Physics for Scientists and Engineers, Vol. 1
Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
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Chapter 13, Problem 89P

(a)

To determine

Volume of the balloon

(a)

Expert Solution
Check Mark

Answer to Problem 89P

  69.67 m3

Explanation of Solution

Given:

Density of air =ρa=1.3 kgm3

Density of helium =ρHe=0.18 kgm3

Mass of skin of balloon =mb=1.5 kg

Weight of skin of balloon =wb

Weight of the load =wL=750 N

Force of buoyancy =FB

Volume of the balloon =Vb

Formula Used:

Weight is given as

  w=mg

Force of buoyancy is given as

  FB=ρVg

Calculation:

Weight of the skin of the balloon is given as

  wb=mb gwb=(1.5)(9.8)wb=14.7 N

Weight of the helium in the balloon in downward direction is given as

  wHe=ρHeVbg

Force of buoyancy on the balloon in upward direction is given as

  FB=ρa Vb g

Using equilibrium of force in vertical direction, we get the force equation as

  FB=wb+wHe+wLρa Vb g=14.7+ρHeVbg+750(1.3) Vb (9.8)=(0.18)Vb(9.8)+764.7(12.74) Vb =(1.764)Vb+764.7(12.741.764) Vb =764.7 Vb =764.710.976 Vb =69.67 m3

Conclusion:

Hence,the volume of the balloon comes out to be 69.67 m3 .

(b)

To determine

The initial acceleration of the balloon.

(b)

Expert Solution
Check Mark

Answer to Problem 89P

  5.2 ms2

Explanation of Solution

Given:

Density of air =ρa=1.3 kgm3

Density of helium =ρHe=0.18 kgm3

Mass of skin of balloon =mb=1.5 kg

Weight of skin of balloon =wb

Weight of the load =wL=900 N

Mass of the load =mL

Force of buoyancy =FB

Volume of the balloon =Vb=2(69.67)=139.34 m3

Acceleration of the balloon =a

Formula Used:

Weight is given as

  w=mg

Force of buoyancy is given as

  FB=ρVg

Mass is given as

  mass =weightgm = wg

According to Newton’s second law, we have

  Fnet=ma

Calculation:

Weight of the skin of the balloon is given as

  wb=mb gwb=(1.5)(9.8)wb=14.7 N

Weight of the helium in the balloon in downward direction is given as

  wHe=ρHeVbg

Force of buoyancy on the balloon in upward direction is given as

  FB=ρa Vb g

Mass of the load is given as

  mL=wLgmL=9009.8mL=91.8 kg

Using the forces in vertical direction, the force equation as

  FBwbwHewL=(mb+mHe+mL)aFBwbwHewL=(mb+ρHeVb+mL)aρa Vb gwbρHeVb gwL=(mb+ρHeVb+mL)a(1.3)(139.34)(9.8)14.7(0.18)(139.34)(9.8)900=(1.5+(0.18)(139.34)+91.8)a614.7=(118.4)aa=5.2 ms2

Conclusion:

Hence, the initial acceleration of the balloon comes out to be 5.2 ms2 .

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Physics for Scientists and Engineers, Vol. 1

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