Dot Physics

Watermelon Collisions – ouch

Through random surfing, I found this clip from The Amazing Race (which is apparently some type of reality show). Don’t really know the set up except that it appears some girl is trying to launch watermelons with a slingshot. This looks bad, but she seems to not be seriously injured.

Watermelon smashed on face. Wow. What can I we calculate here? Bring in the video analysis.

How fast was the watermelon going?

First, this is not a very good quality video. The frame rate sucks and there is a very slight panning and zooming (which I will ignore) Second, I really don’t have anything to scale the video so I just assumed the girl-launcher was about 1.5 meters tall. Just a guess. Using Tracker Video analysis, I get the following data (where the x-direction is along the direction of motion of the melon):

i-090c80725805a3e03616b4a2388fc93b-2010-09-09_data_tool.jpg

This shows the motion of the melon both while being launched and when coming back. The first thing I did was to fit a parabola to the very beginning motion. This will give me the initial acceleration with a value of about 120 m/s2. Zowza.

I can also get an estimate for the initial and final velocity by fitting a linear function to the data. Note – the melon is actually accelerating (due to the gravitational force) but it is moving so fast, I can ignore this. Doing so, I get a launch speed of about 15 m/s and a returning speed of also about 15 m/s (this is good). First, if the melon gets stuck in the launcher then it should have the same return speed that it had launching (energy conservation). Also, 15 m/s seems like a reasonable speed (around 33 mph).

What about the impact?

This is a little bit more complicated. First, there is the initial impact and then there is the recoil of the head. Here is a plot of the head as a function of time (mostly in the direction of recoil)

i-3d59a00838e637a3fd84ee414eb7be3d-2010-09-09_data_tool_1.jpg

I guess the first thing to do would be to estimate the acceleration of the head. This is where you would get an injury, if the acceleration was too high. Really, there is only a couple of frames with the head getting hit. I don’t think I can get that from video. But I can get it, oh yes, I can. All I need from the video is the recoil distance. Let me say that the head recoils a distance of 0.2 meters. The other thing I need to know is the final speed of the melon. No clue here. Let me just say that it is going half as fast as it was when it hit (the pieces of the melon are still moving after the collision).

Here is a diagram of the melon at the beginning and at the end of the collision:

i-298dda2faa8d8821bc8e53b53086ffa6-2010-09-09_untitled_8.jpg

Since everything is in the same direction, I can use the scalar-kinematic equation:

i-acec13b6e51e9e377ced701a05a068bb-2010-09-09_la_te_xi_t_1_22.jpg

Using an initial and final velocity of 15 m/s and 7.5 m/s as well as a distance of 0.2 meters, I get an acceleration of 422 m/s2 (oh, this is the average acceleration). This is about 43 g’s. Clearly enough to smash the melon. What about the head? Does that mean the head had the same acceleration? No. First, it has a different mass. Second, it is connected to the rest of the body so that there are other forces on it.

Perhaps with a better quality video, I could get a little more detail.

Comments

  1. #1 Kurt
    September 9, 2010

    Based on the way the head deflected, I think there was actually a second watermelon from over on the grassy knoll.

    Seriously, though, this woman has a possible concussion, and they didn’t halt filming to get her medical attention?

  2. #2 Rob (no, the other Rob)
    September 9, 2010

    Kurt, that was my thought as well. I’ve never watched the show – in fact, I’ve never watched any so-called “reality show.” I’m sure participants have signed onerous assumption of risk forms and waived all rights but this smacks of gross negligence. It’s hardly conceivable that she doesn’t have at least a concussion based not only on her statements of blurred vision and not being able to feel her face but on Rhett’s analysis. I’m sure that the attorneys looked it over before letting it air. I wonder if this came from a broadcast or if it was a bootleg?

  3. #3 CCPhysicist
    September 9, 2010

    Yet another example showing that the human body is pretty tough. That watermelon never had a chance.

    One detail, Rhett:
    That rubber tubing slingshot is essentially a spring, so you shouldn’t be expecting a parabolic fit with constant a.

    Regarding the likely concussion:
    No court could ever find the hostess/actress negligent because it would first have to be shown that she is expected to know anything that isn’t in her script. The producers, on the other hand, had better hope they have a medic rushing to the set in panic mode.

  4. #4 stripey_cat
    September 10, 2010

    So, she has a possible unassessed concussion, and they’re exposing her to a *second* blow to the head?! Giving her a few minutes to see how she does is one thing, but risking a second impact?

  5. #5 tiarisius
    September 10, 2010

    I agree with stripey_cat. Liam Neeson’s wife fell backwards and bumped her head (seemed very minor compared to the watermelon!!). She walked away laughing about it…by nightfall she was brain dead!! The contestant (Claire) said she had a headache and “couldn’t see straight”…it could have been caused by broken blood vessels already putting pressure on the brain. They definitely should have checked pupil response to say the least. What about something BEFORE this happened…no offer of a bike helmet-face guard?!? Nothing?
    Epic Fail!! I’ll NEVER watch this show!! Do they think we’re THAT stupid?
    Here’s the link about Liam’s wife and her fall at the beginner’s slope:
    http://www.imdb.com/news/ni0714386/

  6. #6 tiarisius
    September 10, 2010

    I was so caught up in the disbelief of their negligence of her welfare that I forgot to say… Thank you Rhett for doing the math on this, I wondered about the speed of impact when I saw the blurred photo. I wanted to add something, the rebounding of the brain inside the head due to speed of impact and secondary impact- head vs. ground (behind her).
    Rhett wrote:”This is about 43 g’s. Clearly enough to smash the melon. What about the head? Does that mean the head had the same acceleration? No. First, it has a different mass. Second, it is connected to the rest of the body so that there are other forces on it.”
    The human skull is a vessel for the brain, a jelly-type substance, which recoils within the rough interior of the skull cavity many times after initial impact resulting in abrasions, etc. There is also the secondary impact of the head hitting the ground at almost as great a speed… and the factor of the object (watermelon) being small and spheroid as compared to an oblong-shaped watermelon which would have broken more easily upon impact, releasing some of the force compared to the smaller one. I’m amazed she’s alive and can still see and hear. (as far as I know). Thanks for your awesome work and website, Rhett!! You have a great way of explaining things for us. Hope you know you really are appreciated.

  7. #7 John
    September 10, 2010

    Rhett,
    Maybe you’ve answered this question, but I was wondering what software you use to make your diagrams….

  8. #8 Rhett Allain
    September 11, 2010

    @John,

    I use Apple’s keynote software to make the diagrams and then I just take a screen shot of it to make it a jpg.

  9. #9 John
    September 12, 2010

    Rhett,
    Do you use LaTexIt to typeset the labels?

  10. #10 Rhett Allain
    September 12, 2010

    @John,

    Right – LaTexit

  11. #11 film izle
    October 12, 2010

    Kurt, that was my thought as well. I’ve never watched the show – in fact, I’ve never watched any so-called “reality show.” I’m sure participants have signed onerous assumption of risk forms and waived all rights but this smacks of gross negligence. It’s hardly conceivable that she doesn’t have at least a concussion based not only on her statements of blurred vision and not being able to feel her face but on Rhett’s analysis. I’m sure that the attorneys looked it over before letting it air. I wonder if this came from a broadcast or if it was a bootleg?