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Chapter 6: Q80P (page 147)

Calculate the magnitude of the drag force on a missile 53 cmin diameter cruising at 250 m/sat low altitude, where the density of air is1.2kg/m3. AssumeC=0.75.

Short Answer

Expert verified

The magnitude of the drag force is D=6.2脳103N.

Step by step solution

01

Given data 

  • Radius of missile: R=532cm=0.265m.
  • Velocity=250m/s .
  • The density of air: 蚁=1.2kg/m3.
  • Drag coefficient: C=0.75.
02

Understanding the concept

The problem is based on the concept of drag force. In fluid mechanics, it is the force acting opposite to the relative motion of any object moving with respect to a surrounding fluid.

Formula:

D=12C蚁Av2

Where c = drag coefficient

蚁= density of the medium

A = area of cross-section of the body

v = the velocity of the body through the medium

03

Step 3: Calculate the magnitude of the drag force on a missile

The magnitude of drag force on the missile:

D=12C蚁Av2=12C蚁A蟺R2v2

Substitute values in the above expression, and we get,

D=12脳0.75脳1.2kg/m3脳3.14脳0.265m2脳250m/s2D=6201.7N

Thus, the magnitude of the drag force is6.2脳103N .

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