In science one year, we did a test of dropping a water bottle from different heights over a Pringle, and we had to protect the Pringle with a paper. But how would increasing the height increase the force is the mass and acceleration is the same?
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A lot of these responses are over complicating things so I’m going to try and break it down a little more, then I’ll add the math stuff (which would be unintelligible for 5 year olds) at the end.
What you really care about is something called MOMENTUM, not simply FORCE. The transfer of momentum is what determines how much damage is done to the chip that your water bottle is dropped on.
Think about it this way, if the water bottle is sitting on the table, it is still subject to gravity. That same force (F=ma) is being applied to it, but it’s not crushing anything. It’s not even moving. The gravity doesn’t go away just because the bottle is resting on something. So why does it suddenly become damaging when the bottle is allowed to MOVE as a result of gravity?
This is because the bottle, while at rest on the table, is not changing MOMENTUM. However, when you drop it through the air, it first gains momentum while falling. Then it transfers that momentum to whatever it lands on. When you drop the bottle from higher up, it has more time to gather momentum while falling, and this does more damage when it transfers that momentum as it comes into contact with the chip and the surface around the chip. The deeper reason behind this is that the momentum is gained over a (relatively) long time compared to the time it takes to be transferred to the chip. The bottle may fall for 1 or 2 seconds, but if it comes to a stop nearly instantly upon landing on the ground (and it does) all of that momentum is transferred very quickly, which effectively resorts in a stopping force that is much greater than the force that was applied to accelerate it.
Now, for the math. As you stated, F = ma. So how does momentum (sometimes also called impulse, just a little fyi) relate to force?
There are two common formulas for calculating momentum, and we denote it with the letter “p”. These formulas are:
p = mv, and p = Ft
Here, m is mass, v is velocity, F is force (as above) and t is time. There are a couple of different ways to look at how this relates to force, but I think this will make it the most clear:
p = mv, while F = ma. Okay, so they are both directly proportional to the mass, but what is the difference between acceleration (a) and velocity (v)? Velocity is determined by accelerating for some period of time, right? Like in your car, if you hold the gas pedal down to the floor for 2 seconds, or 5 seconds, in which case will you be going faster? In which case will you do more damage if you hit something?
Similarly, some others have hinted at the relationship implied by the equation p = Ft. If you are going to be struck by something, say a boxer being punched, you can actually dramatically reduce the force by leaning away as the blow lands. It might seem insignificant to move away at 0.5 mpH from a fist flying at you at 20 mpH, but if the momentum would otherwise be transferred near instantaneously, and you can double the time (t) it takes to absorb the blow by leaning away, you effectively half the force (F).
Hope this helps a little bit. Definitely got a little bit above eli5 territory, but I wanted to be thorough.
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