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Balls A and B of equal mass are floating in a swimming pool, as shown below. Which will produce a greater buoyant force?
- a)Ball A
- b)Ball B
- c)The forces will be equal.
- d)It is impossible to know without knowing the volume of each ball.
Correct answer is option 'A'. Can you explain this answer?
Balls A and B of equal mass are floating in a swimming pool, as shown below. Which will produce a greater buoyant force?
a)
Ball A
b)
Ball B
c)
The forces will be equal.
d)
It is impossible to know without knowing the volume of each ball.
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Orion Classes answered |
The buoyant force (Fbuoy) is equal to the weight of water displaced, which is quantitatively expressed as
Fbuoy = mfluid displacedg = ρfluidVfluid displacedg
The volume of displaced fluid is equal to the volume of the ball. The density of the fluid remains constant. Therefore, because ball A has a larger volume, it will displace more water and experience a larger buoyant force.
The volume of displaced fluid is equal to the volume of the ball. The density of the fluid remains constant. Therefore, because ball A has a larger volume, it will displace more water and experience a larger buoyant force.
The figure shown represents a section through a horizontal pipe of varying diameters into which four open vertical pipes connect. If water is allowed to flow through the pipe in the direction indicated, in which of the vertical pipes will the water level be lowest?
- a)Pipe 1
- b)Pipe 2
- c)Pipe 3
- d)Pipe 4
Correct answer is option 'B'. Can you explain this answer?
The figure shown represents a section through a horizontal pipe of varying diameters into which four open vertical pipes connect. If water is allowed to flow through the pipe in the direction indicated, in which of the vertical pipes will the water level be lowest?
a)
Pipe 1
b)
Pipe 2
c)
Pipe 3
d)
Pipe 4
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Orion Classes answered |
It is not necessary to do any calculations to answer this question. The open vertical pipes are exposed to the same atmospheric pressure; therefore, differences in the heights of the columns of water in the vertical pipes is dependent only on the differences in hydrostatic pressures in the horizontal pipe. Because the horizontal pipe has variable cross-sectional area, water will flow the fastest and the hydrostatic pressure will have its lowest value where the horizontal pipe is narrowest; this is called the Venturi effect. As a result, pipe 2 will have the lowest water level.
Objects A and B are submerged at a depth of 1 m in a liquid with a specific gravity of 0.877. Given that the density of object B is one-third that of object A and that the gauge pressure of object A is 3 atm, what is the gauge pressure of object B? (Note: Assume atmospheric pressure is 1 atm and g = 9.8 m/s2).- a)1 atm
- b)2 atm
- c)3 atm
- d)9 atm
Correct answer is option 'C'. Can you explain this answer?
Objects A and B are submerged at a depth of 1 m in a liquid with a specific gravity of 0.877. Given that the density of object B is one-third that of object A and that the gauge pressure of object A is 3 atm, what is the gauge pressure of object B? (Note: Assume atmospheric pressure is 1 atm and g = 9.8 m/s2).
a)
1 atm
b)
2 atm
c)
3 atm
d)
9 atm
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Orion Classes answered |
The absolute and gauge pressures depend only on the density of the fluid, not that of the object. When the pressure at the surface is equal to atmospheric pressure, the gauge pressure is given by Pgauge = ρgz, where ρ represents the density of the fluid, not the object. These objects are also at the same depth, so they must have the same gauge pressure.
Which of the following data sets is sufficient to determine the linear speed through an area of a rigid pipe?- a)The cross sectional area in another segment of pipe and the cross sectional area in the region of interest
- b)The Reynolds number, viscosity of the fluid, density, and diameter of the pipe
- c)The radius of the pipe, pressure gradient, viscosity, and length of the pipe
- d)The absolute pressure and density
Correct answer is option 'C'. Can you explain this answer?
Which of the following data sets is sufficient to determine the linear speed through an area of a rigid pipe?
a)
The cross sectional area in another segment of pipe and the cross sectional area in the region of interest
b)
The Reynolds number, viscosity of the fluid, density, and diameter of the pipe
c)
The radius of the pipe, pressure gradient, viscosity, and length of the pipe
d)
The absolute pressure and density
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Orion Classes answered |
The data given in choice (C) are sufficient to determine the flow rate through Poiseuille's law, which can then be used to determine the linear speed by dividing by the cross-sectional area (which could be determined from the radius, as well). Choice (A) would be sufficient if we also knew the flow rate in the other segment of pipe; one could use the continuity equation to determine the linear speed. The data in choice (B) could be used to determine the critical speed at which turbulent flow begins, but there is no indication that there is turbulent flow. The data in choice (D) could be used to determine the depth of an object in a fluid.
Two wooden balls of equal volume but different density are held beneath the surface of a container of water. Ball A has a density of 0.5 g/m3, and ball B has a density of 0.7 g/cm3. When the balls are released, they will accelerate upward to the surface. What is the relationship between the acceleration of ball A and that of ball B?- a)Ball A has the greater acceleration.
- b)Ball B has the greater acceleration.
- c)Balls A and B have the same acceleration.
- d)It cannot be determined from information given.
Correct answer is option 'A'. Can you explain this answer?
Two wooden balls of equal volume but different density are held beneath the surface of a container of water. Ball A has a density of 0.5 g/m3, and ball B has a density of 0.7 g/cm3. When the balls are released, they will accelerate upward to the surface. What is the relationship between the acceleration of ball A and that of ball B?
a)
Ball A has the greater acceleration.
b)
Ball B has the greater acceleration.
c)
Balls A and B have the same acceleration.
d)
It cannot be determined from information given.
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Orion Classes answered |
Using Newton's second law, Fnet = ma, we obtain the following equation:
Fbuoy ? mg = ma
Thus,
Both balls experience the same buoyant force because they are in the same liquid and have the same volume (Fbuoy = ρVg). Thus, the ball with the smaller mass experiences the greater acceleration. Because both balls have the same volume, the ball with the smaller density has the smaller mass (m = ρV), which is ball A.
Fbuoy ? mg = ma
Thus,
Both balls experience the same buoyant force because they are in the same liquid and have the same volume (Fbuoy = ρVg). Thus, the ball with the smaller mass experiences the greater acceleration. Because both balls have the same volume, the ball with the smaller density has the smaller mass (m = ρV), which is ball A.
A low-pressure weather system can decrease the atmospheric pressure from 1 atm to 0.99 atm. By what percent will this decrease the force on a rectangular window from the outside? (Note: Assume the window is 6 m by 3 m and the glass is 3 cm thick.)- a)1%
- b)10%
- c)1/3%
- d)30%
Correct answer is option 'A'. Can you explain this answer?
A low-pressure weather system can decrease the atmospheric pressure from 1 atm to 0.99 atm. By what percent will this decrease the force on a rectangular window from the outside? (Note: Assume the window is 6 m by 3 m and the glass is 3 cm thick.)
a)
1%
b)
10%
c)
1/3%
d)
30%
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Orion Classes answered |
This question is a simple application of the definition of pressure, which is force per area. If pressure decreases 1 percent and area does not change, the force will be decreased by 1 percent. Note that the other measurements given do not play a role in our calculations.
A hydraulic lever is used to lift a heavy hospital bed, requiring an amount of work W. When the same bed with a patient is lifted, the work required is doubled. How can the cross-sectional area of the platform on which the bed is lifted be changed so that the pressure on the hydraulic lever remains constant?- a)The cross-sectional area must be doubled.
- b)The cross-sectional area must be halved.
- c)The cross-sectional area must be divided by four.
- d)The cross-sectional area must remain constant.
Correct answer is option 'A'. Can you explain this answer?
A hydraulic lever is used to lift a heavy hospital bed, requiring an amount of work W. When the same bed with a patient is lifted, the work required is doubled. How can the cross-sectional area of the platform on which the bed is lifted be changed so that the pressure on the hydraulic lever remains constant?
a)
The cross-sectional area must be doubled.
b)
The cross-sectional area must be halved.
c)
The cross-sectional area must be divided by four.
d)
The cross-sectional area must remain constant.
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Orion Classes answered |
This question tests our understanding of Pascal's principle, which states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel. We are told that the work required to lift the bed with the patient is double the work needed to lift just the bed. In other words, the force required doubles when both the bed and the patient have to be lifted. To maintain the same pressure, we must double the cross-sectional area of the platform of the hydraulic lever on which the patient and the bed are lifted.
A water tower operator is interested in increasing the pressure of a column of water that is applied to a piston. She hopes that increasing the pressure will increase the force being applied to the piston. The only way to increase the pressure is to alter the speed of the water as it flows through the pipe to the piston. How should the speed of the water be changed to increase the pressure and force?- a)Increase the speed
- b)Decrease the speed
- c)Release water intermittently against the pipe
- d)The speed of water will not change pressure at the piston.
Correct answer is option 'B'. Can you explain this answer?
A water tower operator is interested in increasing the pressure of a column of water that is applied to a piston. She hopes that increasing the pressure will increase the force being applied to the piston. The only way to increase the pressure is to alter the speed of the water as it flows through the pipe to the piston. How should the speed of the water be changed to increase the pressure and force?
a)
Increase the speed
b)
Decrease the speed
c)
Release water intermittently against the pipe
d)
The speed of water will not change pressure at the piston.
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Orion Classes answered |
This is a basic interpretation of Bernoulli's equation that states, at equal heights, speed and pressure of a fluid are inversely related (the Venturi effect). Decreasing the speed of the water will therefore increase its pressure. An increase in pressure over a given area will result in increased force being transmitted to the piston.
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