Physics, Car Wrecks, and Newton's Laws

March 23, 2006 2:04 PM

I am interested in the physics of motor vehicle accidents. The most basic question I have is which of Newton's laws, if I am understanding them properly, is at work in the following situations: 1) You're driving in a straight line and suddenly you jerk the wheel in one direction. This makes the car start to roll. 2) You're driving and you fall asleep at the wheel, so the car drifts to one side. You wake up suddenly, jerk the wheel in the opposite direction, and the car starts to roll. 3) You round a sharp curve too fast and roll the car. If anybody would like to give detailed explanations of the physics of each of these situations, hopefully without calculus, that would be great, as well. thanks!
posted by soulbarn to science & nature (12 comments total)

In each case the turning force on the car is exerted through the tires at the bottom but the momentum effectively acts on the center of mass, above the tires. Thus tall SUVs tend to roll more, in general.
posted by exogenous at 2:07 PM on March 23, 2006

Umm, that would be the first law.
posted by exogenous at 2:08 PM on March 23, 2006

inertia: the car "wants" to continue to move, but the tires hold the bottom part. the upper part moves forward, the bottom part stays still, which means rolling.

If the track was slippery (rain, snow, ice, oil), it would be very hard to make it roll: in all these cases it would continue to move (slipping) in the original direction, completely ignoring wheels.
posted by qvantamon at 2:29 PM on March 23, 2006

Inertia (law one).

In each case the car has too much inertia in each direction to be overcome by the car's handling system. That is, the car can only deal with so much inertia and keep the wheels on the ground.

Remember that changing direction is acceleration, too, so turning a car requires force. It's possible to turn the car too sharply, so that the force the wheels apply to turn the car is smaller than the force of the existing inertia the car has. Said inertia then has to roll the car, as it is now working against the handling system.
posted by teece at 2:32 PM on March 23, 2006

The friction between the tires and the road exerts a force on the car, but it's applied specifically to the lower part of the car. Since the car has momentum in the forward direction, pushing on the lower part of the car creates torque (twisting force) which makes the car rotate.
posted by knave at 2:42 PM on March 23, 2006

And you want the Moose Test.

"The test became widely known when Swedish motor journalists overturned the Mercedes-Benz A-Class in the moose test,"

posted by krisjohn at 3:05 PM on March 23, 2006

An abrupt movement of the steering wheel od a car by itself usually doesn't result in a rollover, but a spin. (Mercedes Benz A-class notwithstanding.)

Of course, leaving the road, or driving a high centre of gravity SUV means all bets are off.
posted by Neiltupper at 4:23 PM on March 23, 2006

Sometimes it helps to reformulate these scenarios. For example, imagine taking a cup and placing it upside down on a piece of paper. This represents the car on the ground -- remember that in normal circumstances the job of the tires is to grip the road, so from the point of view of the tire there is no movement.. If you now move the piece of paper around slowly the cup will move with it, but if you quickly yank on the piece of paper you can make the cup turn over on its side. This is because you are applying a force at the bottom edge of the cup, but its inertia acts at its center of gravity which is somewhere in the middle. This means you create a moment which is what will result in the turning over. If all the force was applied at or near the center of gravity it would be impossible to create this turning or twisting moment -- this is why cars low to the ground are very hard to flip, because the force at the tires is much closer to the center of gravity.
posted by Rhomboid at 4:23 PM on March 23, 2006

Good thinking Rhomboid. Just made me think of this example: You are rollerblading along, rolling at a constant speed, and then you skate off the path and onto some grass. The grass slows your skates down tremendously, and the result (if you don't react quickly), is the top part of your body keeps going forward and you fall face first. Very similar phenomenon. It requires a force to be applied outside of the center of mass (in this case, at your feet), which creates the torque I mentioned earlier.
posted by knave at 4:27 PM on March 23, 2006

These would be cases of the first two. You have a car traveling at a given momentum which it will maintain into the tree ahead of you unless you jerk the wheel (1st law). As your tires interact with the road below the car's center of mass, they apply a net force acting against your current acceleration (2nd law). You have angular acceleration because your tires are not causing a net force in the same direction as the tree.

The important thing that causes the roll is the net torque (think of the tires as a person yanking at your ankles) versus dynamic friction and your rotational inertia. Cars with a high center of mass (like an SUV) are more likely to roll just the way a tall skinny person is easier to yank off his feet.

This is of course, overly simplified, but might shed a bit of light on the basic physics.
posted by onalark at 6:33 PM on March 23, 2006

[onalark: static friction, surely, unless the car is already skidding, or hydroplaning, or whatever.]

I think it has less to do with your rotational inertia, which would determine how fast the car is tumbling once it rolls, as it does with the width of the wheelbase as compared to the height of the center of mass. The torque applied to the car-as-a-whole by the turn has to be counteracted in order to keep the car from actually rolling; the only place that counteracting torque can come from is from the wheels. The car's weight shifts to one pair of wheels and off of the other, and the resulting difference in force on the wheels produces another torque on the car, which hopefully cancels out the first torque. If not --- if all of the weight is shifted off of one pair of wheels --- then the car starts to actually rotate, that is, it rolls over.
posted by hattifattener at 6:48 PM on March 23, 2006

Hmnn, I consider myself corrected :)
posted by onalark at 8:37 AM on March 24, 2006