A section of uniform pipe is bent into an upright U shape and partially filled with water, which can then oscillate back and forth in simple harmonic motion. The inner radius of the pipe is r = 0.024 m. The radius of curvature of the curved part of the U is R = 0.23 m. When the water is not oscillating, the depth of the water in the straight sections is d = 0.37 m. Enter an expression for the mass of water in the tube, in terms of the defined quantities and the density of water, ρ. Use the approximation r << R. Calculate the mass of the water, in kilograms. Take ρ = 1000 kg/m3. Enter an expression for the force constant of the U-shaped column of water when displaced from equilibrium, in terms of the defined quantities, ρ, and g. This constant is analogous to the spring constant in Hooke’s law. Find the value of the force constant, in newtons per meter. Take ρ = 1000 kg/m3 and g = 9.81 m/s2. Calculate the period of oscillation, in seconds.
A section of uniform pipe is bent into an upright U shape and partially filled with water, which can then oscillate back and forth in
Enter an expression for the mass of water in the tube, in terms of the defined quantities and the density of water, ρ. Use the approximation r << R.
Calculate the mass of the water, in kilograms. Take ρ = 1000 kg/m3.
Enter an expression for the force constant of the U-shaped column of water when displaced from equilibrium, in terms of the defined quantities, ρ, and g. This constant is analogous to the spring constant in Hooke’s law.
Find the value of the force constant, in newtons per meter. Take ρ = 1000 kg/m3 and g = 9.81 m/s2.
Calculate the period of oscillation, in seconds.
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