There are three forces acting on the debris. First, there is the downward pull of gravity (F_{G}) due to its interaction with the Earth. This force depends on both the mass (m) of the object and the gravitational field (g = 9.8 newtons per kilogram on Earth).

Next, we have the driving force (F_{B}). When an object is submerged in water (or any other liquid), there is a buoyant force from the surrounding water. The magnitude of this force is equal to the weight of the displaced water, so it is proportional to the volume of the object. Note that both gravity and buoyancy depend on the size of the object.

Finally, we have a drag force (F_{D}) due to the interaction between the moving water and the object. This force depends on both the size of the object and its relative speed with respect to the water. We can model the magnitude of the drag force (in water, not to be confused with air resistance) using Stoke’s lawaccording to the following equation:

In this expression, R is the radius of the spherical object, μ is the dynamic viscosity, and v is the velocity of the fluid relative to the object. In water, the dynamic viscosity has a value of about 0.89 x 10^{-3} kilograms per meter per second.

Now we can model the motion of a rock versus the motion of a piece of gold in moving water. However, there is a small problem. According to Newton’s second law, the net force on an object changes the speed of the object, but as the speed changes, so does the force.

One way to deal with this problem is to break each object’s motion into small time intervals. During each interval, I can assume that the net force is constant (which is roughly true). With a constant force I can then find the speed and position of the object at the end of the interval. Then all I have to do is repeat the same process for the next interval.