Consider the telescoping boom and cockpit of the firetruck shown in Fig. 2.12(a). Assume that the telescoping boom \(P Q R S\) is supported by a strut \(Q T\), as shown in Fig. 2.129. Determine the cross section of the strut \(Q T\) so that the natural time period of vibration of the cockpit with the fireperson is equal to \(1 \mathrm{~s}\) for the following data. Assume that each segment of the telescoping boom and the strut is hollow circular in cross section. In addition, assume that the strut acts as a spring that deforms only in the axial direction.

Data:
Lengths of segments: \(P Q=3.6 \mathrm{~m}, Q R=3 \mathrm{~m}, R S=2.4 \mathrm{~m}, T P=0.9 \mathrm{~m}\)
Young's modulus of the telescoping arm and strut \(=200 \mathrm{GPa}\)
Outer diameters of sections: \(P Q=5 \mathrm{~cm}, Q R=3.75 \mathrm{~cm}, R S=2.5 \mathrm{~cm}\)
Inner diameters of sections: \(P Q=4.5 \mathrm{~cm}, Q R=3.25 \mathrm{~cm}, R S=2 \mathrm{~cm}\)
Weight of the cockpit \(=50 \mathrm{~kg}\)
Weight of fireperson \(=100 \mathrm{~kg}\)

Figure 2.12:-

Transcribed Image Text:

S A3,13 R A2, 12 -A1,41 Strut 3' FIGURE 2.129 Telescoping boom and cockpit of fireman.