A river does 6,500 j of work on a water wheel every second. The wheel 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?
6,500 J x 0.12 = ?
B. 1 J/s = 1 watt.
780 J/s
To find the answers to these questions, we'll need to use the formulas for work and power.
A. The work done by the river on the water wheel is given as 6,500 J per second. The efficiency of the wheel is given as 12%. To find the work the axle of the wheel can do (W_axle), we can use the formula:
W_axle = W_river / efficiency
where W_river is the work done by the river on the water wheel.
Substituting the given values, we have:
W_axle = 6,500 J / 0.12
Calculating this, we find:
W_axle ≈ 54,167 J
Therefore, the axle of the wheel can do approximately 54,167 Joules of work.
B. The power output of the wheel can be calculated using the formula:
P = W / t
where P is the power, W is the work, and t is the time.
In this case, we are given that the work done by the river is 6,500 J per second. So, the power output (P) of the wheel in 1 second would be equal to the work done:
P = 6,500 J
Therefore, the power output of the wheel in 1 second is 6,500 watts (J/s).