A large balloon of mass 222 kg is filled with helium gas until its volume is 324

Question

A large balloon of mass 222 kg is filled with helium gas until its volume is 324 m3. Assume the density of air is 1.29 kg/m3 and the density of helium is 0.179 kg/m3.
(a) Draw a free-body diagram for the balloon. (Do this on paper. Your instructor may ask you to turn in this work..)

(b) Calculate the buoyant force acting on the balloon.
N

(c) Find the net force on the balloon and determine whether the balloon will rise or fall after it is released.
N


(d) What maximum additional mass can the balloon support in equilibrium?
kg

(e) What happens to the balloon if the mass of the load is less than the value calculated in part (d)?
a. The balloon and its load will accelerate downward.
b. The balloon and its load will accelerate upward.
c. The balloon and its load will accelerate horizontally.
d. The balloon and its load will remain stationary.


(f) What limits the height to which the balloon can rise? (Select all that apply..)
a. pressure of the surrounding air
b. density of the surrounding air
c. temperature of the surrounding air
d. the hemisphere in which the balloon is locate

Explanation / Answer

(b)

Buoyant force is
F = (pair - phelium)Vg = 3505 N

(c)

Weight = 228 x 9.8 = 2234 N

Net upward force = 3505 - 2234 = 1270 N

(d)

In equilibrium: Fnet=0:

3505 = (228 + m)(9.8)

=> m 130kg

(e)

It will float up but with lesser acceleration.

(f)

temp and pressure of the surr air does affect;

but density of the surrounding air covers all these (its a supraset of conditions).

Hope this helps.

Please rate.

Cheers

:)

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