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Tube curvature radius

Curvature of a curve. The curvature of the plane curve is a tangent to the curve of a certain point on the tangent of the angle of the arc length of the rotation rate, the definition of the differential to show the extent of the curve deviate from the line.

When the K=lim| / alpha Delta Delta s| Delta s tends to 0, K is the definition of curvature.

The reciprocal of curvature is the radius of curvature.

Radius of curvature is used to describe the curve of a certain extent of the curve of the curve of the extent of the special, such as: a circle radius of curvature of a circle is exactly equal to the radius of the circle, may be able to understand: that is, that a section of the curve as possible differential, until the end of a circular arc, the radius of this circle, personal understanding

For example

Application problems of curvature and curvature radius

A plane along a parabolic path y= (x^2) /10000 (Y axis vertical, the unit is m) for diving flight, in

The speed of the aircraft at the origin of O is v=200m/s. Pilot weight G=70kg. Find the plane dive to the most

Low that is the origin of the O at the time of the seat to the pilot's reaction.

Solution:

Y=x^2/10000

Y''=1/2x/10000=x/5000

=1/5000 "Y

Requires the aircraft to dive to the origin of the O seat to the pilot's anti force, so that x=0, then:

Y''=0

=1/5000 "Y

Into the formula of curvature radius P =1/k=[(1+y''^2) ^ (3/2), y, =5000 M / "

So the centripetal force of F=mv^2/ P =70*200^2/5000=560 pilots by cattle

To dive to the origin of the aircraft to the O position of the pilot's anti force

R=F+mg=560+70*9.8=1246N