Question

A balloon filled with helium gas has an average density of ρb = 0.41 kg/m3. The density of the air is about ρa = 1.23 kg/m3. The volume of the balloon is Vb = 0.069 m3. The balloon is floating upward with acceleration a.

a) Express the weight of the balloon, W, in terms of ρ_b and V_b.

b) Calculate the numerical value of W in N.

c) Express the buoyant force F_b in terms of ρ_a and V_b.

d) Calculate the numerical value of F_b in N.

e) Express the total force F in terms of W and F_b assuming upward is the positive direction.

f) Calculate the numerical value of F in N.

g) Express the acceleration a in terms of F, ρ_b and V_b.

Answer 1

a)

Weight of ballon is given as:

b)

Numerical value of weight of ballon :

c)

Buoyancy for on balloon is:

d)

Numerical value of buoyancy force is :

e)

Net upward force on balloon is:

f)

Numerical value of net upward force is:

g)

Let the balloon is accelerating upward with acceleration 'a' then value of 'a' is given as :