Homework 3 Problem 2.127 8 of 10 > The hot-air balloon contains air having a tem

Question

Homework 3 Problem 2.127 8 of 10 > The hot-air balloon contains air having a temperature of 180 F while the surrounding air has a temperature of 60°F The densities of air at 180 F and 60 F are 0.00193 slug/ft3 and 0.00237 slug/ft3, respectively. The volume of air the balloon contains is 140(103) ft The empty weight of the balloon is 200 lb .(Figure 1) Part A Determine the maximum weight of the load the balloon can lift Express your answer to three significant figures and include the appropriate units Figure 1 of 1 Submit Previous Answers Request Answer Incorrect; Try Again; 4 attempts remaining Provide Feedback Next >

Explanation / Answer

Buoyancy force equation, F = Vg is used to solve this

Where F is the Buoyancy force,

is the density difference,

V is the displaced volume of air = volume of air inside the baloon

And

g is the gravitational constant (equal to 32.2 feet per second per second)

Given volume of air = 140(10)3 ft3

Density = (0.00237 - 0.00193) slug/ft. = .00044 slug/ft.

Using Newton's third law; the maximum weight it could carry equals to the lifting force of the balloon.

Fmax=Vg

= 0.00044 slug/ft. x 140(10)3 ft3 x 32 ft./sec2

=1971.2 lbs

Weight of empty ballon = 200 lbs

SO extra weight it can carry= 1971.2 – 200

=1771.2 lb

=1771 lb (approx.)

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