A horizontal water jet from a nozzle of constant exit cross section impinges normally on a stationary vertical flat plate. A force F is required to hold the plate against the water stream. If the water velocity is doubled, the necessary holding force F…
Question
A horizontal water jet from a nozzle of constant exit cross section impinges normally on a stationary vertical flat plate. A force F is required to hold the plate against the water stream. If the water velocity is doubled, the necessary holding force F…
Solution
The force required to hold the plate against the water stream is directly related to the momentum of the water jet. The momentum of an object (in this case, the water jet) is given by the product of its mass and velocity.
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If the velocity of the water is doubled, the momentum of the water jet will also double. This is because the mass of the water jet remains constant (since the exit cross section of the nozzle is constant), so if you double the velocity, you double the momentum.
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The force required to hold the plate against the water stream is equal to the change in momentum of the water jet per unit time. Since the water jet is hitting the plate and coming to a stop, the change in momentum is equal to the initial momentum of the water jet.
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Therefore, if the momentum of the water jet doubles (because the velocity is doubled), the force required to hold the plate against the water stream will also double.
So, if the water velocity is doubled, the necessary holding force F will also be doubled.
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