A stream of water strikes a stationary turbine blade horizontally, as the drawing illustrates. The incident water stream has a velocity of +16.0 m/s, while the exiting water stream has a velocity of -16.0 m/s. The mass of water per second that strikes the blade is 41.0 kg/s. Find the magnitude of the average force exerted on the water by the blade.
To find the magnitude of the average force exerted on the water by the blade, we can use Newton's second law of motion, which states that force is equal to the rate of change of momentum.
The rate of change of momentum is given by the formula:
Force = ( momentum final - momentum initial ) / time.
In this case, the momentum of the water stream changes from its initial value to its final value when it hits the turbine blade. Since momentum is equal to mass multiplied by velocity, we can calculate the initial and final momentum of the water stream.
The initial momentum is given by:
Initial momentum = mass × initial velocity
The final momentum is given by:
Final momentum = mass × final velocity
The average force exerted on the water by the blade can then be calculated by subtracting the initial momentum from the final momentum and dividing by time.
Now let's plug in the given values:
Mass of water per second (m) = 41.0 kg/s
Initial velocity (v₁) = +16.0 m/s
Final velocity (v₂) = -16.0 m/s
Calculating the initial momentum:
Initial momentum = m × v₁
Initial momentum = 41.0 kg/s × +16.0 m/s
Calculating the final momentum:
Final momentum = m × v₂
Final momentum = 41.0 kg/s × -16.0 m/s
Calculating the average force:
Average force = (Final momentum - Initial momentum) / time
Since the time is not given in the problem, we cannot calculate the exact force without that information.