Air (ρ = 1.23 kg m−3 ) leaving a 3-cm-diameter pipe strikes a plate that can rotate about a pivot. The force exerted on the plate by the air jet is counteracted by a spring. When the velocity of the air jet leaving the pipe is 50 m s−1 , the plate is perfectly vertical and the spring is displaced from its equilibrium position by 2 cm. The spring is attached to the plate 1.5 cm above the pivot, and the center of the air jet strikes the plate 2 cm below the pivot. The air jet maintains a constant area between the pipe and the plate, the force exerted by the air jet is evenly distributed across its area, and the pressure inside the free air jet is equal to atmospheric pressure. Using this information, determine the spring constant.
Air (ρ = 1.23 kg m−3 ) leaving a 3-cm-diameter pipe strikes a plate that can rotate about a pivot. The force exerted on the plate by the air jet is counteracted by a spring. When the velocity of the air jet leaving the pipe is 50 m s−1 , the plate is perfectly vertical and the spring is displaced from its equilibrium position by 2 cm. The spring is attached to the plate 1.5 cm above the pivot, and the center of the air jet strikes the plate 2 cm below the pivot. The air jet maintains a constant area between the pipe and the plate, the force exerted by the air jet is evenly distributed across its area, and the pressure inside the free air jet is equal to atmospheric pressure. Using this information, determine the spring constant.
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