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?
In: 152
The acceleration here is *the sudden stop at the end*. Remember, “acceleration” only means “*change* in speed”.
The bottle dropped from higher up was falling for longer, so it reached a higher speed, so it experienced a larger acceleration when it stopped moving, so there was more force.
The thing that matters more for crushing is the total energy, not the force.
The energy transferred to the thing you are dropping is given by the force x the distance travelled in the direction of that force (the maths is a bit more complicated but we won’t worry about that for now).
Drop something from twice the height it gains twice the energy, it has twice the energy to dissipate into whatever it hits.
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.
The answer is that the a is bigger. Not because it’s falling from higher but because it’s traveling faster. When the object hits the ground, it’s going from some speed to 0, and it has to do that in the same amount of time regardless of how fast it’s going. I am ignoring impulse here, this is actually what’s different but this is something you won’t go over just yet. So because the speed is going from x to 0 and then from 2x to 0 or whatever, in the same time, remember that acceleration is v/t, the v is bigger so the a is bigger. Transfer that bigger a over to a bigger F when using F=ma.
Force is how hard something is being pulled, not how fast it is moving. Even if gravity were to “stop” midway to the effect that F = ma = m*0 = 0, the object would still be moving and falling. What you have left is momentum i.e., velocity times mass. A faster moving object means more momentum.
Where acceleration is a = F/m = d / t^2, and v = d / t, we can substitute v = a * t = F * t / m.
Velocity is proportional to how much time the force is applied. Momentum is proportional to velocity. The faster the object, the more momentum will need to be transferred. More transferred momentum is like a bigger “hit” to the receiving object.
Something that has always interested me is that every object that has mass has gravity, therefore more massive objects (ignoring friction) do actually fall faster to earth than less massive ones. This is because the more massive objects is pulling the earth to it faster than the less massive objects. It’s negligible though. I’d love to see this in action though. I’d love to see a super precise calculation between the items
Gravity acceleration is measured in meters per second squared.
This means that an object taking more seconds to fall will have more acceleration.
So F=ma, which has an a for acceleration, has more acceleration when there is more height.
The force of gravity and acceleration going down is the same at both heights, but the acceleration (deceleration) and force from the ground stopping the object isn’t. That second force depends on how fast the object was going, what it’s made of, and what the ground is made of.
The object dropped from twice the height has twice the speed, and an impact with the ground has a limited distance (at most the size of the object if it’s not denting the ground) to stop the object, which means that the faster object is going to experience more force.
Because in that situation the a=acceleration=g=gravity=9.8m/s^2
The longer it falls the faster it gets, until it reaches terminal velocity. As you are raising the height, you are increasing the total potential energy. The potential energy converts to kinetic energy during the fall. When the object stops and hits the ground, all this energy is released. Energy releases in the form of deformation of the object, heat and sound.
The force acting on the falling pringle can is somewhat irrelevant to your question, gravity exacts a constant acceleration on the pringles can while it falls, this is the correlation between gravity and the pringles can, what matters in your scenario of “protecting it” is the force that acts upon the pringle can once it hits the ground.
Force can be calculated as the change in momentum over time, where momentum is mass * velocity, velocity increases the longer it is accelerating due to gravity. Aka a pringle can falling 20m/s has an increased momentum, double of a pringle can falling 10m/s.
So you end up with a pringle can with a momentum of 20*{mass of pringle can} (dropped from a greater height) or 10*{mass of pringle can} (dropped from a lower height), now the change in time upon impact is going to be nearly instant in both scenarios (both will stop near instantaneously). So the impact force has double the momentum divided by the same change in time, the impact force is doubled in this scenario. Because the impact force or kinetic energy on the greater height is double of that on the lower height this means the impact to your can is “harder” on the greater height.
Latest Answers