Final answer:
The work done on debris by air resistance as it falls down a vertical mine shaft is 189.6 joules, calculated by finding the difference between the initial potential energy and the final kinetic energy.
Step-by-step explanation:
To determine the work done on the debris by air resistance as it falls down the mine shaft, we need to apply the principles of work, kinetic energy, and potential energy. Initially, the debris has potential energy due to its height above the bottom of the shaft. As it falls and gains speed, this potential energy is converted into kinetic energy. However, by the time it reaches the bottom, it has less kinetic energy than expected because air resistance has done work against it, effectively 'using up' some of the potential energy.
The initial potential energy (Ui) is given by Ui = mgh, where m is mass, g is the acceleration due to gravity, and h is the height. The kinetic energy (Kf) at the bottom is given by Kf = ½mv², where v is the velocity. The work done by air resistance is then the difference between the initial potential energy and the final kinetic energy: Workair = Ui - Kf.
Let's calculate:
Therefore, the air resistance does 189.6 joules of work on the debris during its fall.