Of Unladen Sparrows and Peanut M&Ms


I know that this blog is read by scientists and engineers, so I’m hopeful of some kind of answer to the question on my mind this afternoon.

And this probably reveals more about my idle mind than anything else.

Let us suppose that an unnamed man is traveling northbound on a still day in a van with the windows rolled down. Let us further suppose that he is traveling at 60 MPH and eating from a bag of Peanut M&Ms. And let us suppose, hypothetically, of course, that this man decides to throw one M&M out the window at a right angle to the direction of travel. And for argument’s sake, let us say that he throws the M&M at a speed of 30 MPH.

Given that the average mass of a peanut M&M is 2.5 grams (I happen to be in possession of the very bag from which the subject M&M was extracted – don’t ask how), what would the path of this M&M look like if traced along the ground?

For a time, as the M&M is in the man’s hand, it will trace a straight line parallel to the road. I understand that once thrown and until the M&M leaves the van, it will trace a curve of some kind. But I assume that all of that changes once it hits the air moving alongside the van.

But does it go immediately backwards (tests have suggested that this is not the case)? Does it continue on the same curve it began while still in the van? Is the curve violently altered by the wind?

I suspect that the exact path would be effected by the shape of the van and the consequent air turbulence immediately alongside the van. I’m hoping that is inconsequential to the final picture and can be ignored.

These are the questions which puzzle my mind.

Weird. I know.

8 thoughts on “Of Unladen Sparrows and Peanut M&Ms

  1. Gus/Adri

    To make it simpler and eliminate the wind effects (you didn't specify that there is no cross wind), assume further that you are traveling in a vacuum! But this is your trip, not mine.-ge

  2. Randy Greenwald

    Hypothetically, me. Hypothetically, of course. Which, hypothetically, raises the whole 'in their right mind' question. But it was all in the hypothetical interest of science.

  3. Gail and Keith

    Okay. You're off the hook. Inquiring minds do want to know and we'll accept this excus…er, reason as a valid one in the interest of science. G

  4. Staci Thomas

    Dr. Pap, professor in the Civil Engineering Department at Virginia Tech, could answer these questions for you. He could even teach you how to solve them if you enrolled in his class called "Dynamics", a required class for students who have a dream of becoming Civil Engineers. The problem is that if you go and have a bunch of kids, you'll forget the formulas that you never thought you'd forget and you won't be able to provide the answers to these questions.Staci

  5. Randy Greenwald

    For what it is worth, the track of the M & M, against all logic, appears to maintain a fairly linear course once exiting the van. But, sigh, short of enrolling in a course at VTU, I'm condemned to never knowing for sure.

  6. Greg

    To start with, let's ignore gravity.Then, when you throw it, for the first few inches it flies straight towards the window, slowing down slightly because of air friction. The force on the M&M is in the opposite direction to its motion because (from the M&M's viewpoint) that's the direction that the wind of its motion comes from.Now, as it goes through the open window, it suddenly goes out into rapidly moving air. All of a sudden, the wind that the M&M sees is mostly sideways. So, air friction starts pushing it towards the back of the car.Air friction is still doing the same thing — it's still slowing down the M&M relative to the air, but now the air around the M&M is moving rapidly backwards (relative to the car).So, from your viewpoint, the M&M starts a smooth backwards curve as it goes through the plane of the window.From the viewpoint of someone sitting on the roadside it's a little simpler.The M&M starts out moving forward at 60 mph in the car, then when you throw it, it's moving diagonally forward and sideways in a straight line.Once it goes through the plane of the window, it just slows down, that's all. Of course, the thing is, the car doesn't slow down, so the car gets ahead of the M&M.If you turn on gravity, it gets a bit more complex, but only because the M&M is now accelarating downwards.

  7. Randy Greenwald

    Thank you, thank you, thank you, Greg. I'd love to know who you are, but you write as if you know what you are talking about, so you've persuaded me! Thanks.

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