Hooke's law

Fs = íkx

Fs = spring force

k = spring constant

x = displacement of end from rest point

What is the force exerted by the

spring?

Fs = íkx

Fs = í(4.2 N/m)(0.36 m)

Fs = í1.5 N (to the left)

5.24 - Air resistance

Air resistance: A force that opposes motion in

air.

If you parachute, or bike or ski, you have experienced air resistance. In each of these

activities, you move through a fluid í air í that resists your motion. As you move

through the air, you collide with the molecules that make up the atmosphere. Although

air is not very dense and the molecules are very small, there are so many of them that

their effects add up to a significant force. The sum of all these collisions is the force

called air resistance.

Unlike kinetic friction, air resistance is not constant but increases as the speed of the

object increases. The force created by air resistance is called drag.

The formula in Equation 1 supplies an approximation of the force of air resistance for

objects moving at relatively high speeds through air. For instance, it is a relevant

equation for the skysurfer shown in Concept 1, or for an airplane. The resistance is

proportional to the square of the speed and to the cross sectional area of the moving object. (For the skysurfer, the board would constitute the

main part of the cross sectional area.) It is also proportional to an empirically determined constant called the drag coefficient.

The shape of an object determines its drag coefficient. A significant change in speed can change the drag coefficient, as well. Aerospace

engineers definitely earn their keep by analyzing air resistance using powerful computers. They also use wind tunnels to check their

computational results.

Another interesting implication of the drag force equation is that objects will reach what is called terminal velocity. Terminal velocity is the

maximum speed an object reaches when falling. The drag force increases with speed while the force of gravity is constant; at some point, the

Air resistance

Drag force opposes motion in air

Force increases as speed increases

(^108) Copyright 2007 Kinetic Books Co. Chapter 05