A cylindrical bucket containing freshwater is hanging from a scale in an elevator. A solid cube of mass 0.20kg and volume 1.6×10−4m3 is attached to a light string and held fully submerged at rest in the water. The elevator accelerates upward with magnitude 1.5ms−2. Take g=9.8ms−2 and water density ρw=1000kgm−3.
(a) Calculate the magnitude of the buoyant force exerted on the cube while the elevator accelerates upward. Show all steps in your calculation and include appropriate units.
(b) Determine the tension in the string while the elevator accelerates upward. Indicate direction as well as magnitude.
(c) The string is now cut while the elevator continues its upward acceleration. Calculate the initial acceleration of the cube relative to the elevator immediately after the string is cut. Explain your reasoning.
(d) Finally, imagine the elevator cable snaps and the bucket, water, and cube enter free fall together. What are the tension in the string and the apparent weight of the water as registered by the scale during free fall? Justify your answers.