Chapter 12, Problem 88E

(a)

To determine

Prove that $dp=\rho adx$ using Newton’s second law on volume element.

(b)

To determine

The formula to find pressure at the front surface in terms f $a$ and $x$.

(c)

To determine

The pressure difference in atm.

(d)

To determine

Prove that the horizontal force on balloon is $\rho Va$.

(e)

To determine

Prove that the acceleration of balloon is $\left(\rho /{\rho }_{\text{bal}}\right)a$ and the acceleration relative to car is $a_{\text{rel}}=\left[\left(\rho /{\rho }_{\text{bal}}\right)-1\right]a$ .

(f)

To determine

Explain the movement of balloon using the expression for $a_{\text{rel}}$ obtained in part (e).