feb 16 at 23:31
Does equal but opposite reaction mean equal but opposite force? – user1530249 Feb 16 at 23:33
Yup!  See the edit where I wrote down Newton's third law. – joshphysics Feb 16 at 23:49
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