To find the magnitude of the average force exerted on the water by the blade, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, provided no external forces are acting on the system.
In this case, the system consists of the water stream and the turbine blade before and after the interaction. Since there are no external forces acting on the system, the initial momentum of the water stream must be equal to the final momentum of the water stream and the blade.
The momentum, p, is defined as the product of an object's mass, m, and its velocity, v. So, we have:
Initial momentum = Final momentum
(mass of water stream x initial velocity of water stream) = (mass of water stream x final velocity of water stream) + (mass of turbine blade x velocity of turbine blade)
Let's calculate the momentum of the water stream before and after the interaction:
Initial momentum of water stream = (mass of water per second x initial velocity of water stream)
= (36.0 kg/s) x (+18.0 m/s)
= 648 kg路m/s (momentum in the positive direction)
Final momentum of water stream = (mass of water per second x final velocity of water stream)
= (36.0 kg/s) x (-18.0 m/s)
= -648 kg路m/s (momentum in the negative direction)
Let's assume the mass of the turbine blade is M, and its velocity is V. Therefore, the final momentum of the water stream and the blade is (M + 36.0) x V.
Now, applying the principle of conservation of momentum:
648 kg路m/s = -648 kg路m/s + (M + 36.0 kg/s) x V
Simplifying the equation:
2(648 kg路m/s) = (M + 36.0 kg/s) x V
1296 kg路m/s = (M + 36.0 kg/s) x V
Now, we need to calculate the magnitude of the average force exerted on the water by the blade. This can be done by using Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (螖p) with respect to time (螖t).
Since we know the mass flow rate of the water stream is 36.0 kg/s, the change in momentum 螖p = mass flow rate x change in velocity of water stream = (36.0 kg/s) x [(-18.0 m/s) - (+18.0 m/s)] = -36.0 kg路m/s
As the water stream hits the blade, its momentum changes by -36.0 kg路m/s. Assuming this change in momentum happens over a time interval 螖t, we can express the force as:
Force (F) = Change in momentum (螖p) / Time interval (螖t)
To calculate the average force, we need to find the change in momentum divided by the time it takes for the change to occur.
However, since the problem does not provide information about the time interval, we cannot calculate the specific value of the magnitude of the average force exerted on the water by the blade without knowing the time interval.