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View Full Version : Re: PP126: F-V PARADOX

Stephen Haake
10-22-1999, 01:56 AM
Dear Mel/Biomch list,

Here is my two pennies/cents/pesetas worth on the problem posed.

I tried the following with a trajectory programme that I have. Scenario:
a tennis ball sized ball is thrown flat from 1.5m off the ground. The mass
is varied from 50g to 100g to 200g but has the same drag characteristics
(Cd=0.5).

If the thrower throws at the same velocity then the 50 g balls drops 0.6m
short of the 100g ball while the 200g ball travels 0.3m further. IF the
thrower throws the ball at the same velocity then he/she will throw a
heavier ball further since gravity has less effect on the trajectory (See
Dan Moran's email). A factor of 4 in mass makes a difference of 0.9m with
this scenario.

For the same initial energy (KE) of throw (31.25J) a 200g ball travels 3.6m
shorter than a 100g ball while a 50 g ball travels 4m further. IF the
thrower puts in the same amount of energy then he/she will throw a lighter
ball faster and thus further. A factor of 4 in mass makes a difference of
7.6m with this scenario.

The distance thrown is dominated, therefore, by the amount of energy that
the thrower can put into the ball while the mass of the ball affects the
trajectory of the ball much less.

So the question is, what does a thrower do as the ball gets lighter?
Does the thrower throw faster as the ball gets lighter?
Does the thrower reach some sort of limit in speed due to ability/comfort
while throwing?

Not being a biomechanist I didn't understand the idea behind the
Force/velocity curve in the original posting so I expect the answer is

Thanks to Mel for ruining my work plan for the day by giving me something
enjoyable to do while I should be marking!

Steve Haake

*************************************
Dr Steve Haake,
Sports Engineering Research Group,
Department of Mechanical Engineering,
The University of Sheffield,
Mappin Street,
Sheffield, S1 3JD,
United Kingdom.

Tel (+114) 222 7739
Fax (+114) 222 7853
*************************************

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