Final answer:
A mass of 10 kilograms lifted 10 meters in 5 seconds produces the most power, amounting to 196 watts, as power is the work done divided by the time taken to do the work, and this scenario involves doing the greatest amount of work in the shortest amount of time.
Step-by-step explanation:
The question asks which action would produce the most power, comparing different scenarios of lifting masses over distances in certain periods. Power is defined as the work done per unit of time, where work is the product of force and distance. For lifting objects, the force involved is equivalent to the weight of the object, which is the mass times the acceleration due to gravity (9.8 m/s^2).
Let's calculate the power for each scenario given the formula: Power (P) = Work (W) / Time (t), where Work (W) = Force (F) * Distance (d), and Force (F) in this case is the weight of the mass.
A mass of 10 kilograms lifted 10 meters in 10 seconds: P = (10 kg * 9.8 m/s^2 * 10 m) / 10 s = 98 W
A mass of 5 kilograms lifted 10 meters in 5 seconds: P = (5 kg * 9.8 m/s^2 * 10 m) / 5 s = 98 W
A mass of 10 kilograms lifted 10 meters in 5 seconds: P = (10 kg * 9.8 m/s^2 * 10 m) / 5 s = 196 W
A mass of 5 kilograms lifted 5 meters in 10 seconds: P = (5 kg * 9.8 m/s^2 * 5 m) / 10 s = 24.5 W
Hence, a mass of 10 kilograms lifted 10 meters in 5 seconds would produce the most power, amounting to 196 watts.