Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

(II) How many helium-filled balloons would it take to lift a person? Assume the person has a mass of \({\rm{72 kg}}\)and that each helium-filled balloon is spherical with a diameter of\(33\;{\rm{cm}}\).

Short Answer

Expert verified

The number of balloons required is \(3472.6\;{\rm{balloons}}\) to lift a person.

Step by step solution

01

Concept of volume density

Volume density is the volume of an object per unit density of that object. It is used to deduce the number of particles in a space.

02

Given data

The mass of the person is \({\rm{m}} = 72\;{\rm{kg}}\).

The diameter of the helium-filled balloon is \(d = 33\;{\rm{cm}}\).

03

Calculation of the buoyant force and density

The buoyant force is calculated as:

\({F_{{Bouyant}}}{ = }\rho Vg\)

Here,\(\rho \)is density of fluid, \(V\) is volume occupied and \({\rm{g}}\) is acceleration due to gravity.

The density of a fluid is calculated as:

\(\rho = \frac{m}{V}\)

Here,\(m\)is the mass of the fluid.

Using law of equilibrium of forces, buoyant force will be equal to the force due to weight \({F_{{\rm{weight}}}}\).

\(\begin{aligned}{F_{{\rm{bouyant}}}} &= {F_{{\rm{weight}}}}\\{\rho _{{\rm{air}}}}{V_{{\rm{He}}}}g &= mg + {\rho _{{\rm{He}}}}{V_{{\rm{He}}}}g\\{V_{{\rm{He}}}} &= \frac{m}{{{\rho _{{\rm{air}}}} - {\rho _{{\rm{He}}}}}}\end{aligned}\)

Here, \({\rho _{{\rm{air}}}}\)is the density of air, \({\rho _{{\rm{He}}}}\) is the density of Helium and\({V_{{\rm{He}}}}\) is the volume of helium.

04

Calculation of capacity to lift

The volume of a Helium-filled balloon is:

\({V_{{\rm{He}}}} = N\frac{4}{3}{\rm{\pi }}{r^3}\)

Here, N is the number of balloon and r is the radius.

Substituting the values in the above equation.

\(\begin{aligned}N\frac{4}{3}{\rm{\pi }}{r^3} &= \frac{m}{{{\rho _{{\rm{air}}}} - {\rho _{{\rm{He}}}}}}\\N &= \frac{{3m}}{{4{\rm{\pi }}{r^3}\left( {{\rho _{{\rm{air}}}} - {\rho _{{\rm{He}}}}} \right)}}\end{aligned}\)

Substitute the known values in the above equation to find the number of helium-filled balloon.

\(\begin{aligned}N &= \frac{{3 \times 72\;{\rm{kg}}}}{{4\pi {{\left( {\frac{{33\;{\rm{cm}} \times \frac{{1\;{\rm{m}}}}{{100\;{\rm{cm}}}}}}{2}} \right)}^3}\left( {1.29\;{\rm{kg/}}{{\rm{m}}^3} - 0.179\;{\rm{kg/}}{{\rm{m}}^3}} \right)}}\\N &= 3472.6\;{\rm{balloons}}\end{aligned}\)

Hence, the number of balloons are \(3472.6\;{\rm{balloons}}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You put two ice cubes in a glass and fill the glass to the rim with water. As the ice melts, the water level

(a) Drops below the rim.

(b) Rises and water spills out of the glass.

(c) Remains the same.

(d) Drops at first, then rises until a little water spills out.

Question: You are watering your lawn with a hose when you put your finger over the hose opening to increase the distance the water reaches. If you are holding the hose horizontally, and the distance the water reaches increases by a factor of 4, what fraction of the hose opening did you block?

(II) Poiseuilleโ€™s equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, \(Re\) , exceeds approximately 2000. \(Re\) is defined as

\({\mathop{\rm Re}\nolimits} = \frac{{2\overline v r\rho }}{\eta }\)

where \(\overline v \) is the average speed of the fluid, \(\rho \) is its density, \(\eta \) is its viscosity, and \(r\) is the radius of the tube in which the fluid is flowing. (a) Determine if blood flow through the aorta is laminar or turbulent when the average speed of blood in the aorta \(\left( {{\bf{r = 0}}{\bf{.80}}\;{\bf{cm}}} \right)\) during the resting part of the heartโ€™s cycle is about \({\bf{35}}\;{\bf{cm/s}}\). (b) During exercise, the blood-flow speed approximately doubles. Calculate the Reynolds number in this case, and determine if the flow is laminar or turbulent.

(II) How high would the level be in an alcohol barometer at normal atmospheric pressure?

(II) A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water. When filled with another fluid, the mass is 89.22 g. What is the specific gravity of this other fluid?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free