Calculating Pennies Suspended by Balloon as it Deflates

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In summary, a latex balloon with an excess pressure of 1kPa and a radius of 30cm can be used to suspend pennies in midair as it deflates. The number of pennies it can suspend can be calculated by considering the force of the balloon and the force of the pennies, assuming an elastic collision and using the Bernoulli equation to calculate the velocity of the escaping air molecules. Other simplifying assumptions include air being an ideal gas with a specific heat of (5/2)R and a molar mass of 28g/mol, and the balloon pressure remaining constant as it deflates.
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seeveedubyah
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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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  • #2
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?
 

What is the purpose of calculating pennies suspended by a balloon as it deflates?

The purpose of this experiment is to understand the principles of buoyancy and pressure, and how they affect objects suspended in air.

What materials are needed for this experiment?

The materials needed include a helium balloon, a string, a ruler, a stopwatch, and a set of pennies.

How do you set up the experiment?

First, tie the string to the helium balloon and measure the length of the string. Then, add pennies to the balloon one at a time and record the length of the string after each penny is added. Finally, time how long it takes for the balloon to fully deflate and record the time.

What is the relationship between the number of pennies and the rate of deflation of the balloon?

The more pennies added to the balloon, the faster the balloon will deflate. This is because the weight of the pennies increases the pressure inside the balloon, causing the air to escape more quickly.

What can be concluded from the results of this experiment?

Based on the results, it can be concluded that as the weight of the suspended object increases, the rate of deflation of the balloon also increases. This demonstrates the principles of buoyancy and pressure in action.

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