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 moving object has *kinetic energy*, which is equal to ½mv², where v is the velocity. The faster it’s moving, the more energy it has. When the object hits something, all of that energy needs to go somewhere.
Part of the energy will go back into the object itself (rebounding, like a bouncing ball), another part will go into the object being hit (like a pool ball getting hit by the cue ball), and the last part goes into damaging the objects that collided. How much energy goes into each of these things depends on what the objects are made of.
When an object falls, it accelerates down due to gravity. Gravity puts a force on the object of F = m*G = m*9.81m/s², but the object’s mass is m, so when you work out the acceleration using F = mG and F = ma, you get ma=m*9.81m/s², the m’s cancel, and it turns out that no matter the object’s mass, it always accelerates down at 9.81m/s².
The higher the object has to fall, the longer it accelerates under gravity, and so its velocity when it hits the ground is higher. This means its kinetic energy higher, so there’s more energy available to do damage to the object it’s hitting, in this case breaking up the Pringle more.
When the object is first dropped, it has *gravitational potential energy*. This is expressed by the formula E = m * g * h, where h is the height and g is 9.81m/s². As it falls, all of this energy gets converted into kinetic energy. If you equate the two, m*g*h = ½mv², you can solve for v and find out how fast the object will be going the instant before it hits the ground.
You might also be interested in the force an object feels as it collides with another one. This is harder to figure out, but it’s still just F=ma. The object is moving with velocity v just before the collision, and assuming it doesn’t bounce, it’s moving with velocity 0 after the collision. Collisions aren’t instant, they happen over some distance (in your case, the height of a Pringle). So the force is whatever force you need to bring the object from going at velocity v, to velocity 0, over the distance the collision happens over.
What is that force? The object starts off with a kinetic energy of ½mv² and ends up with 0 (if it doesn’t bounce). Another equation is Energy = Force * Distance, and we can rearrange that to Force = Energy/Distance, so to remove all of that energy over a distance d we’d need an average force of ½mv² / d. In other words, the more distance the collision happens over, the less force the object experiences; the faster the object is going, the more force it will take to decelerate it over the same distance. This is why cars have crumple zones (it lets a collision happen over a greater distance), and why you should drive slower (there will be less force on your body in a collision).
In the Pringle demonstration, the distance the collision happens over is the same (the height of one Pringle), but the kinetic energy is higher after the higher drop, so the object (and the Pringle) have to experience a larger force during the collision, which breaks up the Pringle more.
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