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A frictionless pulley has the shape of a uniform solid disk…

A frictionless pulley has the shape of a uniform solid disk with a mass of 4 kg and a radius of 0.2 m. A box of mass 4 kg is attached to a very light string that is wrapped around the rim of the pulley. The system is released from rest. Determine the magnitude of the linear acceleration of the box in m/s².

A 0.45 kg mass is resting on a vertically oscillating platfo…

A 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.]

An enclosed container is filled with an unknown gas, an unkn…

An enclosed container is filled with an unknown gas, an unknown liquid, and water. h1= [h1] m and h2 = [h2] m. Given that the density of the unknown liquid is 780 kg/m³, the density of water is 1000 kg/m³, and the pressure of the gas is Pgas = [Pgas] × 104 Pa, determine the pressure at the bottom of the container in Pa.