Falling Balloon

Classical Mechanics Level 2

A balloon of gross weight W W newton is falling vertically downward with a constant acceleration a ( < g ) a \ (<g) , find the magnitude of air resistance.

W ( 1 − a g ) W\left( 1-\frac{a}{g}\right) W W W ( a g ) W\left(\frac{a}{g}\right) W ( 1 + a g ) W\left( 1+\frac{a}{g}\right)

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Akshat Sharda by Akshat Sharda , 21, India

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1 solution

Chew-Seong Cheong
Jun 16, 2016

The air resistance is a force given by F a = m a r F_a = ma_r , where m m is the mass of the balloon and a r a_r , the deceleration due to air resistance. Therefore, we have:

F a = m a r We note that m = W g and a r = g − a = W g ( g − a ) = W ( 1 − a g ) \begin{aligned} F_a & = \color{#3D99F6}{m}\color{#D61F06}{a_r} \quad \quad \small \text{We note that } \color{#3D99F6}{m = \frac Wg} \text{ and } \color{#D61F06}{a_r = g-a} \\ & = \color{#3D99F6}{\frac Wg}\color{#D61F06}{(g-a)} \\ & = \boxed{W \left(1-\dfrac ag \right)} \end{aligned}

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Thank you☺ it helps

Sonia Singh - 2 years, 8 months ago

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