Density & Pressure (College Board AP® Physics 1: Algebra-Based): Exam Questions

Figure 1

A group of students are given a cylindrical container half filled with a liquid of unknown density $\rho$. The students have access to an additional container with more of the same liquid, meter sticks, and a pressure sensor. They do not have access to a scale.

i) Indicate quantities that could be measured by the students that would allow them to determine the density of the liquid using a linear graph.

ii) Briefly describe a method to reduce experimental uncertainty for the measured quantities.

i) Indicate what quantities students could graph on the horizontal and vertical axes to create a linear graph that can be used to determine the density of the liquid.

ii) Briefly describe the relationship between the density of the liquid and a feature of the graph from part b)i). Your answer may include an equation that relates the density of the liquid and the chosen feature of the graph.

A group of students are given a beaker with a spout and several irregular objects made from the same material. They also have access to a ruler, a scale, a measuring cylinder and a supply of water.

Students are asked to take measurements to create a graph that could be used to determine the density of the material.

i) Indicate quantities that could be measured by the students that would allow them to determine the density of the material using a linear graph.

ii) Briefly describe a method to reduce experimental uncertainty for the measured quantities.

i) Indicate what quantities students could graph on the horizontal and vertical axes to create a linear graph that can be used to determine the density of the material.

ii) Briefly describe the relationship between the density of the material and a feature of the graph from part b)i). Your answer may include an equation that relates the density of the material and the chosen feature of the graph.

Figure 1

In Figure 1, two containers of different shapes are filled to the top with the same fluid with density $\rho$.

Indicate whether $P_A$ is greater than, less than, or equal to $P_B$. Justify your reasoning using qualitative reasoning beyond referencing equations.

Points A and B are both a distance $d$ above the bottom of their containers.

Determine an expression for the difference between $P_A$ and $P_B$. Give your expression in terms of $H_A$, $H_B$, $\rho$ and physical constants as appropriate.