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A helium-filled balloon (whose envelope has a mass of m₁ = 0.260 kg) is tied to a uniform string of length l = 2.70 m and mass m = 0.050 6 kg. The balloon is spherical with a radius of r = 0.399 m. When released in air of temperature 20°C and density Pair = 1.20 kg/m³, it lifts a length h of string and then remains stationary as shown in the figure below. We wish to find the length of string lifted by the balloon. He (a) When the balloon remains stationary, what is the appropriate analysis model to describe it? Oa particle in equilibrium model a particle under constant acceleration model a particle under constant velocity model the ideal fluid model (b) Write a force equation for the balloon from this model in terms of the buoyant force B, the weight F of the balloon, the weight Fe of the helium, and the weight F of the segment of string of length h. (Use any variable or symbol stated above along with the following as necessary: π. Follow the sign convention that upward is the positive direction.) (No Response) = 0 He (c) Make an appropriate substitution for each of these forces and solve symbolically for the mass m¸ of the segment of string of length h in terms of m₁, r, the density of air Pa, and the density of helium He (Use any variable or symbol stated above along with the following as necessary: л.) ms = (No Response) (d) Find the numerical value of the mass m (No Response) kg (e) Find the length h numerically. (No Response) m

A helium-filled balloon (whose envelope has a mass of m₁ = 0.260 kg) is tied to a uniform string of length l = 2.70 m and mass m = 0.050 6 kg. The balloon is spherical with a radius of r = 0.399 m. When released in air of temperature 20°C and density Pair = 1.20 kg/m³, it lifts a length h of string and then remains stationary as shown in the figure below. We wish to find the length of string lifted by the balloon. He (a) When the balloon remains stationary, what is the appropriate analysis model to describe it? Oa particle in equilibrium model a particle under constant acceleration model a particle under constant velocity model the ideal fluid model (b) Write a force equation for the balloon from this model in terms of the buoyant force B, the weight F of the balloon, the weight Fe of the helium, and the weight F of the segment of string of length h. (Use any variable or symbol stated above along with the following as necessary: π. Follow the sign convention that upward is the positive direction.) (No Response) = 0 He (c) Make an appropriate substitution for each of these forces and solve symbolically for the mass m¸ of the segment of string of length h in terms of m₁, r, the density of air Pa, and the density of helium He (Use any variable or symbol stated above along with the following as necessary: л.) ms = (No Response) (d) Find the numerical value of the mass m (No Response) kg (e) Find the length h numerically. (No Response) m

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter15: Fluids
Section: Chapter Questions
Problem 72PQ: A manometer containing water with one end connected to a container of gas has a column height...
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A helium-filled balloon (whose envelope has a mass of m₁ = 0.260 kg) is tied to a uniform string of length l = 2.70 m and mass m = 0.050 6 kg. The balloon is spherical with a radius of r = 0.399 m. When released in air of temperature 20°C and density Pair = 1.20 kg/m³, it lifts a length h of string and then remains stationary as shown in the figure below. We wish to find the length of string lifted by the balloon. He (a) When the balloon remains stationary, what is the appropriate analysis model to describe it? Oa particle in equilibrium model a particle under constant acceleration model a particle under constant velocity model the ideal fluid model (b) Write a force equation for the balloon from this model in terms of the buoyant force B, the weight F of the balloon, the weight Fe of the helium, and the weight F of the segment of string of length h. (Use any variable or symbol stated above along with the following as necessary: π. Follow the sign convention that upward is the positive direction.) (No Response) = 0 He (c) Make an appropriate substitution for each of these forces and solve symbolically for the mass m¸ of the segment of string of length h in terms of m₁, r, the density of air Pa, and the density of helium He (Use any variable or symbol stated above along with the following as necessary: л.) ms = (No Response) (d) Find the numerical value of the mass m (No Response) kg (e) Find the length h numerically. (No Response) m
Transcribed Image Text:A helium-filled balloon (whose envelope has a mass of m₁ = 0.260 kg) is tied to a uniform string of length l = 2.70 m and mass m = 0.050 6 kg. The balloon is spherical with a radius of r = 0.399 m. When released in air of temperature 20°C and density Pair = 1.20 kg/m³, it lifts a length h of string and then remains stationary as shown in the figure below. We wish to find the length of string lifted by the balloon. He (a) When the balloon remains stationary, what is the appropriate analysis model to describe it? Oa particle in equilibrium model a particle under constant acceleration model a particle under constant velocity model the ideal fluid model (b) Write a force equation for the balloon from this model in terms of the buoyant force B, the weight F of the balloon, the weight Fe of the helium, and the weight F of the segment of string of length h. (Use any variable or symbol stated above along with the following as necessary: π. Follow the sign convention that upward is the positive direction.) (No Response) = 0 He (c) Make an appropriate substitution for each of these forces and solve symbolically for the mass m¸ of the segment of string of length h in terms of m₁, r, the density of air Pa, and the density of helium He (Use any variable or symbol stated above along with the following as necessary: л.) ms = (No Response) (d) Find the numerical value of the mass m (No Response) kg (e) Find the length h numerically. (No Response) m
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