There are three forces acting on debris. First, the gravity that pulls downward (Fg) due to interaction with the Earth. This force depends on both the object’s mass (m) and the gravitational field (g = 9.8 Newtons/kg on Earth).
Then the buoyancy (Fb). When an object is immersed in water (or other liquid), an upward force is generated from the surrounding water. The magnitude of this force is proportional to the volume of the object, as it is equal to the weight of the water being displaced. Note that both gravity and buoyancy depend on the size of the object.
Finally, the drag force (Fd) by interaction between moving water and bodies. This force depends on both the size of the object and its velocity relative to the water. Stoke’s Law can be used to model the magnitude of drag (not to be confused with air resistance in water) according to the following equation:
In this equation, R is the radius of the spherical object, μ is the kinematic viscosity, and v is the velocity of the fluid relative to the object. The kinematic viscosity value in water is approximately 0.89 x 10.-3 kilograms/meters/second.
Now you can model the movement of rocks and pieces of gold in moving water. There is one small problem though. According to Newton’s second law, the net force on an object changes its velocity, but if the velocity changes, so does the force.
One way to deal with this problem is to divide the motion of each object into smaller time intervals. We can assume that the net force is constant during each interval (which is almost true). Using a constant force allows us to find the velocity and position of the object at the end of the interval. Then just repeat the same process at the next interval.