Final answer:
To find the work done on the mouse by air resistance, we calculate the difference between the lost gravitational potential energy and the final kinetic energy, which yields approximately 190 J. As this is not an option, we select the closest available choice, 180 J.
Step-by-step explanation:
The question asks how much work is done on a mouse by air resistance as it falls down a vertical mine shaft and lands at a certain speed. To find this, we use the work-energy principle which states that the work done by all forces is equal to the change in kinetic energy. Since we know the final speed of the mouse and its mass, we can calculate its final kinetic energy. The initial kinetic energy is zero since the mouse starts from rest.
The gravitational potential energy lost by the mouse as it falls is given by mg, where m is the mass, g is the acceleration due to gravity (9.8 m/s2), and h is the height of the fall. For a mass of 0.200 kg (200 g) and a height of 100 m, this is 0.200 kg × 9.8 m/s2 × 100 m = 196 Joules (J). The final kinetic energy is (/2) × v2, where v is the final velocity. With a velocity of 8.0 m/s, this comes to (0.200 kg/2) × (8.0 m/s)2 = 6.4 J.
The work done by air resistance is the difference between the potential energy lost and the final kinetic energy. So, the work done by air resistance is 196 J - 6.4 J = 189.6 J, which rounds up to 190 J, but since that is not an option given, we must consider the closest available choice, which is 180 J (option b).