Acceleration due to gravity, and the force of landing on the ground

[SignSeeker7]

I'm quite confused about impact force and weight, as well as momentum. Assuming someone were to fall from a 5-story building, about 20 m, how would you calculate the force upon impact? I know it involves momentum, but I can't quite grasp it.
Also, if someone fell from the building, but instead of landing on the concrete below, they instead landed on a trampoline or blanket suspended above the ground, something that would slow them down without being lethal, how would you show that? Would it involve the same equation?

EDIT: I'm ignoring air resistance as well. In case that changes things.

 

[Ken G]

The reason you are confused about the "force of landing" is that this is not a well-defined concept without more information being given. You know the force of gravity, and the acceleration it produces (that's just g, a constant), so it's easy to get the velocity upon impact. But how do you convert that into a force? You need to know either the distance over which the falling person is stopped, or the time to stop them. Either of those will let you calculate the force, but even then you have to assume the force is constant, which is not a very good assumption at all. So anything you do is going to be pretty rough. However, if you do have a constant force of impact, and you know the distance over which it applies (so a harder surface would compress a smaller distance, for example), then you just say the force times the distance equals the kinetic energy of the falling person, and you do it all with energy. If you instead know the time it takes the person to stop, you would do it with momentum-- the force times the time must equal the momentum that the falling person acquired while falling.

But what I really want to stress is that you wouldn't know these things in any real application-- you would need a much more complete model of the response of the ground or trampoline or whatever. Then you would need to do a careful calculation of the stopping process, that was much more difficult than the simple calculation of the falling process. So that's why you really don't encounter the "force of impact" very often in basic physics problems.

 

[SignSeeker7]

So would it be bad to assume that the person would stop instantaneously? I would think that would be incredibly difficult to happen in real life.

 

[Ken G]

Yes, instantaneous stopping would require an infinite force. The fact is, we usually choose not to care what the force of stopping is, instead we focus on what is much easier to know-- the energy released when the person is stopped, and the momentum required to stop them. Going deeper into the stopping process is an issue for paratroopers and basketball sneaker designers!

 

[PJC01]

Acceleration due to gravity is a constant value (9.8 m/s^2) that represents the rate at which objects accelerate towards the center of the Earth. This means that if an object is dropped from a height, it will increase in speed by 9.8 m/s every second until it reaches the ground.

The force of landing on the ground is a result of the acceleration due to gravity. When an object falls and hits the ground, the force of impact is determined by its mass and the acceleration due to gravity. This force is commonly known as weight and is measured in units of Newtons (N).

To calculate the force of impact, we can use the equation F=ma, where F is the force, m is the mass of the object, and a is the acceleration due to gravity. In the case of someone falling from a 5-story building, we can assume that the mass of the person is constant and equal to their weight. So, if we take the acceleration due to gravity to be 9.8 m/s^2, the force of impact would be equal to the person's weight multiplied by 9.8 m/s^2.

Now, let's consider the scenario where the person falls onto a trampoline or blanket. In this case, the force of impact would be reduced because the trampoline or blanket would act as a cushion and slow down the person's descent. To calculate this, we would need to take into account the spring constant of the trampoline or the material properties of the blanket, as well as the distance the person falls before coming to a stop.

In general, the equation for momentum (p) is p=mv, where m is the mass of the object and v is its velocity. This equation can also be used to calculate the force of impact, as force is equal to the change in momentum over time (F=Δp/Δt). So, in the case of the person falling onto a trampoline or blanket, the force of impact would be equal to the change in momentum divided by the time it takes for the person to come to a stop.

In conclusion, calculating the force of impact involves taking into account the mass of the object, the acceleration due to gravity, and any external factors such as a trampoline or blanket. The equation F=ma can be used to calculate the force of impact, and the equation p=mv can also be used to take into account the object