Objects A and B are made of the same material with a density of [rho1] kg/m³. Object A is fully submerged in an unknown liquid, and object B is placed on top of A such that only a fraction [f] of object B is submerged. Given that the density of the unknown liquid is [rho2] kg/m³ and the volume of object B is [vB] m3, determine the volume (in m³) of object A.
Read DetailsA 0.45 kg mass is resting on a vertically oscillating platform. The platform undergoes simple harmonic motion. The displacement-time graph of the platform’s motion is shown in the figure. t2= [t2] s. Determine the maximum oscillation amplitude that allows the mass to stay in contact with the platform at all times. [Hint: the supporting (normal) force becomes zero when the mass is about to lose contact with the platform. Consider that the maximum force in SHM is Fmax = m × amax.]
Read DetailsA [L] m long string of a musical instrument has a mass of [m] kg. When the string resonates, it forms a standing wave. The figure shows a snapshot of the standing wave at t = 0. The resulting sound wave in the surrounding air has a wavelength of [lamda] m. Calculate the tension in the string (in Newtons) required to sustain this vibration. The speed of sound wave in air is 340 m/s.
Read DetailsA 2.2 kg mass is attached to a horizontal, massless, ideal spring with a spring constant of 30 N/m. The system undergoes simple harmonic motion, and its velocity-time graph is shown in the figure. v0 = [v0] m/s and t2= [t2] s. Determine the amplitude (A) of oscillation in meters.
Read DetailsA solid cube with a side length of [L] m is completely submerged in an oil-filled container and suspended from a scale by a cable. The density of the cube is [rho2] kg/m³, and the density of the oil is [rho1] kg/m³. What is the reading on the scale (apparent weight) when the cube is fully submerged in the oil? Express your answer in newtons (N).
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