Math Is Fun Forum

Khushboo

Member

Registered: 2007-10-16

Posts: 47

weight of 1kg cotton and Ikg water melon is same, impact not same

I am trying to prepare some activities on units of measurement. During my preparation for the same, i fumbled upon something very peculiar. Lets assume that the weight of 1kg cotton is same as the weight of 1kg water melon. Now when you are hit by both from the same distance, you get hit by the watermelon and you feel hurt but the same is not true for 1 kg of cotton. Though the weight is same still the hit impact is not the same. Why is it so?

Regards

Khushboo Singh

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: weight of 1kg cotton and Ikg water melon is same, impact not same

Because the cotton ball is much softer and thus would absorb the energy from the impact.
It'd have to be pretty big to weigh a kilo, so after being thrown it might have a you-shaped dent in it. The energy of the impact went towards deforming the cotton, which means less was left to hurt you.

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Why did the vector cross the road?
It wanted to be normal.

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: weight of 1kg cotton and Ikg water melon is same, impact not same

1kg of watermelon is much more dense than 1kg of cotton, so when you get hit with the watermelon the force of the impact is much more concentrated than getting hit by the cotton.  That's why cutting tools are sharp: they allow the user to concentrate pressure along a very thin line or small point.

Also, as mathsyperson said, cotton is softer.  When it hits you it deforms, lengthening the amount of time that it's in contact with you.  Think about catching an egg or waterballoon.  You try to make initial contact with your hands away from you and then gently bring your hands into you, to maximize the amount of time that you can slow it down.  It's a matter of acceleration/deceleration.  The more time to have to accelerate/decelerate, the less force you need to apply at any given time.

Lastly, again due to the difference in density, the ball of cotton will be slowed down by air resistance much more than the watermelon.  It will be moving much more slowly by the time it reaches you.  Note that this particular property could be offset by doing the experiment in a vacuum, if you can just figure out a way to survive in such an environment.

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: weight of 1kg cotton and Ikg water melon is same, impact not same

1kg of watermelon is much more dense than 1kg of cotton, so when you get hit with the watermelon the force of the impact is much more concentrated than getting hit by the cotton.  That's why cutting tools are sharp: they allow the user to concentrate pressure along a very thin line or small point.

This has nothing to due with the density.  The very last part you seem to indicate that you meant surface area, which is entirely correct, but again, that is a very different thing than density.

Density will have no impact on the... impact.

Lastly, again due to the difference in density, the ball of cotton will be slowed down by air resistance much more than the watermelon.

Bah!  This is math, there is no such thing as air resistance !

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: weight of 1kg cotton and Ikg water melon is same, impact not same

Bah!  This is math, there is no such thing as air resistance !

why not? i made a lovely model of projectiles with air resistance which modelled terminal velocity nicely ^^ including acceleration, velocity, displacement at time 't'

Last edited by luca-deltodesco (2007-11-26 04:38:50)

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The Beginning Of All Things To End.
The End Of All Things To Come.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: weight of 1kg cotton and Ikg water melon is same, impact not same

As TheDude said: because the cotton is softer and will deform more, the impact will last longer. From Newton's second law, the force applied by the cotton ball/watermelon on you is equal to the change in its momentum over time - so the larger the time, the smaller the force it exerts on you --> the change in momentum will be equal for both objects (providing that they were travelling with the same velocity when they hit you), but the time would be larger for the cotton ball. That's a reason why modern cars are made to crumple - it increases the length of time that the impact lasts for, to reduce the forces involved.

Last edited by Daniel123 (2007-11-26 06:08:51)

NullRoot

Member

Registered: 2007-11-19

Posts: 162

Re: weight of 1kg cotton and Ikg water melon is same, impact not same

EDIT: The first paragraph adds no real value in hindsight; removed.

As Daniel points out, it has to do with the deformation of the cotton. Watermelons contain a large amount of water and water cannot be compressed, so there's very little give when it impacts. Also, their thick, spherical rind makes watermelons very resistant to any change in shape.

Cotton, on the other hand, contains an awful lot of void space. Even if you compress down into something similar to felt, then there's still room for the fibers to move. Especially since there won't be a hard rind to keep it in a spherical shape! If the fibers give when you are struck by the ball, then the ball will absorb most of the impact. A watermelon, being stubbornly resistant to change, is not so kind.

Last edited by NullRoot (2007-11-27 01:29:30)

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Trillian: Five to one against and falling. Four to one against and falling… Three to one, two, one. Probability factor of one to one. We have normality. I repeat, we have normality. Anything you still can’t cope with is therefore your own problem.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: weight of 1kg cotton and Ikg water melon is same, impact not same

Are we talking about mass here? If you are hit by the watermelon or cotton, whether on Earth or in gravity-free outer space, the pain you feel is the same; hence we talking about mass, not weight! Be clear what you’re talking about!

Khushboo

Member

Registered: 2007-10-16

Posts: 47

Re: weight of 1kg cotton and Ikg water melon is same, impact not same

Sorry ...for that

We are talking about weight and not mass here ...

Regards

Khushboo
http://www.inhomeacademy.com

Khushboo

Member

Registered: 2007-10-16

Posts: 47

Re: weight of 1kg cotton and Ikg water melon is same, impact not same

Just a query ....

Same force is exerted when you throw a cotton ball and watermelon ....or the exertions in both the cases vary as the nature of object varies.

regards

khushboo

NullRoot

Member

Registered: 2007-11-19

Posts: 162

Re: weight of 1kg cotton and Ikg water melon is same, impact not same

Weight vs Mass is irrelevant. If they both weigh 1kg, their mass is the same?

I'm going to try a text-based, time-elapse visual to see why one "hurts" more than the other.

00000  <- Represents the closely packed watermelon.
0 0 0 0 0  <- Represents the loosely packed cotton.
  <- Represents our human.

Each 0-unit represents 1/5th of the total weight; 0.2 kg. Let's assume the acceleration of both bodies as a whole are 2m/s²

The moments the cotton impacts our human , it might look similar to this:
   0 0 0 0 0  <-direction of motion, 2m/s²
  0 0 0 0 0
0 0 0 0 0
00 0 0 0
000 0 0
0000 0
00000

As the individual parts collide, they exert their (0.2 * 2) force. The force is spaced out because the object crumples up. You can imagine our human would feel a steady force of 0.4 over 5 'moments'.

If the watermelon hit you, however, it would look like this...
   00000  <-direction of motion, 2m/s²
  00000
00000

And he'd feel the watermelon extert it's force of 2 (0.2*5*2) at 1 'moment'.

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Trillian: Five to one against and falling. Four to one against and falling… Three to one, two, one. Probability factor of one to one. We have normality. I repeat, we have normality. Anything you still can’t cope with is therefore your own problem.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: weight of 1kg cotton and Ikg water melon is same, impact not same

If they both weigh 1kg, their mass is the same?

Who told you weight was measured in kg?

Last edited by JaneFairfax (2007-11-27 02:05:05)

NullRoot

Member

Registered: 2007-11-19

Posts: 162

Re: weight of 1kg cotton and Ikg water melon is same, impact not same

If they both weigh 1kg, their mass is the same?

Who told you weight was measured in kg?

I never said it was? We've been saying all along that the watermelon and the cotton "are the weight of 1kg" (Khushboo) or, more casually, they "weigh 1kg" (mathsyperson, myself). The 'as much as' is normally implied in the casual form, so I was genuinely confused by your statement, I wasn't trying to be rude. I apologise if you felt I was.

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Trillian: Five to one against and falling. Four to one against and falling… Three to one, two, one. Probability factor of one to one. We have normality. I repeat, we have normality. Anything you still can’t cope with is therefore your own problem.

Khushboo

Member

Registered: 2007-10-16

Posts: 47

Re: weight of 1kg cotton and Ikg water melon is same, impact not same

Hi

Sorry for responding so late ....thanxs for the valuable inputs...

Regards

Khushboo