Two identical discs are connected by four bolts of different sizes and mounted on a shaft, as shown in Fig. 9.42. The masses and locations of three bolts are as follows:

\(m_{1}=35 \mathrm{~g}, r_{1}=110 \mathrm{~mm}\), and \(\theta_{1}=40^{\circ} ; m_{2}=15 \mathrm{~g}, r_{2}=90 \mathrm{~mm}\), and \(\theta_{2}=220^{\circ}\); and \(m_{3}=25 \mathrm{~g}, r_{3}=130 \mathrm{~mm}, \theta_{3}=290^{\circ}\). Find the mass and location of the fourth bolt \(\left(m_{c}, r_{c}\right.\), and \(\theta_{c}\) ), which results in the static balance of the discs.

Transcribed Image Text:

O mi m3 x (a) FIGURE 9.42 Two discs connected by bolts. m1 m3 m2 (b)