Pressure AP Physics 1 FRQ – Exam Style Questions etc.
Pressure AP Physics 1 FRQ
Unit 8: Fluids
Weightage : 10-15%
Exam Style Practice Questions,Pressure AP Physics 1 FRQ
Question: (12 points, suggested time 25 minutes)
A group of students design an experiment to investigate the relationship between the density and pressure of a sample of gas at a constant temperature. The gas may or may not be ideal. They will create a graph of density as a function of pressure. They have the following materials and equipment.
- A sample of the gas of known mass Mg in a sealed, clear, cylindrical container, as shown
- above, with a movable piston of known mass mp
- A collection of objects each of known mass mo
- A meterstick
(a)
i. Describe the measurements the students should take and a procedure they could use to collect the data needed to create the graph. Specifically indicate how the students could keep the temperature constant. Include enough detail that another student could follow the procedure and obtain similar data.
ii. Determine an expression for the absolute pressure of the gas in terms of measured quantities, given quantities, and physical constants, as appropriate. Define any symbols used that are not already defined.
iii. Determine an expression for the density of the gas in terms of measured quantities, given quantities, and physical constants, as appropriate. Define any symbols used that are not already defined.
iv. The graph above represents the students’ data. Does the data indicate that the gas is ideal?
Describe the application of physics principles in an analysis of the graph that can be used to arrive at your answer.
Another group of students propose that the relationship between density and pressure could also be obtained by filling a balloon with the gas and submerging it to increasing depths in a deep pool of water.
(b) Why could submerging the balloon to increasing depths be useful for determining the relationship between the density and pressure of the gas?
(c) The balloon is kept underwater in the deep pool by a student pushing down on the balloon, as shown above. Let Vb represent the volume of the inflated balloon, mb represent the mass of just the balloon (not including the mass of the gas), pg represent the density of the gas in the balloon, and pw represent the density of the water. Derive an expression for the force the student must exert to hold the balloon at rest under the water, in terms of the quantities given in this part and physical constants, as appropriate.
▶️Answer/Explanation
Ans:
(a)
i.
The temperature should remain constant if the container remains sealed and away from direct sunlight. Place objects on to the piston one at a time. Density will be Mg divided by the current volume of the gas (πr2h, r and h measured by meter stick). Pressure is equal to the added weight of the piston and objects divided by the area of the piston. Graph density as a function of pressure and repeat with different numbers of objects.
ii.
\(P_{0}=\frac{F_{atm}}{A}\)
Fatm = P.A
\(P = \frac{F}{A}= \frac{F_{p}+nF_{0}+P_{0}A}{\pi r^{2}}\)
\(\frac{g(m_{p}+m_{0})+P_{0}\pi r^{2}}{\pi r^{2}}=P\)
r = radius of piston
P0 = atm pressure
iii.
\(P = \frac{m}{V}\)
\(P = \frac{Mg}{\pi r^{2}h}\)
r = radius of piston
h = height of piston
iv.
The graph shows that density 2 is proportional to pressure. In an ideal gas, pressure in inversely proportional to volume, and volume is inversely proportional to density. Therefore, in an ideal gas, density should be directly proportional to pressure. Since this is not the case for this gas, this gas is not an ideal gas.
(b)
The pressure of the water increases with depth, which would decreases the volume (increasing the density since density is inversely proportional to volume) because of the pressure difference. This allows volume and density to be varied and graphed.
(c)
