Resumen de The Two-Bullet Problem with Constant Magnitude Drag Force
Jennifer Burris, Brooke Hester, Karl C. Mamola
It is common in introductory physics to show that in the absence of air drag an object dropped from rest will reach the level ground at exactly the same time as one that is projected horizontally from the same height.1 However, the situation is different in the presence of a speed-dependent drag force, as either object may hit first or they may hit at the same time. Drag force is quite complex, and the dependence of the drag force on speed is related to a number of factors, some of which are beyond the scope of this paper. Here we specifically discuss the cases of drag forces with a magnitude dependent on an integer power (2, 1, and 0) of the speed v, as these are suitable for study in introductory courses.
If the magnitude of the drag force is dependent on the square of the object’s speed, which is generally the case for objects subject to air resistance in the teaching lab, it’s fairly easy to show that the dropped object is expected to reach the ground first.2 There is experimental evidence that this is in fact the case.3,4 On the other hand, if the drag force is dependent on the first power of the object’s speed, the two objects are expected to fall at exactly the same rate, just as in the case of no drag force.2,3 This would be difficult to test experimentally. A situation with a sufficiently low Reynolds number would likely require that the objects move in a liquid. Furthermore, it would be impossible to show that the fall times are exactly the same; one could only set an upper limit on the time difference.
It occurred to us that there is another form for the drag force that is straightforward to examine both theoretically and in the lab. That is the case of a constant magnitude drag force (one dependent on the zeroth power of the objects’ speed). For example, this occurs when the drag force is due to sliding friction. That situation is the subject of this paper.
