How much would the earth recoil or move if (energy/collision?)

[gills]

How much would the Earth "recoil" or move if...(energy/collision?)

Homework Statement

all 6.5 billion people in the world with an average mass of 70kg, simultaneously jumped off of a 4 meter high platform. What energy would be imparted on the Earth assuming people don't bend their knees when landing?

Homework Equations

E_f = E_i and possibly inelastic collision assuming that people keep their knees locked when landing and bones don't break!:

m1v1 + m2v2 = (m1 + m2)Vf

The Attempt at a Solution

I can do the energy imparted part--->

(1/2)mv^2 = mgh to find velocity of people then plug v into -->

(1/2)mv^2 to find the Energy that would imparted on earth.

I'm having a tough time figuring out how much the Earth would actually "recoil" or move?? Will it even move at all?

 

[MrXow]

The amount that the Earth recoils or move depends on where the energy is imparted to the earth. For example, however unlikely, if everyone did this jump in the state of Kentucky, the Earth would seemingly "recoil" in the opposite direction. However, the entire population of the world does not live in Kentucky the population is more or less distributed evenly, so the recoil would probably not be seen.

 

[ogb p]

I would like to clarify that the Earth would not actually "recoil" or move in response to this scenario. This is because the Earth has a significantly larger mass compared to the combined mass of all humans, and the force exerted by the humans jumping off a 4 meter platform would be minuscule in comparison.

However, if we were to consider the theoretical scenario of all humans jumping off a 4 meter platform simultaneously, the Earth would experience a slight change in its rotational velocity. This is due to the conservation of angular momentum, which states that the total angular momentum of a system remains constant unless acted upon by an external torque. In this case, the humans jumping off the platform would exert a tiny external torque on the Earth, causing a slight change in its rotational velocity.

To calculate the exact amount of change in rotational velocity, we can use the equation:

Δω = (Στ)/I

Where Δω is the change in rotational velocity, Στ is the total torque exerted by the humans, and I is the moment of inertia of the Earth.

However, even with all 6.5 billion people jumping off the platform, the change in rotational velocity would be extremely small and would not be noticeable. So, in conclusion, while the energy imparted on the Earth would be significant, the Earth itself would not "recoil" or move in response to this scenario.