a river does 6500J of work on a water wheel every second.The wheels efficiency is 12 percent.A)How much work in joules can the axle of the wheel do in a second? B)What is the power output of the wheel?
(A) 12% of 6500 J
That would be 780 J (per second).
(B)780 J/s (Watts)
John is using a pulley to lift the sail on his sailboat the sail weight 150 N , and he must lift it 4.0 m
a river does 6500J of work on a water wheel every second.The wheels efficiency is 12 percent.A)How much work in joules can the axle of the wheel do in a second? B)What is the power output of the wheel?
Assuming an ideal pulley system with zero friction, the work done by John to lift the sail is:
Work = force x distance
Work = 150 N x 4.0 m = 600 J
However, in reality, there will be some energy loss due to friction, so the actual work done by John will be slightly higher than 600 J.
To answer these questions, we need to understand the concepts of work, efficiency, and power.
Work (W) is the transfer of energy that occurs when a force is applied over a distance. It is measured in joules (J).
Efficiency (η) is a measure of how effectively a machine or device converts input energy into useful output energy. It is usually expressed as a percentage.
Power (P) is the rate at which work is done or energy is transferred. It is defined as the amount of work done per unit of time and is measured in watts (W), where 1 watt is equal to 1 joule per second (1 J/s).
Given information:
- The river does 6500 J of work on the water wheel every second.
- The wheel's efficiency is 12 percent.
Let's calculate the answers step by step:
A) How much work can the axle of the wheel do in a second?
Since we know the efficiency of the water wheel, we can calculate the output work by multiplying the input work by the efficiency:
Output work = Input work x Efficiency
Output work = 6500 J x 0.12 (12% = 0.12)
Output work = 780 J
Therefore, the axle of the wheel can do 780 joules of work in one second.
B) What is the power output of the wheel?
Power is the rate at which work is done, so we can calculate it by dividing the output work by the time taken:
Power = Output work / Time
Given that the output work is 780 J, we need the time taken for one second, so the time is 1 second.
Power = 780 J / 1 s
Power = 780 W
Therefore, the power output of the wheel is 780 watts.