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Chapter 1: Q26E (page 95)

A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. (a) What is the linear speed of the blade tip, in m/s? (b) What is the radial acceleration of the blade tip expressed as a multiple of g?

Short Answer

Expert verified
  1. The linear velocity of the blade is 195.8 m/s.
  2. The radial acceleration of the blade tip is 11275.8 m/s2or 1.15x103g.

Step by step solution

01

Identification of given data:

The given data can be listed below,

  • The length of blades of rotor is, r = 3.4 m
  • The rate of rotation of rotor is,蝇=550rev/min
02

Concept/Significance of radial acceleration:

The acceleration in a uniform circular motion that is pointed in that direction is referred to as centripetal or radial acceleration.

03

(a) Determination of the linear speed of the blade tip:

The linear velocity of the blade is given by,

v=蝇r

Here, 蝇is the angular velocity of the blade, and r is the radial distance.

Substitute all the values in the above,

v=550rev/s2蟺60rad/srev/min脳3.4m=57.6rev/s3.4m=195.8m/s

Thus, the linear velocity of the blade is 195.8 m/s.

04

(b) Determination of the radial acceleration of the blade tip expressed as a multiple of  g:

The radial acceleration of the object is given by,

ar=v2R

Here, v is the velocity of the blade and R is the radius of rotor.

Substitute all the values in the above.

ar=195.8m/s23.4m=11275.8m/s2g9.8m/s2=1.15脳103g

Thus, the radial acceleration of the blade tip is 11275.8m/s2or1.15脳103g.

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