EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
9th Edition
ISBN: 8220100461262
Author: SERWAY
Publisher: Cengage Learning US
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Question
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Chapter 14, Problem 14.60AP

(a)

To determine

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

(a)

Expert Solution
Check Mark

Answer to Problem 14.60AP

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 14.60AP

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 14.60AP

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 14.60AP

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 14.60AP

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

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

Ch. 14 - A solid iron sphere and a solid lead sphere of the...Ch. 14 - Prob. 14.7OQCh. 14 - One of the predicted problems due to global...Ch. 14 - A boat develops a leak and, after its passengers...Ch. 14 - A small piece of steel is tied to a block of wood....Ch. 14 - A piece of unpainted porous wood barely floats in...Ch. 14 - A person in a boat floating in a small pond throws...Ch. 14 - Rank the buoyant forces exerted on the following...Ch. 14 - A water supply maintains a constant rate of flow...Ch. 14 - A glass of water contains floating ice cubes. When...Ch. 14 - An ideal fluid flows through a horizontal pipe...Ch. 14 - When an object is immersed in a liquid at rest,...Ch. 14 - Two thin-walled drinking glasses having equal base...Ch. 14 - Because atmospheric pressure is about 105 N/m2 and...Ch. 14 - A fish rests on the bottom of a bucket of water...Ch. 14 - You are a passenger on a spacecraft. For your...Ch. 14 - Prob. 14.6CQCh. 14 - Prob. 14.7CQCh. 14 - If you release a ball while inside a freely...Ch. 14 - (a) Is the buoyant force a conservative force? (b)...Ch. 14 - All empty metal soap dish barely floats in water....Ch. 14 - Prob. 14.11CQCh. 14 - Prob. 14.12CQCh. 14 - Prob. 14.13CQCh. 14 - Does a ship float higher in the water of an inland...Ch. 14 - Prob. 14.15CQCh. 14 - Prob. 14.16CQCh. 14 - Prairie dogs ventilate their burrows by building a...Ch. 14 - Prob. 14.18CQCh. 14 - Prob. 14.19CQCh. 14 - A large man sits on a four-legged chair with his...Ch. 14 - Prob. 14.2PCh. 14 - A 50.0-kg woman wearing high-heeled shoes is...Ch. 14 - Estimate the total mass of the Earths atmosphere....Ch. 14 - Calculate the mass of a solid gold rectangular bar...Ch. 14 - (a) A wry powerful vacuum cleaner has a hose 2.86...Ch. 14 - The spring of the pressure gauge shown in Figure...Ch. 14 - The small piston of a hydraulic lift (Fig. P14.8)...Ch. 14 - What must be the contact area between a suction...Ch. 14 - A swimming pool has dimensions 30.0 m 10.0 m and...Ch. 14 - (a) Calculate the absolute pressure at the bottom...Ch. 14 - Prob. 14.12PCh. 14 - Prob. 14.13PCh. 14 - A container is filled to a depth of 20.0 cm with...Ch. 14 - Review. 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A...Ch. 14 - On October 21, 2001, Ian Ashpole of the United...Ch. 14 - How many cubic meters of helium are required to...Ch. 14 - Water flowing through a garden hose of diameter...Ch. 14 - A large storage tank, open at the top and filled...Ch. 14 - Prob. 14.42PCh. 14 - Prob. 14.43PCh. 14 - A village maintains a large tank with ail open...Ch. 14 - A legendary Dutch boy saved Holland by plugging a...Ch. 14 - Water falls over a dam of height h with a mass...Ch. 14 - Water is pumped up from the Colorado River to...Ch. 14 - In ideal flow, a liquid of density 850 kg/m3 moves...Ch. 14 - The Venturi tube discussed in Example 14.8 and...Ch. 14 - Review. Old Faithful Geyser in Yellowstone...Ch. 14 - An airplane is cruising al altitude 10 km. The...Ch. 14 - An airplane has a mass of 1.60 104 kg, and each...Ch. 14 - Prob. 14.53PCh. 14 - The Bernoulli effect can have important...Ch. 14 - Prob. 14.55PCh. 14 - Decades ago, it was thought that huge herbivorous...Ch. 14 - (a) Calculate the absolute pressure at an ocean...Ch. 14 - Prob. 14.58APCh. 14 - A spherical aluminum ball of mass 1.26 kg contains...Ch. 14 - Prob. 14.60APCh. 14 - Review. Figure P14.61 shows a valve separating a...Ch. 14 - The true weight of an object can be measured in a...Ch. 14 - Water is forced out of a fire extinguisher by air...Ch. 14 - Review. Assume a certain liquid, with density 1...Ch. 14 - Prob. 14.65APCh. 14 - Prob. 14.66APCh. 14 - Prob. 14.67APCh. 14 - A common parameter that can be used to predict...Ch. 14 - Evangelista Torricelli was the first person to...Ch. 14 - Review. 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