Question

A balloon filled with helium gas has an average density of Q,-0.41 kg/m'. The density of the air is Qa-1.23 kg/m3. The volume of the balloon is Vb 0.048 m3. The balloon floats upward with acceleration a.

(a) Express the acceleration of the balloon a in terms of the variables given in the problem statement, assuming upwards is the positive direction
Part (b) Calculate the numerical value of a in m/s

Answer 1

a)
`(Qa*g*Vb)-(Qh*Vb*g)=(Qh*Vb*a)\\where \\g=gravity [m/s^2]\\a=acceleration [m/s^2]`

b) a = 19.61[m/s^2]

Step-by-step explanation:

The total mass of the balloon is:

`massball=densityheli*volumeheli\\\\massball=0.41 [kg/m^3]*0.048[m^3]\\massball=0.01968[kg]\\\\`

The buoyancy force acting on the balloon is:

`Fb=densityair*gravity*volumeball\\Fb=1.23[kg/m^3]*9.81[m/s^2]*0.048[m^3]\\Fb=0.579[N]`

Now we need to make a free body diagram where we can see the forces that are acting over the balloon and determinate the acceleration.

In the attached image we can see the free body diagram and the equation deducted by Newton's second law