A stream of water strikes a stationary turbine blade, as the drawing illustrates. The incident water stream has a velocity of +18.0 m/s, while the exiting water stream has a velocity of -18.0 m/s. The mass of water per second that strikes the blade is 73.0 kg/s. Find the magnitude of the average force exerted on the water by the blade.
N
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 momentum of an object is given by the product of its mass and velocity:
Momentum = mass x velocity
In this case, the water stream has an incident velocity of +18.0 m/s and an exiting velocity of -18.0 m/s. The mass of water per second that strikes the blade is 73.0 kg/s.
We can calculate the change in momentum per second as follows:
Change in momentum = mass x (exiting velocity - incident velocity)
= 73.0 kg/s x (-18.0 m/s - (+18.0 m/s))
= 73.0 kg/s x (-36.0 m/s)
= -2636.0 kg·m/s (note the negative sign)
The negative sign indicates that the change in momentum is in the opposite direction of the incident velocity.
Now, we can calculate the force exerted on the water by the blade using Newton's second law:
Force = rate of change of momentum
= change in momentum / time
Since the change in momentum is per second and the question asks for the magnitude of the average force, we can assume that the change in momentum occurs over 1 second.
Therefore, the magnitude of the average force exerted on the water by the blade is:
Force = |change in momentum|
= |-2636.0 kg·m/s|
= 2636.0 N
Hence, the magnitude of the average force exerted on the water by the blade is 2636 N.
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 states that the change in momentum of an object is equal to the net external force acting on it multiplied by the time interval over which the force was applied.
In this case, we can consider the water stream as the object. The change in momentum of the water stream is equal to the mass of water per second multiplied by the change in velocity. The mass of water per second is given as 73.0 kg/s.
The change in velocity can be calculated by subtracting the initial velocity (-18.0 m/s) from the final velocity (+18.0 m/s):
Change in velocity = final velocity - initial velocity
Change in velocity = (+18.0 m/s) - (-18.0 m/s)
Change in velocity = 36.0 m/s
Next, we can calculate the change in momentum:
Change in momentum = mass of water per second * change in velocity
Change in momentum = (73.0 kg/s) * (36.0 m/s)
Change in momentum = 2628.0 kg·m/s
Now, we can calculate the average force exerted on the water by the blade. The average force can be calculated by dividing the change in momentum by the time interval over which the force was applied.
Since the problem does not provide any information about the time interval, we assume that it is one second (Δt = 1s).
Average force = change in momentum / time interval
Average force = 2628.0 kg·m/s / 1s
Average force = 2628.0 N
Therefore, the magnitude of the average force exerted on the water by the blade is 2628.0 N.