# Why does my baby's feeding bottle get smashed in fewer pieces when fuller?

After and after again my baby has tossed in the air his glass made feeding bottle and get it smashed on the floor, I realized that the more the milk the bottle has the fewer fragments I had to collect...

This makes me curious enough but as my level in fluids and physics is at high school, I cannot answer it. What I guess is the more milk means more pulling forces to the glass or the milk, the fluid acts as an absorbent material... Thanks for any answer of you.

PS the milk is powder dissolved with water.

• My guess is that the stresses caused by the impact of the bottle with the floor can be more easily dissipated when the bottle is filled with liquid. When empty, all the stress is contained within the glass at a higher concentration yielding more and smaller pieces of glass. Apr 25, 2019 at 9:57
• @nluigi, nice, +1, but with more milk inside the bottle is heavier and therefor more potential energy which all becomes kinetic when touching the floor... Apr 25, 2019 at 10:04
• agreed, you would need to figure out how much higher the stresses are because of the heavier bottle vs how much more stress can be dissipated because of the liquid. Apr 25, 2019 at 10:41

## 1 Answer

When the bottle is in the air it has a potential energy of $$(m_b+m_m)gh$$. As you mentioned in the comment, more the bottle is filled more will be the potential energy. But in collisions it is not necessary for all the kinetic energy of the bottle to be converted to kinetic energy of the pieces. The energy is converted to break the bottle, to produce some breaking sound, etc.. In the case when the bottle is filled milk, the milk acts as a suspension, i.e it absorbs the energy.

The bottle should be filled to some minimum level before it starts to act like a suspension. If you fill the bottle with very little milk then the increase in kinetic energy due to mass will be more than its ability to absorb energy. So there will be more energy that can be used in breaking the bottle, hence more pieces.

When the bottle is filled with enough milk then the increase in kinetic energy due to mass will be less than its absorbed energy. Hence there will be less energy spent in breaking the bottle.

Mathematically it will look something like this: $$(m_m+m_b)gh= K_{pieces} + E_{break} + E_{milk} +E_{surrounding}$$ When there is very little milk then $$E_{milk}$$ is small. Hence $$E_{break}$$ will be more (since energy is constant). And obviously $$E_{break} \propto N_{pieces}$$. Similarly $$N_{pieces}$$ will be less if $$E_{milk}$$ is more.

Hope this helps.