QoD 06/05/08 Tricky Thursday

[KillerTomato]

Here's something else that's interesting. Admittedly, my source is wikipedia, but...Did you know that Meredith Willson's first name isn't Meredith? It's Robert!

[starfish1113]

Did you know that Meredith Willson's first name isn't Meredith? It's Robert!

[seinfeld]And did you know that "War and Peace" by Tolstoy was originally named "War...What is it Good For"?[/seinfeld]

[KillerTomato]

AJ & Tan:

No, 16000 lb @ 35 MPH doesn't equal 1800 lb @ 55 MPH.

Since the truck will continue to move forward at some rate of speed, its change in speed (acceleration) would be (35-final speed), whereas the Rabbit not only goes from 55 to 0, it ends up going backwards, so its acceleration would be -(55+final speed).

The forces MUST be equal by Newton's Third Law, so the difference is in the rate of acceleration (or in this case deceleration).

Edited after I checked my math and realized I screwed up the signs.

[andrewjackson]

AJ & Tan:

No, 16000 lb @ 35 MPH doesn't equal 1800 lb @ 55 MPH.

Since the truck will continue to move forward at some rate of speed, its change in speed (acceleration) would be (35-final speed), whereas the Rabbit not only goes from 55 to 0, it ends up going backwards, so its acceleration would be -(55+final speed).

The forces MUST be equal by Newton's Third Law, so the difference is in the rate of acceleration (or in this case deceleration).

Edited after I checked my math and realized I screwed up the signs.

So if the forces are equal and opposite why do the vehicles end up going in the original direction of the truck's travel? Seems to me like the truck's "force" was greater than the car's.

Newton's 2nd law says "The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction." The "resultant force" in this collision is what takes both vehicles in the original direction of the truck's travel which is why both the truck and car wind up going in that direction. How can there be a "resultant force" if everything is equal? Why do the car and truck wind up going in any direction if the force exerted by each was equal at the time of the collision?

[mrkelley23]

QoD 06/05/08 Tricky Thursday Answers/Points

5. A tractor trailer and a Volkswagen Rabbit have a head-on collision on a highway. The 16,000 pound truck was traveling north at 35 mph, and the 1800 pound Rabbit was traveling south at 55 mph. Which one exerted the greater force on the other? The forces are equal and opposite. Some of you correctly cited Newton’s second law, which says that force = mass x acceleration. In this case, since the masses are decidedly unequal, so, too, must be the accelerations. But the really operative law is the third law, which says that for every action, there must be an equal and opposite reaction.

No doubt you are correct but having seen a tractor trailer truck and car that had met head on I can say unequivocally that there was nothing equal about the result! I will have to chew on this one a bit more as physics was not really a strong suit. Somehow having trouble getting past the definition of acceleration (none if moving at a constant speed?) versus "deceleration" (negative acceleration?) that results at the time of impact. Since the truck has less deceleration at impact (it is afterall going to plow right through the Rabbit!) perhaps that is what makes up for the greater mass? Hmm...

Your musings are correct. Before the impact, both vehicles are moving at constant speed, which means zero acceleration. As soon as they begin to interact (read: crash), however, they begin to accelerate negatively. The truck's acceleration is far, far smaller in magnitude than the lighter car. The ratio of accelerations will be exactly inverse (disregarding the rather important effect of friction) of the ratio of their respective masses. This is one of the most confusing but important aspects of Newtonian physics as opposed to Aristotelian -- the forces are equal, but the masses and accelerations are not.

I have also seen this question phrased as the collision between a fly and a truck's windshield. The forces are again ideally identical, but in this case the effect of wind resistance has so much effect that I find it even more confusing than the one I used.

[andrewjackson]

I can answer that myself: Momentum. The truck had more momentum than the car before the crash.

OK, maybe I'm coming around on this.

The "force" exerted is equal but it has a very different effect on each vehicle's momentum. The truck is slowed down by the same amount of force as the car. That amount of force is enough to reverse the direction of travel for the car because it has such a small amount of mass.

I'm slow but I get there.

[earendel]

I'll agree with tanstaafl.

I don't see how the small car is going exert as much force as the truck. When the truck and car collide the truck is going to continue forward (albeit at a lower speed) but the car is going to go backward. Why would that be if the force exerted by both vehicles is equal?

You say 1800 pounds at 55 mph = 16,000 pounds at 35 mph.

Let's say a 16,000 pound truck going 35 mph collided head-on with another 16,000 pound truck going 55 mph. Would the force exerted by each still be exactly the same?

There was a similar question as a Car Talk Puzzler a couple weeks ago. IIRC the question was whether it was better to run into an oncoming car or a stationary object like a wall or lamppost. Click and Clack said it was better to hit the wall, and a physicist from Harvard called in the next week to explain why it would be the same.

[mrkelley23]

AJ & Tan:

No, 16000 lb @ 35 MPH doesn't equal 1800 lb @ 55 MPH.

Since the truck will continue to move forward at some rate of speed, its change in speed (acceleration) would be (35-final speed), whereas the Rabbit not only goes from 55 to 0, it ends up going backwards, so its acceleration would be -(55+final speed).

The forces MUST be equal by Newton's Third Law, so the difference is in the rate of acceleration (or in this case deceleration).

Edited after I checked my math and realized I screwed up the signs.

So if the forces are equal and opposite why do the vehicles end up going in the original direction of the truck's travel? Seems to me like the truck's "force" was greater than the car's.

Newton's 2nd law says "The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction." The "resultant force" in this collision is what takes both vehicles in the original direction of the truck's travel which is why both the truck and car wind up going in that direction. How can there be a "resultant force" if everything is equal? Why do the car and truck wind up going in any direction if the force exerted by each was equal at the time of the collision?

Stock classroom answer: if you want to find out what's happening to a body, add up all the forces on that body. The force on the car by the truck, added up with all the forces from other sources, like friction of the tires, weight, normal force, and the car's engine driving force, will equal the car's mass times its acceleration. In this case, since the truck's force is much, much greater than any of the other mentioned forces in that sentence, the acceleration will be large and in the opposite direction of the car's original velocity, which is why the acceleration is negative. But the force on the car by the truck is equal and opposite to the force on the truck by the car. It's just that the sum of forces on the truck make for a far smaller (but still negative) acceleration.

I wish I could draw out the equation for you, along with the force diagram. It's much easier with pictures.

Try this page -- Paul Hewitt explains it better than I can:

http://tinyurl.com/5jn6k3

[jarnon]

I got this right, although I said "Newton's 2nd Law" instead of "Newton's 3rd Law."

There is a similar law concerning gravity. If you drop a weight from a building, the weight (obviously) moves toward the earth. But gravity exerts an equal and opposite force on the earth, and the entire planet moves (a microscopic distance) toward the weight.

[Bob Juch]

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