RocketMan on 5/10/2007 at 16:52
Its not that complicated if you just forget about the road all together. The relative vel between kart and truck is 0. If some piece of the truck comes off, then the road is important cuz the road will slow it down and make it come at the cart with some velocity but it certainly has to be way less than 60 cuz if it were 60 then it would have come to rest on the road. Unless there's a little rocket booster on the fragment that accelerates it to 120 before it hits.....
heywood on 5/10/2007 at 18:18
The tire is rolling on the road, which means the bottom of the tire is stationary and the top of the tire is moving forward at twice the truck's speed. No part of the truck or the tire is moving backward.
Now if this is an explosive blowout and not just a typical delaminated tread, it's possible for air pressure to blow a chunk off the tire. So consider what's happening to the back of the tire where a rearward facing chunk would come from. Before blowout, that part of the tire is simultaneously moving forward at 60 mph and up at 60 mph. So in order for the chunk to have any net rearward velocity relative to the road, the air pressure would have to blow it out at more than 60 mph relative to the tire. That would be pretty impressive, and pretty unlikely.
So, I think it's safe to say that the relative velocity at impact is <= 60 mph.
Mazian on 5/10/2007 at 19:33
Quote Posted by heywood
The tire is rolling on the road, which means the bottom of the tire is stationary and the top of the tire is moving forward at twice the truck's speed. No part of the truck or the tire is moving backward.
This is incorrect. The top half of the tire is always moving forward, and the bottom half is always moving backward (the road has nothing to do with it). In addition, the speed of the tire fragment (relative to the following go-kart) must be calculated by determining where on the tire the fragment came from, measuring the distance from the fragment to the center and figuring out the speed using the rpm's of this particular tire at 60 mph. You then convert this speed to mph to get the ideal case ejection speed.
RocketMan had it right, the relative speeds are zero. It's the rotational speed of the tire that matters.
Swiss Mercenary on 5/10/2007 at 19:56
Quote:
This is incorrect. The top half of the tire is always moving forward, and the bottom half is always moving backward (the road has nothing to do with it).
No. Not if there's a significant amount of traction.
Go take a cup, or a glass.
Roll it.
Notice that every point of it is moving forward, at all times. Just that the points at the top move forward faster then the points at the bottom.
hopper on 5/10/2007 at 20:21
I think Mazian and RocketMan are viewing the truck and the kart as a system with two stationary objects and the wheels spinning at 60 mph (speed on the outer edge), leaving out the road. Which means that any debris flung off the tire will travel at a max. speed of 60 mph against a stationery object.
So heywood and others are viewing the road as part of the system, while Mazian and RocketMan leave it out. This amounts to the same thing, really.
rachel on 5/10/2007 at 20:50
CSI had one thing right at least, in that road are indeed literally littered with tire debris. EVERYWHERE.
Made me wonder if US tires were somehow made out of cardboard and wonder about the quality of mine...
About the physics, dude it's CSI. It looks like it makes sense and it's entertainment. If you try to go deeper than that you're in for disappointment.
The real question for me was, how come the guy's hands were chopped off too? They didn't answer that, the debris only hit the head and the dude riding with the dead guy didn't do it as far as I know. So WHAT HAPPENED HERE?
Mazian on 5/10/2007 at 20:59
I meant that the top and bottom halves are moving toward and away from the kart. The entire truck is not moving at all with relation to the kart. If both vehicles have the same velocity, the road can be said to be acting on them equally and can be eliminated from the system. Unless there's something I'm forgetting; Physics class was a long time ago.
The radius of the tire determines its speed. The outer edge of a tractor tire traveling 60 mph down the road is traveling faster than the outer edge of a little Radio Flyer wagon wheel at the same speed, it's geometry.
Eliminate the speeds of the vehicles (since they're the same) and the road (since they're acting equally on both vehicles) and the system can be reduced down to calculating the velocity of the projectile from an axle-powered rubber fragment launcher.
heywood on 5/10/2007 at 21:11
Quote Posted by Mazian
This is incorrect. The top half of the tire is always moving forward, and the bottom half is always moving backward (the road has nothing to do with it).
Not unless you're doing a burnout. :)
Quote:
In addition, the speed of the tire fragment (relative to the following go-kart) must be calculated by determining where on the tire the fragment came from, measuring the distance from the fragment to the center and figuring out the speed using the rpm's of this particular tire at 60 mph. You then convert this speed to mph to get the ideal case ejection speed.
The rpm and distance from the fragment to the center doesn't matter because you already know how fast the tread of the tire is moving. The bottom of the tire is moving at zero relative to the road and -60 mph relative to the go-kart, and this is true no matter what the diameter of the tire is. Similarly, the top of the tire is moving at +120 mph relative to the road and +60 mph relative to the go-kart no matter what the diameter of the tire is. The top and bottom are the extremes because their velocity is purely horizontal. All other parts of the tire are moving at speeds between -60 and +60 relative to the go-kart.
Quote Posted by hopper
I think Mazian and RocketMan are viewing the truck and the kart as a system with two stationary objects and the wheels spinning at 60 mph (speed on the outer edge), leaving out the road. Which means that any debris flung off the tire will travel at a max. speed of 60 mph against a stationery object.
So heywood and others are viewing the road as part of the system, while Mazian and RocketMan leave it out. This amounts to the same thing, really.
Before the tire separates, yes, it's the same. Once the tire separates, you do have to consider the road, because it will slow any pieces of the tire that are moving relative to it. But either way, the maximum impact speed you can attain is 60 mph.
hopper on 5/10/2007 at 21:34
Yes. I was assuming the relevant tire part would be flying in a more or less straight line, slightly upwards, to chop the dude's head off.
demagogue on 6/10/2007 at 00:05
bah, I'll let the physics students figure this one out and then read their answers.
But the image I have in my mind is a baseball gun (or tennis ball gun).
When the wheels kick out the ball, isn't the muzzle velocity going to be the speed of the wheel spitting it out relative to the muzzle? If the tire bit were just lying still on the street and the truck ran over it ... ok, I see, the tire would match the speed of the road going backwards under it (otherwise it would be in a skid) and so it would just bounce the object up maybe but not spit it back like a baseball gun, right?
But then how is the baseball gun different; how does it work? Is it because (I'm figuring this out as I go) with the baseball gun it has wheels moving on both sides of the ball, spinning relative to the muzzle... but the vehicle tire just has one wheel moving, and even then that one wheel is on a forward-moving vehicle (not spinning on a stationary object like the baseball gun; not unless it's burning out). So again it would just be running over the ball, not spitting it out like the baseball gun.
Ok, I think I just answered my own questions.
