Submersion - MCAT Physical
Card 0 of 203
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?
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?
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
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
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When a copper sphere is suspended from a spring scale in air, the scale reads 
. Assuming the density of copper is 
, what will the scale read if the sphere is lowered (completely submerged) in a large beaker of water?
When a copper sphere is suspended from a spring scale in air, the scale reads
We need to find the buoyant force on the sphere to see how much the scale reading changes.
Buoyant force is given by 
, where V is the volume displaced by the sphere.
We need to find this volume, which also equals the sphere's volume. Given the sphere's mass (m = F/g = 2.94/9.8 = 0.30kg) and density, we can find volume with either 
or 
.
Plugging this volume into the buoyant force equation, together with the density of water (1000 kg/m3) gives the following.
So now the upwards force provided by the scale is reduced by 0.33N.
We need to find the buoyant force on the sphere to see how much the scale reading changes.
Buoyant force is given by
We need to find this volume, which also equals the sphere's volume. Given the sphere's mass (m = F/g = 2.94/9.8 = 0.30kg) and density, we can find volume with either
Plugging this volume into the buoyant force equation, together with the density of water (1000 kg/m3) gives the following.
So now the upwards force provided by the scale is reduced by 0.33N.
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A 100g block of copper, a 100g block of aluminum, and a 100g sphere of gold are placed into a large tub of water. Which object expereiences the greatest buoyant force?
A 100g block of copper, a 100g block of aluminum, and a 100g sphere of gold are placed into a large tub of water. Which object expereiences the greatest buoyant force?
Buoyant force depends only on the density of the fluid, and the volume of fluid displaced, according to 
. Since each object has a density greater than that of water, they will all be completely submerged. So, the volume of fluid displaced equals the volume of the object in each case, meaning that whichever object has the largest volume will experience the greatest buoyant force.
For copper: 
For aluminum: 
For gold: 
Since aluminum has the largest volume, and the largest volume of water displaced, it experiences the greatest buoyant force.
Buoyant force depends only on the density of the fluid, and the volume of fluid displaced, according to
For copper:
For aluminum:
For gold:
Since aluminum has the largest volume, and the largest volume of water displaced, it experiences the greatest buoyant force.
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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?
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?
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.
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.
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An irregular solid has a mass of 
on a laboratory balance. It is suspended by a thread from a spring scale and fully immersed in water. The spring scale reads 
. What is the buoyant force on the solid?
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 
The difference between these values is the buoyant force acting on the solid.
Recall that buoyant force is equal to the weight of water displaced by the object.
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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Two students in a physics class are conducting an experiment to see how different objects displace water in a container. Student A places a lead spherical marble with a radius of 
in the container. Student B places a considerably lighter solid glass sphere in the container, with twice the volume of the lead marble. Which of the following statements is true?
I. The amount of displaced water depends on the mass of a fully immersed object
II. The amount of water displaced depends on the volume of a fully immersed object
III. Student A's object will make the water level rise more than Student B's
IV. Student B's object will make the water level rise more than Student A's
V. From the information given, one cannot determine which object would displace more water
Two students in a physics class are conducting an experiment to see how different objects displace water in a container. Student A places a lead spherical marble with a radius of
I. The amount of displaced water depends on the mass of a fully immersed object
II. The amount of water displaced depends on the volume of a fully immersed object
III. Student A's object will make the water level rise more than Student B's
IV. Student B's object will make the water level rise more than Student A's
V. From the information given, one cannot determine which object would displace more water
This question relates directly to Archimedes' principle considering buoyancy. The take home points of this question are given in the answers:
- The more volume an object occupies, the more water it can displace.
- The mass of an object has no relevance to the amount of water displaced as long the object is fully immersed.
From the second of these two points, we can eliminate statement I since the amount of water displaced is independent of mass. We can also eliminate statements III and V, since the marble with greater volume will displace a greater volume of water. This leaves the correct statements: II and IV.
This question relates directly to Archimedes' principle considering buoyancy. The take home points of this question are given in the answers:
- The more volume an object occupies, the more water it can displace.
- The mass of an object has no relevance to the amount of water displaced as long the object is fully immersed.
From the second of these two points, we can eliminate statement I since the amount of water displaced is independent of mass. We can also eliminate statements III and V, since the marble with greater volume will displace a greater volume of water. This leaves the correct statements: II and IV.
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A soccer ball with a mass of 
and diameter 
is held under water. What is the acceleration of the ball the instant it is released?
A soccer ball with a mass of
To calculate the ball's instantaneous acceleration, we need to calculate the net force on the ball. We can neglect the resistance due to water since we are calculating the net force the moment the ball is released, before it has begun to move. Therefore, there are only two forces on the ball: gravitational force and buoyant force.
Force of gravity:
The bouyant force is simply the force of water that is displaced by the ball:
Now we can calculate the net force on the ball:
We can simply use Newton's second law to calculate the acceleration of the ball:
To calculate the ball's instantaneous acceleration, we need to calculate the net force on the ball. We can neglect the resistance due to water since we are calculating the net force the moment the ball is released, before it has begun to move. Therefore, there are only two forces on the ball: gravitational force and buoyant force.
Force of gravity:
The bouyant force is simply the force of water that is displaced by the ball:
Now we can calculate the net force on the ball:
We can simply use Newton's second law to calculate the acceleration of the ball:
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What is the specific gravity of a boat that has a mass of 6000kg and a volume of 10m3?
What is the specific gravity of a boat that has a mass of 6000kg and a volume of 10m3?
Specific gravity is the density of the substance over the density of water.
Density is given by mass over unit volume.
A boat with a mass of 6000kg and a volume of 10m3 will have a density of 600 kg/m3.
Specific gravity is the density of the substance over the density of water.
Density is given by mass over unit volume.
A boat with a mass of 6000kg and a volume of 10m3 will have a density of 600 kg/m3.
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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.
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: 
. When the object is not accelerating, this reduces to 
.
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 
.
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
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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?
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?
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.
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.
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What is the density of a log that is 25cm long, has a cross sectional area of 5cm2, and weighs 100g?
What is the density of a log that is 25cm long, has a cross sectional area of 5cm2, and weighs 100g?
The density of an object is equal to mass over volume.
Knowing the length and the cross sectional area of the log, we can find its volume.
Plugging in volume and mass into the equation will enable us to find density.
The density of an object is equal to mass over volume.
Knowing the length and the cross sectional area of the log, we can find its volume.
Plugging in volume and mass into the equation will enable us to find density.
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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.
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.
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.
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.
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An object is at equilibrium when 
of the total volume is submerged in gasoline. Find the density of the object.
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 
of the object is submerged, thus 
of the object's total volume will equal the volume of water displaced.
The displaced masses are equal.
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.
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Solid A has a volume of 
and a density of 
. Solid B is cube with sides of 
and has a density of 
.
What is the difference in mass between the two solids?
Solid A has a volume of
What is the difference in mass between the two solids?
The formula for density is:
In the question, we are given the densities of both solids and a means to find their volumes. Using these values, we will be able to determine the mass of each solid.
Now that we know both masses, we can find the difference.
The formula for density is:
In the question, we are given the densities of both solids and a means to find their volumes. Using these values, we will be able to determine the mass of each solid.
Now that we know both masses, we can find the difference.
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Water has a density of 
at a temperature of 
. An certain oil has a specific gravity of 
at this temperature. What is the mass of 
of the oil?
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.
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.
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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?
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.
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.
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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 
of carbon, 
of hydrogen, and 
of oxygen. The researcher wants to perform further analysis on this compound the next day. Before leaving the lab the researcher creates three stock solutions of varying concentrations of this compound: 
(solution A), 
(solution B), and 
(solution C). He stores these solutions overnight at a temperature of 
.
Molecular weight of this compound = 
Which of the following is true regarding the densities of the three stock solutions?
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.
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.
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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 of carbon, of hydrogen, and of oxygen. The researcher wants to perform further analysis on this compound the next day. Before leaving the lab the researcher creates three stock solutions of varying concentrations of this compound: (solution A), (solution B), and (solution C). He stores these solutions overnight at a temperature of 
.
Molecular weight of this compound =
A 
stock solution, solution X, kept at room temperature (
) will have __________ compared to solution A.
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 =
A
Solution A and solution X have the same concentration, therefore, we are only concerned with temperature differences between the two solutions. Density is dependent on temperature: as temperature increases density decreases. Recall the definition of density:
Increasing the temperature will slightly increase the volume of the solution and, subsequently, decrease density. The temperature has no effect on mass. The solution at the higher temperature (solution X) will have a lower density.
Solution A and solution X have the same concentration, therefore, we are only concerned with temperature differences between the two solutions. Density is dependent on temperature: as temperature increases density decreases. Recall the definition of density:
Increasing the temperature will slightly increase the volume of the solution and, subsequently, decrease density. The temperature has no effect on mass. The solution at the higher temperature (solution X) will have a lower density.
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Various sample sizes of a pure, unknown substance are measured for mass (in grams) and volume (in mL). The results are plotted on a graph with grams of the y-axis and milliliters on the x-axis. Which of the following results most likely indicates experimental error?
Various sample sizes of a pure, unknown substance are measured for mass (in grams) and volume (in mL). The results are plotted on a graph with grams of the y-axis and milliliters on the x-axis. Which of the following results most likely indicates experimental error?
Plotted in this way, the slope of the line is equal to the density of the substance.
We would expect the line to be linear and positive. A slope close to zero could indicate that the data was not graphed optimally or that the density is extremely small, and a density greater than one is possible (anything that sinks in water has a density greater than one). A negative density would indicate that greater masses of this substance have smaller volumes, which, for a pure substance, does not make sense.
Plotted in this way, the slope of the line is equal to the density of the substance.
We would expect the line to be linear and positive. A slope close to zero could indicate that the data was not graphed optimally or that the density is extremely small, and a density greater than one is possible (anything that sinks in water has a density greater than one). A negative density would indicate that greater masses of this substance have smaller volumes, which, for a pure substance, does not make sense.
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Which of these samples, if any, has a volume greater than three liters?
Which of these samples, if any, has a volume greater than three liters?
Solving this question requires that we use the given densities to convert mass to volume.
We see that only the aluminum sample has a volume over three liters.
Solving this question requires that we use the given densities to convert mass to volume.
We see that only the aluminum sample has a volume over three liters.
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