A river does 6,500 J of work on a water wheel every second. The wheel's efficiency is 12%.
a. How much work in joules can the axle of the wheel do?
b. What is the power output of the wheel in 1 s?
To answer these questions, we need to use the concept of efficiency. Efficiency measures how much useful work is obtained from the input energy. It is expressed as a percentage.
The efficiency of the wheel is given as 12%, which means only 12% of the input energy is converted into useful work, while the rest is lost as waste heat or other forms of energy.
a. To find out how much work the axle of the wheel can do, we need to multiply the input work by the efficiency.
The equation for efficiency is:
Efficiency = output work / input work
Rearranging the equation, we can find the output work:
Output work = Efficiency * Input work
In this case, the input work is given as 6,500 J, and the efficiency is 12% or 0.12.
Output work = 0.12 * 6,500 J
Output work = 780 J
Therefore, the axle of the wheel can do 780 J of work.
b. The power output of the wheel can be calculated using the equation:
Power = Work / Time
Since we have already found the work done by the axle in part a (780 J), we can calculate the power output in 1 second.
Power = 780 J / 1 s
Power = 780 watts
Therefore, the power output of the wheel in 1 second is 780 watts.