A-LevelPhysicsOscillations9702/41 · Oct/Nov 2018 · Q37 Marks

A U-tube contains liquid, as shown in [Figure 3.1]. The total length of the column of liquid in the tube is L. The column of liquid is displaced so that the change in height of the liquid in each arm of the U-tube is x, as shown in [Figure 3.2]. The liquid in the U-tube then oscillates with simple harmonic motion such that the acceleration a of the column is given by the expression a = –(2g/L)x where g is the acceleration of free fall.

(a)Calculate the period T of oscillation of the liquid column for a column length L of 19.0 cm. T = .......................................................... s[3]
(b)(i)Suggest one cause of the damping.[1]
(b)(ii)Calculate the loss in total energy of the oscillations during the first 2.5 periods of the oscillations. energy loss = .......................................................... J[3]

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Mark scheme

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[C1] ω² = 2g / L
[C1] T = 2π/ω
[A1] ω² = (2 × 9.81)/0.19 = 103 (rad² s⁻²), so ω = 10.2 (rad s⁻¹), T = 2π/10.2 = 0.62 s
[B1] e.g. viscosity of liquid/friction within the liquid/viscous drag/friction between walls of tube and liquid
[C1] (maximum) KE = ½mv₀² and v₀ = ωx₀ or energy = ½mω²x₀²
[C1] change = ½ × 18 × 10⁻³ × 103 × [(2.0 × 10⁻²)² – (0.95 ×10⁻²)²]
[A1] = 2.9 × 10⁻⁴ J

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