An oceanographic laboratory is testing a new cylindrical micro-pinger designed to monitor deep-ocean currents. The micro-pinger is modeled as a uniform solid cylinder. It is dropped vertically from a stationary drone into a tank containing silicone oil of density 960 kg m−3960\text{ kg m}^{-3}960 kg m−3.
The cylinder has mass 1.4×10−2 kg1.4 \times 10^{-2}\text{ kg}1.4×10−2 kg, diameter 1.8×10−2 m1.8 \times 10^{-2}\text{ m}1.8×10−2 m, and length 9.5×10−2 m9.5 \times 10^{-2}\text{ m}9.5×10−2 m.
Calculate the density of the cylinder's material.
Suggest why a material with this density is appropriate for modeling an oceanographic buoy or similar float.
The cylinder is released from rest. The lowermost end of the cylinder is originally at a height h=0.80 mh = 0.80\text{ m}h=0.80 m above the oil surface. Calculate the speed of the cylinder just before it hits the oil. (Take g=9.81 m s−2g = 9.81\text{ m s}^{-2}g=9.81 m s−2 and ignore air resistance.)
Describe the three forces acting on the cylinder when it is fully submerged and moving vertically downwards before coming to rest. State their directions.
Describe and explain how the resultant force on the cylinder varies from the moment it is fully submerged until it reaches its deepest point.
A graph of the experimental data showing the maximum penetration depth DDD reached in the oil for different initial drop heights hhh is shown below:
The laboratory technician needs to double the drop height of the probe from 0.3 m0.3\text{ m}0.3 m to 0.6 m0.6\text{ m}0.6 m. He claims that the depth of the test tank must also be doubled to prevent the probe from hitting the bottom.
Use the graph to explain whether you agree with this claim.
