Five balls move through the air as shown in FIGURE. All

Chapter 6, Problem 18CQ

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QUESTION:

Five balls move through the air as shown in FIGURE Q6.18. All five have the same size and shape. Air resistance is not negligible. Rank in order, from largest to smallest, the magnitudes of the accelerations \(a_{\mathrm{a}}\) to \(a_{\mathrm{c}}\). Some may be equal. Give your answer in the form \(\mathrm{a}>\mathrm{b}=\mathrm{c}>\mathrm{d}>\mathrm{e}\) and explain your ranking.

                     

Equation Transcription:

Text Transcription:

a_a

a_e

a>b=c>d

Questions & Answers

QUESTION:

Five balls move through the air as shown in FIGURE Q6.18. All five have the same size and shape. Air resistance is not negligible. Rank in order, from largest to smallest, the magnitudes of the accelerations \(a_{\mathrm{a}}\) to \(a_{\mathrm{c}}\). Some may be equal. Give your answer in the form \(\mathrm{a}>\mathrm{b}=\mathrm{c}>\mathrm{d}>\mathrm{e}\) and explain your ranking.

                     

Equation Transcription:

Text Transcription:

a_a

a_e

a>b=c>d

ANSWER:

Step 1 of 2

Our aim here is to arrange the acceleration on the balls in the descending order.

The balls are acted by the gravity and the drag force due to air.

The air drag is given by

                                            \(D=\frac{1}{2} C \rho A v^{2}\)

Where \(C\) is the drag coefficient and smaller for aerodynamically shaped bodies like the sphere. \(\rho\) is the density of air

\(A\) is the area of the body

\(v\) is speed of the body

Here the balls have the same size and the area must be constant. The density and drag coefficient are also constant. The drag force only depends on the speed of the objects and mass independent.

                                                \(D \propto v^{2}\)

Since the drag force is directly proportional to the square of the speed, the acceleration of the objects will be affected. The drag force keeps on increasing as the speed increases. And it results in the decrease in the acceleration.

 

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