MCAT Physical : Fluids and Gases
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Example Questions
Example Question #1 : Density
A 200-gram object is placed into a bucket of water and floats so that its top edge is just below the surface of the water. Which best describes the density of this object?
Density of water is 1000kg/m3.
If the object is at rest, the net force on it must equal 0. At any point in the liquid, the total downwards force is described as the difference between the gravitational force and bouyant force: 
Plugging in the equations for these forces respectively yields 
Since mass is the product of density and volume, 
Note that in this case the object's volume equals the volume of liquid displaced, since the object is completely submerged. So, the volumes on either side cancel, as does gravity, leaving just 
Example Question #11 : Fluids And Gases
An ice cube is placed into a glass containing an unknown liquid. If the ice cube sinks to the bottom, which of the following conclusions could be made?
No conclusions can be made unless the mass of the ice cube is known
The liquid has a density less than that of water
No conclusions can be made unless the temperature of the liquid is known
The liquid has a density greater than that of water
The density of the liquid is equal to the density of water
The liquid has a density less than that of water
The density of ice is less than that of water (density of ice = 0.92 g/cm3, density of water = 1 g/cm3). Ice will only sink in liquids that are less dense than 0.92 g/cm3. Since ice will only sink in liquids that are less dense than water, the unknown liquid must have a lower density than that of water.
Example Question #11 : Submersion
Phase diagrams are used to depict changes in the properties of a solution at different temperatures and pressures. Below is a phase diagram of a polar solution.
The density of the solution in section 1 is __________ the density of the solution in section 2.
less than
equal to
greater than
less than
The slope of the solid/liquid phase transition line can predict the comparative density of the solution in each section. A negative slope indicates that the solid phase is less dense than the liquid phase. A positive slope indicates that the solid is more dense. In the above phase diagram, the slope is negative, indicating that the solid is less dense than the liquid.
Example Question #2 : Density
An object is at equilibrium when 
To solve, we can equate the volume of the gasoline displaced to the volume of the portion of the object that is submerged.
We know that 
The displaced masses are equal.
Example Question #11 : Fluids And Gases
Water has a density of 
The formula for density is:
Specific gravity is the density of a material relative to the density of water.
We are given the specific gravity of the oil and the density of water, allowing us to calculate the density of the oil.
Returning to the equation for density, we can use the density of the oil to find the mass on one liter.
Example Question #87 : Ap Physics 2
A given iceberg floats such that 90% of its volume is below water. Supposing that the iceberg is composed of pure water, what is the density of the saltwater in which the iceberg floats?
We can solve this question by using a density ratio, given by the equation:
We know the density of ice, and we can find the ratio of the densities by using buoyancy. If the iceberg were completely submerged, then we could conclude that the density of the ice was equal to the density of the salt water. Since the iceberg is 90% submerged, we can conclude that the density of the ice is 90% of the density of the salt water.
Use this ratio and the density of ice to solve for the density of the salt water.
Example Question #11 : Fluids And Gases
A researcher performs an elemental analysis on a compound. He finds that the compound is made up of only carbon, hydrogen, and oxygen atoms. He isolates a pure sample of the compound and finds that this sample contains 
Molecular weight of this compound =
Which of the following is true regarding the densities of the three stock solutions?
Density is a measure of concentration, defined as mass per unit volume.
Since the stock solutions contain different concentrations, the density of each solution must be different. The solution with the highest concentration will contain the highest density, and the solution with lowest concentration will contain the lowest density. The order of increasing density is solution A, solution B, and solution C. Solution C is the most concentrated and will contain the greatest amount of mass per unit volume, followed by solution B and solution A.
Remember that concentration can be defined in various ways: molarity, molality, mass percent, density, etc. Increasing concentration means you are increasing all of these quantities. Also remember that the density of the compound remains the same in each solution; only the solutions, as a whole, have different densities.
Example Question #13 : Submersion
Use the following information to answer questions 1-6:
The circulatory system of humans is a closed system consisting of a pump that moves blood throughout the body through arteries, capillaries, and veins. The capillaries are small and thin, allowing blood to easily perfuse the organ systems. Being a closed system, we can model the human circulatory system like an electrical circuit, making modifications for the use of a fluid rather than electrons. The heart acts as the primary force for movement of the fluid, the fluid moves through arteries and veins, and resistance to blood flow occurs depending on perfusion rates.
To model the behavior of fluids in the circulatory system, we can modify Ohm’s law of V = IR to ∆P = FR where ∆P is the change in pressure (mmHg), F is the rate of flow (ml/min), and R is resistance to flow (mm Hg/ml/min). Resistance to fluid flow in a tube is described by Poiseuille’s law: R = 8hl/πr4 where l is the length of the tube, h is the viscosity of the fluid, and r is the radius of the tube. Viscosity of blood is higher than water due to the presence of blood cells such as erythrocytes, leukocytes, and thrombocytes.
The above equations hold true for smooth, laminar flow. Deviations occur, however, when turbulent flow is present. Turbulent flow can be described as nonlinear or tumultuous, with whirling, glugging or otherwise unpredictable flow rates. Turbulence can occur when the anatomy of the tube deviates, for example during sharp bends or compressions. We can also get turbulent flow when the velocity exceeds critical velocity vc, defined below.
vc = NRh/ρD
NR is Reynold’s constant, h is the viscosity of the fluid, ρ is the density of the fluid, and D is the diameter of the tube. The density of blood is measured to be 1060 kg/m3.
Another key feature of the circulatory system is that it is set up such that the organ systems act in parallel rather than in series. This allows the body to modify how much blood is flowing to each organ system, which would not be possible under a serial construction. This setup is represented in Figure 1.
A red blood cell floating in the body weighs 27 picograms and has a volume of 40.0 * 10-12cm3. What is the buoyant force on the red blood cell?
4 * 10-7N
4 * 10-13N
2.7 * 10-10N
2.7N
4 * 10-13N
To answer this question, we use Fb = Vgρ, where V is volume, g is gravity, and ρ is the density of the fluid.
In this case we can use the density of blood, since it is given in the passage as 1060kg/m3. Since the density is in cubic meters, we have to make sure that the volume is also converted to cubic meters.
(4.0 * 10-11)x (1 * 10-6m/ 1cm) = 4 * 10-17m3
Fb = (4.0 x 10-17m3) (10 m/s2) (1.06 x 103kg/m3) = 4 * 10-13N
Example Question #14 : Submersion
Two identical balloons, balloon A and balloon B, are filled with gas A and gas B, respectively. In which described scenario will the balloon rise the fastest?
Balloon B at
All scenarios describe equal rising rates
Balloon B at
Balloon A at
Balloon A at
Balloon B at
As temperature increases, density decreases.
In a free body diagram of each balloon, the only forces acting in the vertical direction are gravity and buoyant force.
These forces act in opposite directions, with the buoyant force pulling up and gravity pulling down.
As gas B is heated to the higher temperature, the density decreases. Gas B already has a lower density than gas A; heating it simply intensifies this discrepancy. As the density decreases, the force of gravity on the balloon decreases as well, allowing a greater net force in the upward direction due to the buoyant force.
The net upward force experienced by balloon B at the highest temperature will be greater than any of the other scenarios listed, resulting in the greatest upward acceleration.
Example Question #12 : Fluids And Gases
An irregular solid has a mass of 
The difference between the mass as measured in air and the mass as measured when it is suspended in water is the mass of the displaced water, easily reduced to the volume of the solid.
First calculate the weight of the solid in air.
In water, it weighs 
Recall that buoyant force is equal to the weight of water displaced by the object.
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