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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Acceleration is a function of time and a higher drop increases the time thus the force unless you have passed the point of terminal velocity.
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.
What is important is what acceleration is vs speed. If you use a car instead, you can get the car to accelerate over a certain distance. If the car can still accelerate further, giving it more road will result in more speed at the end
When you’re back in vertical acceleration with gravity, it’s the exact same F=ma Newton taught us, except that the bottle doesn’t carry its own engine. The engine is Earth gravity and the acceleration is always full throttle
F = ma. Good start!
Now let’s talk about the collision. That’s going to be p(momentum) = mv.
p(falling object) will be compared to the material strength of the object it’s hitting. If it’s a direct hit on a solid flat surface, we’ll ignore pressure, and just work with a single point (P(pressure) = F/A, for reference).
We can calculate V by doing V=d/t. Fairly easy in this case. If you didn’t measure it, we can also do v = at. And if you don’t have the distances we can just compare using v1 =d/t v2 = 2d/t. In this case we immediately see a big change in v1 and v2.
Momentum is conserved. So p1 = p2 + (material strength).
As far as material properties goes, that’s a whole science in its own. I’m breaking it down into one single variable here but realistically there’s a ton of variables and different measurements that might be relevant that I don’t know enough about to get into.
What causes damage in a collision is impulse(I) and impulse is the change in momentum/time.
Momentum is the mass of the object times the speed at which it is moving.
The longer something falls the more time in the air the force of gravity has to accelerate it. So if it falls for 1 second it’ll be going a certain speed, but if it falls for 2 seconds it’ll be going a lot faster. (Ignoring terminal velocity). Therefore if the object that’s been falling longer has more speed and therefore more momentum and will undergo more impulse (have a harder collision) when it hits the ground.
If it lands on a soft squishy material, it’ll take a lot longer to come to a complete stop and have even less impulse and be more likely to survive the fall. That’s why helmets and bubble wrap work.
Eventually, height stops mattering as the object reaches its max velocity and is just falling at that speed (terminal velocity).
So when the water bottle hits the pringle it deaccelerates (negative acceleration) which exerts a force on the water bottle and the pringle, when you increase the height, the time that the water bottle spends accelerating increases, bigger velocity, means a bigger deacceleration, and therefore a bigger force
Net force while falling is gravity (ignoring wind resistance)
Reaction force while landing is related to how fast you are going and what you hit.
F=ma is the instantaneous force being exerted on an object.
So if you pick something up, and hold it in your hand, the weight you’re feeling in your palm is F=ma (in this case a being gravity, or g)
Now how high you hold the object, adds a third component, height. Which gives you a new equation.
Fp=mgh (Fp or PE) this is the potential energy that the object has, picking something up adds potential energy to the object, the higher you pick it up, the more energy, hence why it takes more energy to pick something up, or walk up stairs, than it does to just stand still or walk forward. Since m and g are constant, if you want to increase h, you need to add energy to the object in some way.
So this means if you had 2 equal sized balls on the ground, then picked up one in each hand, lifted the one in your left hand to a meter, and the one in your right hand to 2 meters, the object in your right hand would be storing twice as much potential energy. So when you drop them, you can expect the ball on the right to hit the ground with double the amount of force.
And that’s because as soon as you let go of the ball, it’s potential energy starts becoming kinetic energy. If we assumed both balls weigh 1kg, then the left ball should hit the ground with 9.81J of force, and the ball on the right would hit with 19.62J of force.
And we can prove this with the Kinect energy formula, KE=0.5mv^2, now this part gets trick, because we need to figure out the velocity that both object will have when they hit the ground. But we have their heights and accelerations. So that’s to Torricelli, we have a convenient formula that the velocity of an object falling from rest is v^2=2g(h) so after falling 1 meter it would be 4.429m/s. And this is where we see why the energy scale in a linear relationship with height. Most people know that with KE, the energy is proportional with an increase in mass, but squared to its velocity, so a an object with double the speed with have much more force than an object with double the weight. But with a falling object, while it’s speed increases linearity with time, it’s increase in velocity actually decreases every meter. Which might not be intuitive at first, but it’s because the fast an object travels, the less time it spends accelerating. So while it take 1 meter to accelerate to 4.429m/s and object needs to for 4meters to have double the speed, and then 16m to double again, for every doubling of speed, you need to square the distance an object falls.
What this means, is we have a directly linear relationship between the height of an object, and the kinetic energy it gains while falling. So double the height, double the energy, because even though the velocity has a greater impact, the increase in velocity per unit of height offsets it exactly.
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