Calculating Pennies Suspended by Balloon as it Deflates

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SUMMARY

The discussion centers on calculating the number of pennies a latex balloon can suspend as it deflates, given specific parameters: an excess pressure of 1 kPa and a radius of 30 cm. The balloon deflates in 5 seconds, and the air is treated as an ideal gas with a molar mass of 28 g/mol. Key equations include the first and second laws of thermodynamics, with the assumption that the balloon pressure remains constant during deflation. The primary challenge is determining the force exerted by the deflating air stream and its relationship to the weight of the pennies.

PREREQUISITES
  • Understanding of ideal gas laws and properties
  • Familiarity with thermodynamic principles, specifically the first and second laws
  • Basic knowledge of fluid dynamics, particularly Bernoulli's equation
  • Ability to perform calculations involving force, mass, and momentum
NEXT STEPS
  • Study the ideal gas law and its applications in thermodynamics
  • Learn about Bernoulli's equation and its implications for fluid flow
  • Explore the concepts of momentum and impulse in physics
  • Investigate the principles of elastic collisions and their calculations
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This discussion is beneficial for physics students, educators, and anyone interested in applying thermodynamic principles to real-world scenarios, particularly in fluid dynamics and mechanics.

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Homework Statement


A latex balloon, inflated to an excess pressure of 1kPa and a radius of 30cm, is attached to a
smooth nozzle, initially stoppered. The stopper is removed, and the balloon deflates in 5
seconds. Imagine that you are using the air stream exiting the balloon to suspend pennies in midair. How many pennies (3g each) can the balloon suspend in midair as it deflates? To
simplify the problem, make the following simplifying assumptions: 1) air is an ideal gas, with CV= (5/2)R and a molar mass of 28g/mol (i.e, air is mostly nitrogen); 2) the balloon pressure
remains constant as it deflates; 3) the volume of the balloon when deflated is small.


Homework Equations


First and second law of thermo, dU/dt +Δ((v^2/2 + gz +H)m) =Q +Ws


The Attempt at a Solution


So, work is done by the balloon deflating. The balloon's actual volume can be calculated given the radius. The Force of the balloon must be equal to the force of the pennies. I'm confused as to what i can assume in this problem. I'm not sure if it's isenthalpic or not. There's no heat being added to the system so Q=0.
 
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Since no one has answered for days, just a stab in the dark:

∫F dt = Δp where
F = force holding up pennies = const.
integration time is 5 s
p is change in momentum of the air molecules from when they exit the stopper until after they've impacted on the pennies.

I would assume an elastic collision so that
Δp = 2p = mv
m = mass of air over the 5s
v = escaping molecules' velocity

Think Bernoulli for v?
 

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