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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Because when you double the height the force (gravity) is able to accelerate the object for a longer time.
Force is not the same thing as energy of momentum.
So when the object falls for twice as long it gains much more kinetic energy.
And that kinetic energy is what you need to protect against, it’s the difference between someone gentle throwing a baseball at you, and a pro pitcher throwing a baseball at you as hard as they can. The second one has way way way more kinetic energy.
Tl:dr “force” does not equal “energy” you can be sitting perfectly still on the ground not moving and still have the force of gravity on you.
The force that changes is the force you need to slow down the faster moving object over the same short distance.
Same reason that a car will be more damaged by hitting a brick wall if it’s had a longer distance to accelerate first. The same brick wall is still stopping the same car, but it has to slow it down to zero from a higher impact speed.
The force in this case is from “speed” to “stopped” i.e. the acceleration from falling speed to hitting the ground. Dropped from higher, it gets much greater “speed” and then the acceleration from hitting the ground is X to 0, i.e. larger.
a = vf−vit = Δvt
t = time. The larger T gets, the larger a gets. The larger a gets, the larger F gets.
How does the velocity just before impact change with different heights? When dropped from a higher height, the object impacts the ground with a higher speed, right? Another way to look at this is by potential energy to kinetic energy conversion.
https://en.wikipedia.org/wiki/Crumple_zone
Increasing the time and distance of an impact results in smaller peak forces. Peak forces are what break things.
I had the same question when learning F = ma.
In this case, the force you are concerned with isn’t gravity, but the force of the Pringle/paper trying to *stop* the water bottle – in other words, accelerate it from its current velocity to 0 in a *very* short amount of time. A water bottle moving faster requires even more acceleration to slow it to 0, and thus the Pringle/paper needs to apply more force. By Newton’s first law, that same force also gets applied to the Pringle/paper.
Materials and devices that help safely stop a fall tend to work by being easy to deform (think a foamy pad or something), which basically allows the object to continue moving for a bit longer rather than stop all at once. This increase in the time to stop means a lower acceleration and thus a lower force imparted on both objects. From an energy perspective, some of the energy of the falling object gets transferred into the deformation of the foamy material instead of the (possible) deformation/breaking of the falling object.
The acceleration due to gravity doesn’t change with height, nor does the force imparted by gravity on the object, so your intuition is correct there.
Acceleration due to gravity is the same, so the force of gravity is the same. But the force of gravity isn’t the relevant force here. What we want is the force of the bottle pushing down on the chip, and the equal and opposite force of the chip pushing up on the bottle.
In the case that the chip doesn’t break, the bottle quickly decelerates from whatever it’s speed was to 0.
In the case that the chip breaks, the top of the chip quickly accelerates from 0 to whatever the speed of the bottle is.
So the acceleration, and therefore the force, depends on the speed of the bottle at the moment of contact. This is where height and gravity become relevant. The greater the height, the faster the bottle during impact.
If something gets crushed or break, in general suffers plastic deformation, it requires energy. Thats pretty much the starting point of inelastic collisions. In such collisions the kinetic energy isn’t conserved but goes into the plastic deformation of the object.
Kinetic energy is a function of velocity. If you drop something from a greater height it will reach a higher velocity before it hits the ground. (assuming no air resistance) More velocity means more kinetic energy and unless the object bounces back significantly most of that kinetic energy goes into deforming the object.
So force here is not that relevant or rather useful when we talk about the impact of some thing like a projectile (a bullet) we care about its kinetic energy because the destructive power (how much it can deform materials) is directly linked to its kinetic energy. Thats why you often hear people referring to these as kinetic energy weapons.
Deceleration is a type of acceleration. They’re treated the same in the math.
The deceleration—the change in velocity at the moment the object hits the ground—is what fits into the “a” in that formula, not the acceleration due to gravity.
Acceleration due to gravity is still relevant because the object that fell further experienced that acceleration longer. That means it reached a higher velocity and therefore experienced greater deceleration when the velocity of the object suddenly dropped to zero as it contacted the ground. The force of impact scales with that deceleration.
A faster falling object needs to decelerate more to stop in the same time/distance. Therefore, it applies more force to you when it hits you and your body decelerates it.
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