Dot Physics

A physics question. Answer quick!

I have always wanted to ask a question like this – but never found the right test for it. Perfect for a blog.

Question:

Suppose you are in your car at a stop light behind a truck. The truck is pulling a trailer with a rollable tractor on it.

i-bf2d003cab99953df81f77c10cec1d80-tractor-1.jpg

When the light turns green, the truck starts to accelerate. However, the cable holding the tractor to the trailer breaks and the tractor starts to roll off the trailer. You are right behind the trailer. What do you do?

Do you have an answer yet? You should probably come up with one quickly. That tractor is rolling off now. I will put the answer below.

Answer:

The best thing to do would be to stop and stay where you are. Although the tractor is rolling backwards with respect to the trailer, it is still moving forward (even if a little). In the case of zero friction, the tractor would stay in the exact same position on the road (which is still in front of you). In the case of a little friction, there will be a slight friction force pushing in the direction of the motion of the truck. This small friction force will slightly increase the momentum (and thus speed) of the tractor.

Comments

  1. #1 Uncle Al
    March 23, 2009

    As with all managerial assignments, the proper response is to do nothing. How many FEMA employees were discharged for cause after Hurricane Katrina in New Orleans? One. How much funding simply vanished into the night? More than a $billion. One stands amazed there is any poverty remaining in Louisiana. Perhaps replacement inventory was shipped in.

  2. #2 Dave
    March 23, 2009

    Answer: Start speed-dialing my lawyer. ;-)

    As the tractor comes off of the trailer, the wheels will give the tractor a slight backwards velocity (Consider the vector force diagram as the wheels are partially off of the edge of the trailer.). This may or may not be enough to cause it to be propelled into you, thus damaging your vehicle and causing a tort. You could, of course, rapidly back up to avoid the falling tractor. But, to do so would expose you to liability if you happened to back up into something/someone behind you, which would be a negligent act on your part for not adequately checking for clearance before backing up. Thus, the (legally) safest approach may be to do nothing and then sue for damages.

    Dave

    P.S. I’m not a lawyer (fortunately for y’all). ;-)

  3. #3 Sarah
    March 23, 2009

    The other answer is not to tailgate! You don’t want your front bumper under the overhang of the tractor.

    On a similar note, I heard recently that the best advice when the car in front of you spins out or loses control is to drive towards the spot where they lost control. Chances are they won’t be there by the time you get there, and you can’t reliably predict where they are going.

  4. #4 Blaise Pascal
    March 23, 2009

    I agree with Dave’s physics. Until the tractor actually falls of the trailer it will not be moving towards you, so staying put is reasonable. But when it hits the edge, it will likely gain some momentum towards you, and may even end up rolling backwards at you.

  5. #5 Anonymous Coward
    March 23, 2009

    I’ll ditto Dave and Blaise.

    Depending on the level of tractor-trailer friction (which will accelerate the tractor to the right in the earth frame) and the dynamics of the tractor falling off the back edge (which will accelerate the tractor to the left in the earth frame), the tractor could be moving either to the right or to the left in the earth frame by the time it touches the ground.

    Perhaps we could consider an infinitely thin tractor, or a trailer bed infinitely close to the ground?

    P.S. For an experimental realization of the above, you might enjoy:
    http://www.youtube.com/watch?v=x_4TqtHATWI

  6. #6 Stephanie Chasteen
    March 23, 2009

    I showed my true stripes as a physicist in my answer — I also figured you should stay still. But as the other respondents showed, the “physics world view” doesn’t take into account the “true life world view” in which the flatbed is slightly elevated from the ground.

    This reminds me of a most wonderful talk by Eric Mazur — The Make Believe World of Real-World Physics (http://blog.sciencegeekgirl.com/2008/07/26/the-make-believe-world-of-real-world-physics-eric-mazur/). He asked a bunch of physicists which trajectory a ball would follow when dropped by a person walking, and showed three illustrations. The physicists answered in the physics way — that it will follow a parabolic path landing at the person’s feet (since it already had horizontal velocity). The “regular people” answered that it would fall pretty much straight down. Which, if you watch a video, is really what it does — a person doesn’t walk fast enough for the parabolic trajectory to be evident.

    So, the clear-cut “physics” answer doesn’t always jibe with the messier “real life” answer.

  7. #7 Rhett
    March 23, 2009

    @AC – awesome video of the carts coming out the truck.