Question

An 80 kg skydiver falls through air with a density of 1.15 kg/m3 . Assume that his drag coefficient is C=0.57. When he falls in the spread-eagle position his body presents an area A1=0.94 m2 to the wind, whereas when he dives head first, with arms close to the body and legs together his area is reduced to A2=0.21 m2 . What are the terminal speeds in both cases?

Answer 1

An 80-kg skydiver falls through air with a density of 1.15 kg/m³. Assume that his drag coefficient is c_d = 0.57. When he falls in the spread-eagle position, as shown in Figure 4.21a, his body presents an area A₁ = 0.94 m² to the wind, whereas when he dives head first, with arms close to the body and legs together, as shown in Figure 4.21b, his area is reduced to A₂ = 0.21 m².

PROBLEM

What are the terminal speeds in both cases?

SOLUTION

We use equation 4.14 for the terminal speed and equation 4.15 for the air resistance constant, rearrange the formulas, and insert the given numbers:

These results show that, by diving head first, the skydiver can reach higher velocities during free fall than when he uses the spread-eagle position. Therefore, it is possible to catch up to a person who has fallen out of an airplane, assuming that the person is not diving head first, too. However, in general, this technique cannot be used to save such a person because it would be nearly impossible to hold onto him or her during the sudden deceleration shock caused by the rescuer's parachute opening.

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Tribology

What causes friction? The answer to this question is not at all easy or obvious. When surfaces rub against each other, different atoms (more on atoms in Chapter 13) from the two surfaces make contact with each other in different ways. Atoms get dislocated in the process of dragging surfaces across each other. Electrostatic interaction (more on this in Chapter 21) between the atoms on the surfaces causes additional static friction. A true microscopic understanding of friction is beyond the scope of this book and is currently the focus of great research activity.

The science of friction has a name: tribology. The laws of friction we have discussed were already known 300 years ago. Their discovery is generally credited to Guillaume Amontons and Charles Augustin de Coulomb, but even Leonardo da Vinci may have known them. Yet amazing things are still being discovered about friction, lubrication, and wear.

FIGURE 4.22

Cut-away drawing of a microscope used to study friction forces by dragging a probe in the form of sharp point across the surface to be studied.

Perhaps the most interesting advance in tribology that occurred in the last two decades was the development of atomic and friction force microscopes. The basic principle that these microscopes employ is the dragging of a very sharp tip across a surface with analysis by cutting-edge computer and sensor technology. Such friction force microscopes can measure friction forces as small as 10 pN = 10^?11 N. Shown in Figure 4.22 is a cut-away schematic drawing of one of these instruments, constructed by physicists at the University of Leiden, Netherlands. State-of-the-art microscopic simulations of friction are still not able to completely explain it, and so this research area is of great interest in the field of nanotechnology.

Friction is responsible for the breaking off of small particles from surfaces that rub against each other, causing wear. This phenomenon is of particular importance in high-performance car engines, which require specially formulated lubricants. Understanding the influence of small surface impurities on the friction force is of great interest in this context. Research into lubricants continues to try to find ways to reduce the coefficient of kinetic friction, ?_k, to a value as close to zero as possible. For example, modern lubricants include buckyballs