There are three forces acting on the rubble. First, the downward gravitational force (Fg) in consequence of interaction with the Earth. This force relies on each the mass (m) of the thing and the gravitational field (g = 9.8 newtons per kilogram on Earth).
Then we have now the buoyant force (Fb). When an object is submerged in water (or any fluid), there may be an upward pushing force from the encircling water. The magnitude of this force is the same as the burden of the displaced water, so it’s proportional to the amount of the thing. Note that each the gravitational force and the buoyant force rely on the scale of the thing.
Finally, we have now the force of resistance (Fd) as a consequence of the interaction between the moving water and the thing. This force relies on each the scale of the thing and its relative speed relative to the water. We can model the magnitude of the drag force (in water, to not be confused with air resistance) with Stoke’s lawbased on the next equation:
Illustration: Rhett Allain
In this expression, R is the radius of the spherical object, μ is the dynamic viscosity, and v is the speed of the fluid relative to the thing. In water, the dynamic viscosity is roughly 0.89 x 10-3 kilograms per meter per second.
Now we will model the movement of the rock versus the movement of a bit of gold in moving water. However, there may be one small problem. According to Newton’s second law, the online force on an object changes its speed—but because the speed changes, so does the force.
One method to cope with this problem is to divide each object’s motion into small time intervals. During each interval I can assume that the resultant force is constant (which is roughly true). Given a relentless force, I can then find the speed and position of the thing at the tip of the interval. Then just repeat the identical process for the subsequent interval.
