# Calculating force after collision

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Hi, How to calculate the 'force' after a collision between 2 objects, given - movement direction vector of object1/2 - velocity of object1/2 - mass of object1/2 - Eventually, the collision point Its not for physical purposes, so force doesn't have to be really realistic. Its ment for calculating how damage I should give a car after a collision. For example, a head on head collision does way more damage than if both cars would hit each others on the sides. This formula should also work for non-moving objects, like a rock. They don't have velocity or a direction of course, only mass. Greetings, Rick

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A simple way of doing this would be to find the relative velocity of one object (A) to the other object (B). Then you can calculate an inelastic collision using conservation of energy or momentum assuming object B is initially at rest in this relative frame. If one of the objects is something stationary like a giant rock, then all the remaining energy (after what's lost due to in-elasticity/deformation) goes back into the car. This is a simple particle-based approach, so maybe for a car you'd also want to look into rotational energy as well. It's not easy to get a good looking car collision without some more complex modeling, but I've never tried it myself so you might get acceptable results.

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Hi Rick. I have two suggestions.
You can go for the... "fake it!" approach, or the more realistic one...
Fake it!
It holds, in elastic collisions, that the relative speeds of the two objects with respect to each other, are interchanged -and change sign- upon collision, no matter their mass. This means that the velocities of the objects are merely swapped after collision. Object A will continue to travel at the direction of B before collision, and vice versa.
This means that the faster an object B moves, the more the object A will be affected when these two collide.
I know this was pretty much intuitive, I just wanted to make my point...
So, you can simply use the other object's linear momentum as a direct measure, of how much "damage force" you should apply to an object upon a collision.
Keep in mind though, that if any damage is implied, both objects will have to bounce off at smaller speed, since some energy will have been consumed by the inelastic collision. If you want 50% of the body's energy to be 'lost in the collision', you can do sth like that:
(kinetic energy after collision) == coefficient*(kinetic energy before collision)
and solve for the magnitude of the velocity after collision

The other way, the more "realistic way", has to do with impulses. Upon collision of two objects, 2 impulses are applied to them, that result to the instantaneous change in direction/velocity.
From the impulse, we can find just how must force we must apply to an object -within a specific time interval- in order to change its speed to another predefined value.
The formula is: mass*deltaVelocity = Force*deltaTime
'deltaTime' should be the duration of the collision in seconds, 'Force' is supposed to be constant, solve for it and you're ready.

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You could use the dot product between the relative velocity of the two colliding objects and the vector in the direction of the collision as a measure of amount of force. If you want to go in more detail take a look at http://www.d6.com and look for Chris Hecker.

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