Chapter 6, Problem 69A

Glue a penny to a string. When in a moving automobile, hang the string and penny out a window. Tt will be swept backward due to air resistance. When the string makes an angle of $45°$, easily seen with a protractor, the air resistance on the coin equals the weight of the coin. A look at the speedometer tells you the coin’s terminal speed in air! Do you see why the angle makes a difference?

To determine

To Explain: The angle makes the difference in the reading of the speedometer.

Explanation of Solution

Introduction:

The drag force varies directly with the square of the speed of the object such that

  $F_D\propto v^2$

Or,

  $F_D=b{v}^2$

Where, b is the proportionality constant which is equal to the $b=0.5C\rho A$

So, the above expression becomes,

  $F_D=0.5C\rho A{v}^2$

The drag force magnitude increases until this magnitude become equals to the gravitational force as velocity of the person increases. Thus, it produces a zero-net force. The terminal speed is depending on the inclination angle. As the angle increases, the speed also increases and hence, the drag force also increases.

Conclusion:

Thus, the angle makes the difference.