Suggests that some of the data should be removed before analyzing the drag data set. Redo Exercise 6.27 after removing this data.
Construct a plot that reveals a likely systematic problem with the drag (see Exercise 6.27) data set. Speculate about a potential cause for this.
In the absence of air resistance, a dropped object will continue to accelerate as it falls. But if there is air resistance, the situation is different. The drag force due to air resistance depends on the velocity of an object and operates in the opposite direction of motion. Thus as the object's velocity increases, so does the drag force until it eventually equals the force due to gravity. At this point the net force is 0 and the object ceases to accelerate, remaining at a constant velocity called the terminal velocity. Now consider the following experiment to determine how terminal velocity depends on the mass (and therefore on the downward force of gravity) of the falling object. A helium balloon is rigged with a small basket and just the right ballast to make it neutrally buoyant. Mass is then added and the terminal velocity is calculated by measuring the time it takes to fall between two sensors once terminal velocity has been reached. The drag data set contains the results of such an experiment conducted by some undergraduate physics students. Mass is measured in grams and velocity in meters per second. (The distance between the two sensors used for determining terminal velocity is given in the height variable.) Determine which of the following "drag laws" matches the data best:
- Drag is proportional to velocity.
- Drag is proportional to the square of velocity.
- Drag is proportional to the square root of velocity.
- Drag is proportional to the logarithm of velocity.