Question

8(a)(i). State the reason why simple harmonic motion is periodic.
8(a)(ii). State two factors affecting the period of oscillation of a simple pendulum.
8(a)(iii). Sketch a graph of the total mechanical energy, E, against displacement, y, for the motion of a simple pendulum from one extreme position to the other.
8(b). The diagram below illustrates an oscillatory pendulum. Calculate the workdone in raising the pendulum to point B, if the mass of the bob is 50g. [g=10ms⁻²]
8(c). A spiral spring of spring constant, k, and natural length, l, has a scale pan of mass 0.04kg hanging on its lower end while the upper end is firmly fixed to a support. When an object of mass 0.20 kg is placed on the scale pan, the length of the spring becomes 0.055 m and when the object is replaced with another object of mass 0.28 kg, the length of the spring becomes 0.6 m. Calculate the values of k and l. [g=10 ms⁻²]

Accepted Answer

(a)(i) Simple harmonic motion is periodic due to the balance between the restoring force and the inertial force or weight of the oscillating body.
(ii) Factors affecting the period of oscillation of a simple pendulum: length of the pendulum; acceleration due to gravity.
(iii) The graph of total mechanical energy E against displacement y is a horizontal straight line (constant), since total energy (KE+PE) remains constant throughout SHM, while kinetic energy and potential energy vary in a complementary sinusoidal manner between the extremes.

(b) Workdone = mgl(1-cosθ) = 0.05×10×0.6×(1-cos60°) = 0.05×10×0.6×(1-0.5) = 0.15 J.

(c) Using Hooke's law with the two given loads and extensions, and solving the resulting simultaneous equations: k=80 Nm⁻¹ and l=0.0025 m (i.e. l₀=0.0025m, before adding e₁=0.055-0.0025 and e₂=0.6-0.0025 as the extensions for each load).

WAEC Physics 2023 Theory — Question 8

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