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#1 2007-11-17 21:34:02

pwjac
New Member
Registered: 2007-11-17
Posts: 3

Falling Pears

In the area of London where I live, the local council has decided to cut down all the pear trees in public spaces:(.

The reason is because somebody was hit by a falling pear and complained to the authorities.

I have been trying to determine if a falling pear could cause a serious injury. A search of the literature shows the g-forces of over 50g are associated with serious brain damage. Need to compute the g-force of a falling pear on an adult head.

Should I work out the force the head uses to stop the pear (F = change of momentum / time) and then calculate the g-force on the head using F = m.a (where m = mass of head)?

Furthermore, I have been looking into the story that falling coconuts kill more people in the tropic than snakes. According to Wikipedia, the a falling coconut can exert a force equivalent to 1000kg. Based on a 4kg coconut with a final velocity of 25 m/s this seems very high? Any ideas on how this force was calculated?

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#2 2007-11-18 10:27:15

Martin
Moderator
From: Earth
Registered: 2004-10-04
Posts: 367

Re: Falling Pears

pwjac wrote:

...A search of the literature shows the g-forces of over 50g are associated with serious brain damage.

Can you point me to some references?

...Should I work out the force the head uses to stop the pear (F = change of momentum / time) and then calculate the g-force on the head using F = m.a (where m = mass of head)?

The force that the head exerts on the pear is indeed the change in the pear's momentum over time (which is the same as the mass of the pear times its deceleration) as it comes to a stop when striking the head. By Newton's Third Law, the force that the pear exerts on the head is precisely the same.

But, quite frankly, I'm not sure that the g-force approach really applies in this instance. It seems to me (and this is strictly a lay opinion) that the injury caused by a falling pear will have a lot less to do with g-force effects than with kinetic damage—the kind that a bullet to the head might deliver. So, were it me, I might first do some research to discover the amount of mechanical energy that the head can absorb before sustaining serious injury. I'd then compare that to the kinetic energy of the pear (for some nominal values of mass and velocity) upon striking the head.

Furthermore, I have been looking into the story that falling coconuts kill more people in the tropic than snakes. According to Wikipedia, the a falling coconut can exert a force equivalent to 1000kg. Based on a 4kg coconut with a final velocity of 25 m/s this seems very high? Any ideas on how this force was calculated?

I don't understand what "a force equivalent to 1000kg" means: In the mks system, kg ("kilogram") is the standard unit of mass, not force—the standard unit of force is n ("newton"). So, perhaps you can point me to that Wikipedia article as well?


The truth is out there.

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#3 2007-11-18 22:55:20

pwjac
New Member
Registered: 2007-11-17
Posts: 3

Re: Falling Pears

Thanks for your suggestions. I agree g-force is really not the best way to look at the problem. However there is a lot of data on sport injuries whcih uses g-forces to quantify the force used to sustain an injurty and that is why I tried to calculate a value for a falling pear.


The figure of 50 g for serious head injury was conservative (more like 200 g). However a car crash can cause forces of about 50 g on the body.

As regards, the "1000 kg" force for the coconut the article in Wikipedia (under coconuts if you want to check it out) quoted a force of 1 tonne. I think they meant the force of the falling coconut was 10 000 N

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