Calculating Force of Two Objects Colliding at 17 mph

[BBluford]

Does anyone know how to determine:

If two objects are traveling toward one another at an equal speed (say, 17 mph), what is the equivalent force upon impact of an object (let's assume same weight if that matters) colliding with a stationary object?

Specifically two objects of the same weight colliding at 17 mph = one object colliding with a stationary object at X mph.

 

[rcgldr]

Depends if the collision is elastic or inelastic, and the relative mass of the two objects. The force involved depends how compressable the objects are.

 

[BBluford]

okay, here are the specifics. I'm a sports guy with a Finance background who is writing a book, so bear with me. I'm trying to explain what the equivalent of two 225 football players running into each other at 17 mph (roughly a 4.6 forty-yard dash) to a person sitting in a car and crashing into a wall. At what speed would the collision be roughly the same?

 

[rcgldr]

Assuming the two players stop after the collision as opposed to bouncing off at some speed, then it's like one of the players is unmovable (braced against a wall) and the other hits him at 17 mph. If in the orignal collision, each player bounces backwards at about 2 mph, then it's like a moving player hitting an unmovable player at 19 mph. A car analogy doesn't work well, because the passenger is secured by belts.

The situation get's more complicated if you consider the individual parts, such as the effect of helmet to helmet collisions.

The maximum acceleration is also related to how much "give" there is in the players equipment and their bodies.

 

[BBluford]

LOL..I know there's more to it, but I'm looking for a simple, approximated analogy. Let's assume it's two cars, then. If two cars hit head on at 20 miles per hour. That collision is equal to a single car hitting an immovable wall going at what speed?

 

[rcgldr]

If two cars hit head on at 20 miles per hour. That collision is equal to a single car hitting an immovable wall going at what speed?

20 mph. Both cars go from 20 mph to 0 mph.

 

[BBluford]

Never mind. I'll try to find the answer somewhere else. I'm probably not asking correctly. I know intuitively that two objects of the same mass moving towards one another at the same exact speed will generate more impact than a single object of that same size would generate if running into a stationary object (eg. a wall). My question is how much fast would the single object have to be moving to generate the same force upon impact.

 

[rcgldr]

If two cars hit head on at 20 miles per hour. That collision is equal to a single car hitting an immovable wall going at what speed?

20 mph. Both cars go from 20 mph to 0 mph.

I know intuitively that two objects of the same mass moving towards one another at the same exact speed will generate more impact than a single object of that same size would generate if running into a stationary object (eg. a wall).

It will generate more total impact, but not more impact per object.

Imagine that the stationary object has a mirrored surface. A car collides into the unmovable mirror at 20 mph. How would this "look" any different than two cars colliding head on at 20 mph each?

... or imagine that two cars heading towards each other both collide into an unmovable wall that is between the two cars, and that both cars hit the unmovable wall at the same time. How would this be significantly different than the cars hitting directly head on?

 

[Michael C]

I know intuitively that two objects of the same mass moving towards one another at the same exact speed will generate more impact than a single object of that same size would generate if running into a stationary object (eg. a wall).

Your intuition is leading you astray. rcgldr is right: there is twice as much energy dissipated in the two object crash, but that means that the same amount of energy is dissipated per object.

Mythbusters did the experiment with two identical cars, each running at 50 mph, crashing head-on. The amount of damage to one of the cars in the two-car crash was the same as the damage to one car that crashed against a wall at 50 mph:

 

[Paradox?]

so to actualy answer his question he could say that two football players hitting each other at 17mph is the same as one football player hitting the other who is stationary at 17mph?

im guessing he wants the equivalent "force" of impact between two football players hitting each other and a car hitting a wall.

so he can write, "if two football players running at 17mph hit each other it is the same force as a car traveling at x speed hitting a wall"?

correct?