Students are given a large container holding a fixed volume of an unknown liquid. They are asked to determine the density of the liquid, but have no measuring equipment. Students are then given samples of four solids with known mass, volume, and density. Data for these four regularly shaped samples, and whether they sank or floated when placed in the unknown liquid, are shown below.

Based on this data, which of the following is the most likely density of the unknown liquid?

Two identical containers, 1 and 2, hold different volumes of the same ideal fluid. Container 2 holds twice the fluid volume of container 1. A pressure sensor is used to measure the gauge pressure $P$ of each fluid at different vertical distances $h$ below the surface of the fluid. The graph of $P$ vs $h$ for container 2 is shown below:

Which of the following correctly depicts the $P$ vs $h$ graph for container 1?

Questions 3 and 4 refer to the following.

A hospital patient is receiving intravenous (IV) fluids. The IV fluid flows from a raised cylindrical container, down through a thin tube, to a patient’s arm. The cylindrical container has a radius $r$ = 0.10m, and the IV fluid has a density $\rho$ = 1020 kg/m³. The depth of the fluid in the container is $d$, and it decreases over time as the IV fluid flows to the patient. The bottom of the fluid container hangs a distance of $L$ = 0.40 meters above the patient’s arm.

Hospital staff must be alerted if the fluid depth in the container, $d$, reaches 0.02 meters so they can replace it with a new full container. A pressure sensor is placed at the bottom of the thin tube near the patient’s arm.

What will the pressure sensor reading be when the bag needs to be replaced?

*Use $g$ = 10 m/s²

A hospital patient is receiving intravenous (IV) fluids. The IV fluid flows from a raised cylindrical container, down through a thin tube, to a patient’s arm. The cylindrical container has a radius $r$ = 0.10m, and the IV fluid has a density $\rho$ = 1020 kg/m³. The depth of the fluid in the container is $d$, and it decreases over time as the IV fluid flows to the patient. The bottom of the fluid container hangs a distance of $L$ = 0.40 meters above the patient’s arm.

Hospital staff must be alerted if the fluid depth in the container, $d$, reaches 0.02 meters so they can replace it with a new full container. A pressure sensor is placed at the bottom of the thin tube near the patient’s arm.

A nurse replaces an empty IV fluid container with a full container. The initial pressure reading at the bottom of the thin tube near the patient’s arm is 6.12 kPa.  What is the initial Volume of the IV fluid in the container?

*Use $g$ = 10 m/s²

Two identical cylinders, labeled A and B, each of height $H$ and radius $R$ are filled completely with water. Tight-fitting pistons are placed in contact with the fluid at the top of each cylinder; the mass of the piston is negligible compared to the mass of the fluid in the cylinder. Next, different numbers of blocks, each of mass $m$ are added to the top of the cylinders as shown in the diagram. The mass of the fluid in each container is $\frac{2}{3} m$.

How does the pressure at the bottom of Cylinder B compare to the pressure at the bottom of Cylinder A?

A toy boat of mass $m$ displaces a total water volume of 2V_o as it floats on the water. How much additional mass would you need to add to the boat so that it displaced a total water volume of 3V_o while still floating?

Questions 7 and 8 refer to the following.

A small balloon is attached to the bottom of an aquarium using a rope. The balloon stays at a constant height above the base of the water filled tank. The rope exerts a Tension force F_T on the balloon, the balloon has an average density $\rho_B,$ the water has a density $\rho_W,$ the balloon occupies a volume $V_B$, and $g$ is the acceleration due to gravity near the Earth’s surface. Which of the following correctly describes the forces acting on the balloon as it maintains this height in the water?

Which of the following would increase the size of the buoyant force acting on the balloon?

A teacher gives a group of students some data from an experiment that was used to determine the mass of an unknown solid. Data points were collected using a force probe, a graduated cylinder, and a known amount of water. The experimental setup is shown in the picture above. The teacher only gives data from when the solid was partially submerged, not completely submerged. The data collected are shown in the graph above.

Using the data, determine the mass of the block.

A plastic cylindrical container is filled with water. A hole is made in the side of the cylinder so that water is free to escape. The water initially follows the parabolic path shown in the diagram above. The distance, $d$, from the edge of the cylinder to where the water lands, the water height, $h$, above the hole, and the exit velocity, $v$, will all change as water flows from the hole. Which of the following relationships will produce a linear graph for this scenario?