Two cars are driving in opposite directions at 60mph and have a head-on collision...?

Question

Cont: I was told the damage from such a head-on collision is equivalent to one of the cars, hitting a wall at 60mph. Why- if two cars are driving at 60mph, isn't that like one car driving at 120mph (if you pretend it's standing still)...so how could the damage be the same?

Answer 1

workinman has good instincts. He got it right.

The reason 2 cars each going 60 aren't the same as 1 car going 120 is this: The damage is proportional to the energy turned into heat by the collision. The initial energy is all kinetic, which for 2 cars is 2 * (mv^2)/2 = mv^2 (v being 60 mph)

for 1 car going 120 mph, KE = 1 * (m(2v)^2)/2 = 2mv^2

So the total energy is twice as much with 1 car going twice the speed. Not only that, but all the energy will be expended on damaging only 1 car, not 2, so the total damage would be 4 times as much to the single car going twice as fast. Note: To be technically correct, the speeds should be converted to feet/sec, but for comparative purposes, this serves no purpose.

To all the rest of you who blew it, don't feel bad. You're in good company. Marilyn Vos Savant (known as the highest IQ in the world and writer of the column 'ask Marilyn' in Parade magazine) also blew this one about 10 years ago and got a lot of comments from myself and others to whom the answer seemed clear. She printed a revised answer in a subsequent column.

Answer 2

Momentum is conserved.

How do you reconcile that with a car going 60 mph hitting a stationary wall? Where does the car's momentum go?

You have to consider that the wall is fastened to the earth. As the car accelerates to 60 mph a certain force acts over a relatively long time against the ground to impart momentum to the car. At the same time, the ground "pushes" against the car for that same amount of time and the earth/wall system undergoes an equal and opposite change in momentum. No net force- no net change in momentum. The car "speeds up"- the earth "slows down".

When the car hits the wall, the earth/wall system "gives back" the momentum it acquired-- but over a much shorter period of time. The momentum exchange is equal and opposite- but the short time involved means that the forces- and thus the accelerations- are huge (force times the time interval equals mass times the velocity change).

For the wall to remain stationary from the (non-inertial i.e. accelerated) point of view of somebody standing next to it- the wall would have to be hit by a "virtual" car with equal and opposite momentum at the same time the actual car hit it. The "virtual" car is an artifact of the accelerated frame of reference and is simply the earth/wall system "giving back" the momentum it acquired while the car accelerated.

You might find it useful to visualize the system relative to its center of mass-- which would be very close to the center of the earth. As the car accelerates, it also spins the earth underneath it. Relative to the center of mass, the moving car hits a moving wall and both come to rest after the collision.

Should a westbound 120 mph car collide inelastically with an identical one at rest- the two cars would stick together and continue west at 60 MPH after the collision-- which is not the situation we have here.

Answer 3

It is true that the total energy of the two cars IS the same as one (identical) car going 120 mph. BUT: cars are designed to absorb some of the energy of a collision. Cars crumple. Walls DON'T crumple.

So you can't do a direct comparison. I'm not so sure that it's the same as hitting a wall at 60 ... maybe someone's studied that, but there are too many variables ... it would be somewhat different every time.

Answer 4

You were told wrong.

Accidents are described by total speed of collision, so the damage in this case would be equivalent to one of the cars hitting a wall at 120 mph.

Answer 5

The situation is more complex than everyone is indicating. When dealing with collisions, the velocity of the objects is only a small part of the equation ... we must also consider the mass of each object, as the overall momentum each is equal to its mass * velocity.

Also it is important to take into account how the scenario takes place :

If we presume the mass of each vehicle is identical and they "bounce" off each other on impact, each will be imparted with half of the combined momentum.

If the vehicles become entangled together, they effectively fuse to become a single object and different results will take place ... especially if one vehicle has a greater mass than the other.

Another potential scenario is for one of the vehicles to have greater mass and the two cars do not become entangled, then vehicle with less mass will bounce off the other ... slowing the larger vehicle, but not stopping it from moving forward.

Answer 6

You'd be right. It's 120 mph. Whether or not the damage is the same will depend on far too many variables. Physics states that two bodies impacting each other at opposite directions (let's say at 60 mph), then it is equivalent to one object hitting another at rest at 120 mph.

Answer 7

You are right -- in collisions the transferred momentum depends on the relative speeds of the two cars, which is 60 + 60 = 120 mph.

Answer 8

no, you were told right. these people here don't know anything. when you hit a wall at 60, you go from 60 to 0 in 1 sec. when you hit another car drivingat you at 60, you STILL go from 60 to 0 in 1 sec. it is the same force absobed by the wall as by the other car. it is NOT the same as hitting a wall at 120

Answer 9

Because
If they way the same
and hit strait on
they will both come to a abrupt stop
so what is the differance

1 Car hitting a unmoveable object comes to a abrupt stop
2 Cars hitting a unmoveable object comes to a abrupt stop
All 3 of the above cars came to a abrupt stop

Your friend is correct

Answer 10

It is a closing speed of 120 so that would be the impact speed of hitting the preverbial wall. However physics is a little more specific than that and the mass of the vehicles counts too. So if one vehicles mass is significantly higher than the other it will impart more force because it will follow through so to speak!!!