(10%) Problem 2: A section of uniform pipe is bent into an upright shape and par
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Question
(10%) Problem 2: A section of uniform pipe is bent into an upright 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 = 0.019 m. The radius of curvature of the curved part of the U is R = 0.15 m. When the water is not oscillating, the depth of the water in the straight sections is d= 0.37 m. ©theexpertta.com 20% Part (a) Enter an expression for the mass of water in the tube, in terms of the defined quantities and the density of water, p. Use the approximation rExplanation / Answer
(A) length of tube on 1 side.
L = d + (pi R / 2)
total length = 2 d + pi R
volume = pi r^2 (2 d + pi R)
mass = rho pi r^2 (2 d + pi R)
(B) m= (1000) (pi x 0.019^2) (2x0.37 + pi 0.15)
m = 1.374 kg
(C) suppose its is dispalced by distance x then,
F = rho pi r^2 ((L + x ) - (L - x)) g
F = 2 rho pi r^2 g x
k = 2 rho pi r^2 g
(d) k = 2 x 1000 x pi x 0.019^2 x 9.81 = 22.25 N/m
(e) T = 2 pi sqrt(m/k) =1.56 sec
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