On October 21, 2001, Ian Ash pole of the United Kingdom achieved a record altitude of powered by toy balloons filled with helium. Each filled balloon had a radius of about and an estimated mass of . (a) Estimate the total buoyant force on the balloons. (b) Estimate the net upward force on all balloons. (c) Ash pole parachuted to the Earth after the balloons began to burst at the high altitude and the buoyant force decreased. Why did the balloons burst?
(a) The total buoyant force on the balloons is .
(b) The net upward force on all balloons is .
(c) Atmospheric pressure at this high altitude is much lower than at Earth’s surface, so the balloons expanded and eventually burst.
When an object is partially or fully submerged in a fluid, the fluid exerts on the object an upward force called the buoyant force.
According to Archimedes’s principle, the magnitude of the buoyant force is equal to the weight of the fluid displaced by the object:
Where, is the buoyant force, is the density of the air, gravitational acceleration, and volume displaced.
The total buoyant force of the toy balloons is define as below.
Estimate the net upward force by applying Newton’s second law in the vertical direction:
This net force was sufficient to lift Ash pole, his parachute, and other supplies.
Atmospheric pressure at this high altitude is much lower than at Earth’s surface, so the balloons expanded and eventually burst.
The human brain and spinal cord are immersed in the cerebrospinal fluid. The fluid is normally continuous between the cranial and spinal cavities and exerts a pressure of to of above the prevailing atmospheric pressure. In medical work, pressures are often measured in units of millimeters of because body fluids, including the cerebrospinal fluid, typically have the same density as water. The pressure of the cerebrospinal fluid can be measured by means of a spinal tap as illustrated in Figure P14.20. A hollow tube is inserted into the spinal column, and the height to which the fluid rises is observed. If the fluid rises to a height of , we write its gauge pressure as . (a) Express this pressure in Pascal’s, in atmospheres, and in millimeters of mercury. (b) Some conditions that block or inhibit the flow of cerebrospinal fluid can be investigated by means of Queckenstedt’s test. In this procedure, the veins in the patient’s neck are compressed to make the blood pressure rise in the brain, which in turn should be transmitted to the cerebrospinal fluid. Explain how the level of fluid in the spinal tap can be used as a diagnostic tool for the condition of the patient’s spine.
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