Introduction

          The goal of our project was to analyze the behavior of high-speed pellets traveling through a bi-layered suspension of oil and water. Our hopes were to see the effect of the interface between the oil and water on the deceleration of the pellet.

          To see the effect of the interface, we would need to analyze two different subjects: a pellet going through a tank of water, and a pellet going through a tank with layers of oil and water. We could then use physics to determine the effect of the interface.  This is similar to work done by Matthew Hinshaw ¹ who did work with pellets traveling through water alone.

Theory

          The deceleration of an object due to drag is dependent on the velocity of the object through the substance that is acting as the drag medium. This is why cars have a top speed, the force of the tires can no longer overcome the force of the drag made by the air; balancing the forces and resulting in a steady velocity. In the case of a high-speed pellet the very small time interval we are observing within makes the force of gravity negligible.  Thus, we can say that only the drag force is acting upon the pellet.

          As deceleration is dependent on velocity, then as the liquids slow the pellet, the rate at which it slows, or decelerates, also decreases. The change in deceleration can be determined using several factors; the force of gravity, velocity, and a constant that varies depending on the drag medium. This constant is what we used to determine the effect of the interface. In the case of gravity, the small mass of the pellet and high velocity make weight a negligible factor, leaving velocity - which we can determine from our photos – and the drag constant, which we can determine from several measurements in our photos.

          To determine whether or not there is some effect associated with passing through the interface between the liquids, we look for deviation from the theoretical fit, or a change in the constant K, which we will define shortly. If the drag constant is the same between the tank of water, and the water portion of the dual liquid tank, then we can see that there is no effect. However, if the constant changes, we can infer that the interface has some effect.

                                    We know that the drag force is proportional to the square of velocity.

                              Because F=ma, the mass of our pellets is constant, and we ignore the gravitational force, we can say that the acceleration is equal to some constant, K, multiplied by the square of velocity.

                            Definition of acceleration

                    Separate variables and integrate from initial to final velocity.

                         Equation for velocity

                        Definition of velocity

                        Separate variables and integrate from initial to final position.             

                Final equation for position