AP Physics 1: Algebra-Based Unit 8: Fluids Practice Exam

1. [Skill: 2A | Topic: 8.1] A student measures the mass and volume of four samples at room conditions. The results are shown. Sample 1: mass = 120 g, volume = 150 cm^3 Sample 2: mass = 120 g, volume = 60 cm^3 Sample 3: mass = 200 g, volume = 250 cm^3 Sample 4: mass = 90 g, volume = 30 cm^3 Which sample has the greatest density?

2. [Skill: 1B | Topic: 8.1] Three substances are placed into identical open-top containers. Observations: • Substance X keeps its own shape when removed from the container. • Substance Y stays in the container but forms a level surface and takes the container’s shape. • Substance Z expands to fill the entire container and can be compressed noticeably when a piston is used. Which statement best identifies X, Y, and Z based on the microscopic interactions that determine macroscopic properties?

3. [Skill: 3A | Topic: 8.1] A student tests compressibility by trapping a sample in a sealed cylinder with a movable piston. The student records the volume as the external pressure is increased. [Image Cue]: Graph, "Volume vs. Pressure for Two Samples", x-axis: Pressure (kPa) from 100 to 400, y-axis: Volume (cm^3) from 40 to 80. Sample A line is nearly horizontal at about 60 cm^3 across the entire pressure range. Sample B line decreases from about 60 cm^3 at 100 kPa to about 45 cm^3 at 400 kPa. Which conclusion is best supported by the graph?

4. [Skill: 5A | Topic: 8.1] A model of an ideal fluid is used to predict the motion of fluid through a straight pipe. The model assumes the fluid is incompressible and has no viscosity. Which statement correctly contrasts this ideal-fluid model with real fluids such as water or air under everyday conditions?

5. [Skill: 4A | Topic: 8.1] An astronaut conducts two demonstrations in a spacecraft: Demonstration 1: A small amount of water released in the cabin forms a floating spherical droplet. Demonstration 2: Air released from a container spreads through the cabin. Based on the definition of a fluid, which claim is best supported?

6. [Skill: 2.A | Topic: 8.2] A student pushes straight down with a constant force of 20 N on two different surfaces. Surface 1 has area 2.0 cm^2. Surface 2 has area 0.20 cm^2. The force is always perpendicular to the surface. Which of the following best compares the pressure exerted on Surface 2 to the pressure exerted on Surface 1?

7. [Skill: 6.B | Topic: 8.2] A pressure sensor is placed in a large tank of water that is at rest. The sensor is rotated so that its sensing surface faces upward, sideways, and downward at the same location in the water. In all three orientations, the sensor reports the same pressure. Which of the following best explains why the pressure reading does not depend on the orientation of the sensor at that point in the fluid?

8. [Skill: 2.A | Topic: 8.2] A diver is at rest at a depth of 5.0 m below the surface of a lake. Assume the lake water is incompressible with density $\rho = 1.0 \times 10^3\ \mathrm{kg/m^3}$ and the atmospheric pressure at the surface is $P_{atm} = 1.01 \times 10^5\ \mathrm{Pa}$. Take $g = 9.8\ \mathrm{m/s^2}$. What is the absolute pressure of the water at the diver’s location?

9. [Skill: 5.B | Topic: 8.2] A student investigates how gauge pressure depends on depth in an unknown liquid. The student uses a pressure probe and records the gauge pressure at several depths. [Image Cue]: Data table, "Gauge Pressure vs Depth", columns labeled depth h (m) and gauge pressure P_gauge (Pa). Data points: (0.00 m, 0 Pa), (0.20 m, 1600 Pa), (0.40 m, 3200 Pa), (0.60 m, 4800 Pa). Assuming $g = 9.8\ \mathrm{m/s^2}$ and the liquid is incompressible, what is the best estimate of the liquid’s density?

10. [Skill: 1.A | Topic: 8.2] A container is open to the atmosphere and holds water at rest. The container has a wide section connected to a narrow vertical tube (an irregular shape), but the water is continuous throughout. Two points, A and B, are located in the water at the same vertical depth below the water’s surface. Point A is in the wide section; point B is in the narrow tube. [Image Cue]: Diagram, "Irregular Container with Two Points", showing an open container with a wide reservoir connected to a narrow vertical tube; a single horizontal dashed line at depth h below the free surface passes through both points A (wide side) and B (narrow tube). Which of the following best describes the absolute pressures $P_A$ and $P_B$ at points A and B?

11. [Skill: 2A | Topic: 8.3] A horizontal cylindrical pipe of constant cross-sectional area A contains a nonviscous fluid of density ρ. Consider a short cylindrical “plug” of fluid of length L inside the pipe. The pressure on the left face of the plug is P_L and the pressure on the right face is P_R, with P_L > P_R. Which expression best gives the acceleration of the fluid plug (magnitude and direction)?

12. [Skill: 5A | Topic: 8.3] A student fully submerges several objects in water and measures the volume of water displaced by each object. The density of water is 1000 kg/m^3 and g = 9.8 m/s^2. Table 1: Measured displaced volumes - Object X: V_disp = 2.5 × 10^-4 m^3 - Object Y: V_disp = 5.0 × 10^-4 m^3 What is the magnitude of the buoyant force on Object X while it is fully submerged?

13. [Skill: 6A | Topic: 8.3] A cube is held at rest while fully submerged in a fluid. The cube experiences fluid pressure on all of its faces. Which statement best explains the physical origin of the buoyant force on the cube?

14. [Skill: 2A | Topic: 8.3] A solid object of mass 0.80 kg and volume 6.0 × 10^-4 m^3 is released from rest while fully submerged in oil of density 900 kg/m^3. Neglect drag. Take g = 9.8 m/s^2. What is the object’s initial acceleration (magnitude and direction) immediately after release?

15. **1. [Skill: 2.A | Topic: 8.4]** Water (treated as an incompressible fluid) flows steadily through a horizontal pipe. At point 1 the pipe has cross-sectional area $A_1 = 6.0\times 10^{-4}\ \text{m}^2$ and the water speed is $v_1 = 2.0\ \text{m/s}$. Downstream at point 2 the pipe narrows to cross-sectional area $A_2 = 2.0\times 10^{-4}\ \text{m}^2$. Which of the following is the best prediction for the water speed $v_2$ at point 2?

16. **2. [Skill: 2.B | Topic: 8.4]** A Venturi tube (a pipe that narrows and then widens) carries water in steady flow. Point 1 is in the wider section and point 2 is in the narrow throat. The tube is horizontal, so $y_1 = y_2$. A student measures the speed in the throat to be greater than the speed in the wide section. Which of the following statements best describes the pressure comparison between the two points?

17. **3. [Skill: 2.A | Topic: 8.4]** A large tank is open to the atmosphere and is filled with water to a height of 1.20 m above the bottom. A small hole is made in the side of the tank at a point 0.20 m above the bottom. Assume the tank is large enough that the speed of the water surface is negligible. What is the approximate speed of the water as it exits the hole? Use $g = 9.8\ \text{m/s}^2$.

18. **4. [Skill: 4.A | Topic: 8.4]** Water flows steadily through a pipe that rises in elevation and narrows. Point 1: $A_1 = 4.0\times 10^{-4}\ \text{m}^2$, $y_1 = 0.00\ \text{m}$, pressure $P_1 = 180\ \text{kPa}$. Point 2: $A_2 = 2.0\times 10^{-4}\ \text{m}^2$, $y_2 = 1.0\ \text{m}$. The speed at point 1 is $v_1 = 3.0\ \text{m/s}$. Assume incompressible, nonviscous flow and take $\rho = 1000\ \text{kg/m}^3$ and $g = 9.8\ \text{m/s}^2$. What is the pressure $P_2$ at point 2 (approximately)?