A helium-filled balloon (whose envelope has a mass of m = 0.260 kg) is tied to a uniform string of length = 2.50 m and mass m = 0.049 9 kg. The balloon is spherical with a radius of r = 0.398 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? O the ideal fluid model a particle in equilibrium model a particle under constant velocity model O a particle under constant acceleration 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 FHe 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: . Follow the sign convention that upward is the positive direction.) = 0 sty (c) Make an appropriate substitution for each of these forces and solve symbolically for the mass me of the segment of string of length h in terms of m, r, the density of air pa, and the density of helium PHe (Use any variable or symbol stated above along with the following as necessary: TT.) m₂ = (d) Find the numerical value of the mass m₂. kg (e) Find the length h numerically. m
A helium-filled balloon (whose envelope has a mass of m = 0.260 kg) is tied to a uniform string of length = 2.50 m and mass m = 0.049 9 kg. The balloon is spherical with a radius of r = 0.398 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? O the ideal fluid model a particle in equilibrium model a particle under constant velocity model O a particle under constant acceleration 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 FHe 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: . Follow the sign convention that upward is the positive direction.) = 0 sty (c) Make an appropriate substitution for each of these forces and solve symbolically for the mass me of the segment of string of length h in terms of m, r, the density of air pa, and the density of helium PHe (Use any variable or symbol stated above along with the following as necessary: TT.) m₂ = (d) Find the numerical value of the mass m₂. kg (e) Find the length h numerically. m
College Physics
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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(a) When the balloon remains stationary, what is the appropriate analysis model to describe it?
- \( \circ \) the ideal fluid model
- \( \circ \) a particle in equilibrium model
- \( \circ \) a particle under constant velocity model
- \( \circ \) a particle under constant acceleration model
(b) Write a force equation for the balloon from this model in terms of the buoyant force \( B \), the weight \( F_b \) of the balloon, the weight \( F_{\text{He}} \) of the helium, and the weight \( F_s \) of the segment of string of length \( h \). (Use any variable or symbol stated above along with the following as necessary: \( \pi \). Follow the sign convention that upward is the positive direction.)
\[
\Sigma F_y = \, \boxed{} \, = 0
\]
(c) Make an appropriate substitution for each of these forces and solve symbolically for the mass \( m_s \) of the segment of string of length \( h \) in terms of \( m_b, r, \) the density of air \( \rho_{\text{air}}, \) and the density of helium \( \rho_{\text{He}} \). (Use any variable or symbol stated above along with the following as necessary: \( \pi \).)
\[
m_s = \, \boxed{}
\]
(d) Find the numerical value of the mass \( m_s \).
\[
\boxed{} \, \text{kg}
\]
(e) Find the length \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08aa0b19-cba0-4fd4-b1f6-356b8c0f7ad5%2F0037d428-e71a-4f08-a60e-d1bf8ec10a2d%2Fxk74f5i_processed.png&w=3840&q=75)
Transcribed Image Text:A helium-filled balloon (whose envelope has a mass of \( m_b = 0.260 \, \text{kg} \)) is tied to a uniform string of length \( \ell = 2.50 \, \text{m} \) and mass \( m = 0.049 \, \text{kg} \). The balloon is spherical with a radius of \( r = 0.398 \, \text{m} \). When released in air of temperature 20°C and density \( \rho_{\text{air}} = 1.20 \, \text{kg/m}^3 \), 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.
(a) When the balloon remains stationary, what is the appropriate analysis model to describe it?
- \( \circ \) the ideal fluid model
- \( \circ \) a particle in equilibrium model
- \( \circ \) a particle under constant velocity model
- \( \circ \) a particle under constant acceleration model
(b) Write a force equation for the balloon from this model in terms of the buoyant force \( B \), the weight \( F_b \) of the balloon, the weight \( F_{\text{He}} \) of the helium, and the weight \( F_s \) of the segment of string of length \( h \). (Use any variable or symbol stated above along with the following as necessary: \( \pi \). Follow the sign convention that upward is the positive direction.)
\[
\Sigma F_y = \, \boxed{} \, = 0
\]
(c) Make an appropriate substitution for each of these forces and solve symbolically for the mass \( m_s \) of the segment of string of length \( h \) in terms of \( m_b, r, \) the density of air \( \rho_{\text{air}}, \) and the density of helium \( \rho_{\text{He}} \). (Use any variable or symbol stated above along with the following as necessary: \( \pi \).)
\[
m_s = \, \boxed{}
\]
(d) Find the numerical value of the mass \( m_s \).
\[
\boxed{} \, \text{kg}
\]
(e) Find the length \(
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Step 1: Determine the given data:
VIEWStep 2: (a) Find the Equilibrium model
VIEWStep 3: Free-body diagram
VIEWStep 4: (b) Write the Force equation:
VIEWStep 5: c) Mass of the segment of string
VIEWStep 6: d) Calculate the mass of string of height h:
VIEWStep 7: e) Calculate the height of the string:
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