First reread the explanation of how the wind might drag...

First reread the explanation of how the wind might drag desert stones across the playa. Now assume that Eq. 6-23 gives the magnitude of the air drag force on the typical $20 \mathrm{~kg}$ stone, which presents a vertical cross-sectional area to the wind of $0.040 \mathrm{~m}^{2}$ and has a drag coefficient $C$ of $0.80$. Take the air density to be $1.21 \mathrm{~kg} / \mathrm{m}^{3}$, and the coefficient of kinetic friction to be $0.80$. (a) In kilometers per hour, what wind speed $V$ along the ground is needed to maintain the stone's motion once it has started moving? Because winds along the ground are retarded by the ground, the wind speeds reported for storms are often measured at a height of $10 \mathrm{~m}$. Assume wind speeds are $2.00$ times those along the ground, (b) For your answer to (a), what wind speed would be reported for the storm and is that value reasonable for a high-speed wind in a storm?

Key Concepts

Unit Conversion

Unit conversion involves translating measurements from one set of units to another to ensure consistency and clarity in results. For instance, converting speeds from meters per second to kilometers per hour is common in physics to match the units typically reported in real-world applications.

Wind Speed Variation with Height

Wind speed variation with height refers to the fact that wind speeds can differ significantly at different elevations due to surface friction and atmospheric boundary layer effects. This concept is important when adjusting wind speed measurements taken at a standard height (such as 10 m) to reflect conditions at the ground level.

Force Equilibrium

Force equilibrium occurs when the sum of the forces acting on an object is zero, leading to a constant velocity. In dynamics problems, setting the driving force equal to the resisting forces (such as friction) allows one to solve for unknown variables like the required speed for sustained motion.

Drag Coefficient

The drag coefficient is a dimensionless number that characterizes the resistance an object encounters as it moves through a fluid. It depends on the shape, texture, and flow conditions around the object, and is crucial in determining the magnitude of the aerodynamic drag force.

Drag Force

The drag force is the resistive force that an object experiences as it moves through a fluid, such as air. It is given by the equation F_d = (1/2) C A ? V^2, where C is the drag coefficient, A is the reference area, ? is the fluid density, and V is the relative speed between the object and the fluid.

Kinetic Friction

Kinetic friction is the force that opposes the movement of two sliding surfaces in contact. It is proportional to the normal force acting on the object with the proportionality determined by the coefficient of kinetic friction, playing an important role in scenarios where motion must overcome surface resistance.

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