Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 13, Problem 52P

(a)

To determine

The initial upward acceleration of the balloon when it is released from sea level.

(a)

Expert Solution
Check Mark

Answer to Problem 52P

  45m/s2

Explanation of Solution

Given:

Radius of the balloon (r) is 2.5 m

Total mass (mass of the balloon + mass of the helium + mass of the equipment) (mtotal) is 15 kg.

Formula used:

Physics for Scientists and Engineers, Chapter 13, Problem 52P

FIGURE: 1

In the figure 1, FD is the drag force

  mg is weight of the balloon ( m is total mass of the balloon and g is acceleration due to gravity, g=9.81 m/s2)

  B is buoyant force

Let us apply the Newton’s second law, that is Fy=may to the balloon at the instant it is released

  Bmballoong=mballoonay(1)

Using Archimedes principle, buoyant force (B) acting on the balloon can be expressed as,

  B=wdisplaced fluid=mdisplaced fluidg

Applying m=ρV to the above equation,

  B=ρdisplaced fluidVdisplaced fluidg

  =ρairVballoong

Since balloon is in spherical shape, volume of the balloon is,

  Vballoon=43πr3

And hence, buoyant force,

  B=43πr3ρairg

Where, ρair is density of air which is equal to 1.29 kg/m3g is acceleration due to gravity, g=9.81 m/s2

Substituting for buoyant force in equation (1) ,

  43πr3ρairgmballoong=mballoonay

  ay=1mballoon[43πr3ρairgmballoong]=[43πr3ρairmballoon1]g(2)

Calculation:

Substituting the numerical values in equation (2) ,

  ay=[43π(2.5 m)3(1.29 kg/m3)15 kg-1](9.81 m/s2)=45m/s2

Conclusion:

The initial upward acceleration of the balloon when it is released from sea level is 45m/s2 .

(b)

To determine

The terminal velocity of the ascending balloon.

(b)

Expert Solution
Check Mark

Answer to Problem 52P

  7.33m/s

Explanation of Solution

Given:

Radius of the balloon (r) is 2.5 m

Total mass (mass of the balloon + mass of the helium + mass of the equipment) (mtotal) is 15 kg

Drag force of the balloon is FD=12πr2ρv2

Where, r is radius of the balloon

  ρ is density of the air

  v is balloon’s ascension speed

Formula used:

Let υt be the terminal velocity of the balloon.

Let us apply the Newton’s second law, which is Fy=may to the balloon under terminal speed condition

  Bmg12πr2ρυt2=0

Substituting for B from part (a),

  43πr3ρairgmg12πr2ρυt2=0

  12πr2ρυt2=43πr3ρairgmg

  υt2=112πr2ρ[43πr3ρairgmg]=2[43πr3ρairm]gπr2ρ

  υt=2[43πr3ρairm]gπr2ρ(3)

Calculation:

Substituting the numerical values in equation (3) ,

  υt=2[43π(2.5 m)3(1.29 kg/m3)-15 kg]9.81m/s2π(2.5 m)2(1.29 kg/m3)=7.33m/s.

Conclusion:

The terminal velocity of the ascending balloon is 7.33m/s .

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Titania, the largest moon of the planet Uranus, has 18the radiusof the earth and 1/1700 the mass of the earth. (a) What is the accelerationdue to gravity at the surface of Titania? (b) What is the average densityof Titania? (This is less than the density of rock, which is one piece ofevidence that Titania is made primarily of ice.)
(b) A worker wishes to pile sand onto a circular area in his yard. The radius of the circle is R. No sand is to spill onto the surrounding area; see Fig. Show that the greatest volume of sand that can be stored in this manner is mu,R 3/3 .where us is the coefficient of static friction of sand on sand. (The volume of a cone is Ah/3, where A is the base area and h is the height.)
A car has a drag coefficient Cd kg.m-3. = 0.30, a frontal area of A= 1.9 m² and a mass 1.2 tonnes. The density of air is 1.2 i) What is the drag force when it is traveling at v = 110 kph in a straight line? Fdrag N. Hint: Retain accurate values until the final calculation, but remember significant figures. Enter answer here

Chapter 13 Solutions

Physics for Scientists and Engineers

Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Newton's Third Law of Motion: Action and Reaction; Author: Professor Dave explains;https://www.youtube.com/watch?v=y61_VPKH2B4;License: Standard YouTube License, CC-BY