A researcher investigates the depth ddd below a water surface reached by a cylindrical test probe when dropped from a height hhh above the water surface. The probe is modeled as a uniform cylinder.
The cylinder has mass 6.0×10−3 kg6.0 \times 10^{-3}\text{ kg}6.0×10−3 kg, diameter 1.2×10−2 m1.2 \times 10^{-2}\text{ m}1.2×10−2 m, and length 8.0×10−2 m8.0 \times 10^{-2}\text{ m}8.0×10−2 m.
Calculate the density of the cylinder's material.
Suggest why a material with this density is appropriate to model a floating body such as a diver or a surface probe.
The cylinder is released from rest. The lowermost end of the cylinder is originally at a height h=0.45 mh = 0.45\text{ m}h=0.45 m above the water surface. Calculate the speed of the cylinder just before it hits the water. (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 depth ddd reached for different initial drop heights hhh is shown below:
The researcher needs to double the drop height of the probe from 0.2 m0.2\text{ m}0.2 m to 0.4 m0.4\text{ m}0.4 m. He claims that the depth of the test tank must also be doubled. Use the graph to explain whether you agree with this claim.
