PHYSICS F/ SCI +ENGRS W/ WEBASSIGN ACCES
PHYSICS F/ SCI +ENGRS W/ WEBASSIGN ACCES
10th Edition
ISBN: 9781337888509
Author: SERWAY
Publisher: CENGAGE L
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Chapter 14, Problem 33AP

(a)

To determine

The appropriate model to describe the system when balloon is stationary.

(a)

Expert Solution
Check Mark

Answer to Problem 33AP

The appropriate model to describe the system is particle in equilibrium.

Explanation of Solution

The mass of the balloon is 0.250kg tied to a uniform length 2.00m and mass 0.050kg. The balloon is spherical with radius 0.4m and the density of the air is 1.20kg/m3.

If a system remains stationary, the sum of all forces acted on a system in all direction vertical as well as horizontal is equal to zero. This condition is also called is equilibrium condition.

Conclusion:

Therefore, appropriate model to describe the system is particle in equilibrium.

(b)

To determine

The force equation for the balloon for this model.

(b)

Expert Solution
Check Mark

Answer to Problem 33AP

The force equation for the balloon for this model is BFbFHeFs=0.

Explanation of Solution

In equilibrium condition, sum of all forces in vertical direction is equal to zero.

    Fy=0Fy=BFbFHeFs=0        (I)

Here, B is buoyant force, Fb is the weight of the balloon (envelope), FHe is the weight of the helium gas and Fs is the weight of the string.

Conclusion:

Therefore, the force equation for the balloon for this model is Fy=BFbFHeFs=0.

(c)

To determine

The mass of the string in terms of mb, r, ρHe and ρair.

(c)

Expert Solution
Check Mark

Answer to Problem 33AP

The mass of the string in the terms of mb, r, ρHe and ρair is 43πr3(ρairρHe)mb.

Explanation of Solution

From equation (I),

    BFbFHeFs=0

The buoyant force act on the balloon is equal to the displaced volume of the air by the balloon.

Formula to calculate the buoyant force acting on the balloon is,

    B=ρairg×43πr3

Here, ρair is the density of the air, r is the radius of the balloon and g is the acceleration due to gravity.

Formula to calculate the weight of the balloon is,

    Fb=mbg

Here, mb is the mass of the balloon.

Formula to calculate the weight of the helium gas is,

    FHe=mHeg

Here, mHe is the mass of the helium gas.

Formula to calculate the weight of the string is,

    Fs=msg

Here, ms is the mass of the string.

Substitute ρairg×43πr3 for B, mHeg for FHe, mbg for Fb and msg for Fs in equation (I).

    ρairg×43πr3mbgmHegmsg=0

Formula to calculate the mass of the helium gas is,

    mHe=ρHe×43πr3

Here, ρHe is the density of the helium gas.

Substitute ρHe×43πr3 for mHe in above expression.

    ρairg×43πr3mbgρHe×43πr3gmsg=0

Rearrange the above expression for ms

    ms=ρair×43πr3ρHe×43πr3mbms=43πr3(ρairρHe)mb

Conclusion:

Therefore, the mass of the string in terms of mb, r, ρHe and ρair is 43πr3(ρairρHe)mb.

(d)

To determine

The mass of the string.

(d)

Expert Solution
Check Mark

Answer to Problem 33AP

The mass of the string is 0.0237kg.

Explanation of Solution

From equation (II),

    ms=43πr3(ρairρHe)mb

Substitute 1.20kg/m3 for ρair, 0.250kg for mb, 0.4m for r and 0.179kg/m3 for ρHe to find ms.

    ms=43π(0.4m)3(1.20kg/m30.179kg/m3)0.250kg=0.0237kg

Conclusion:

Therefore, the mass of the string is 0.0237kg.

(e)

To determine

The length h of the string if mass of the string is 0.050kg.

(e)

Expert Solution
Check Mark

Answer to Problem 33AP

The length h of the string is 0.948m if mass of the string is 0.050kg.

Explanation of Solution

From equation (II),

    ms=43πr3(ρairρHe)mb

The mass of the string of height h is equal to the ms×hl.

Substitute ms×hl for ms in above expression.

    ms×hl=43πr3(ρairρHe)mb

Substitute 1.20kg/m3 for ρair, 0.250kg for mb, 0.4m for r, 0.050kg for ms2.0m for l and 0.179kg/m3 for ρHe to find h.

    0.050kg×h2.0m=43π(0.4m)3(1.20kg/m30.179kg/m3)0.250kgh=0.0237kg×2.0m0.050kg=0.948m

Conclusion:

Therefore, the length h of the string is 0.948m if mass of the string is 0.050kg.

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Chapter 14 Solutions

PHYSICS F/ SCI +ENGRS W/ WEBASSIGN ACCES

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