(a) Without changing the magnitude of any of the forces in Example 12.2, how must you adjust the direction of \(\vec{F}_{3}\) to prevent the lever from rotating?

(b) If, instead of adjusting the direction of \(\vec{F}_{3}\), you adjust the magnitude of \(\vec{F}_{2}\), by what factor must you change it?

Data from Example 12.2

Three forces are exerted on the lever of Figure 12.7. Forces \(\vec{F}_{1}\) and \(\vec{F}_{3}\) are equal in magnitude, and the magnitude of \(\vec{F}_{2}\) is half as great. Force \(\vec{F}_{1}\) is horizontal, \(\vec{F}_{2}\) and \(\vec{F}_{3}\) are vertical, and the lever makes an angle of \(45^{\circ}\) with the horizontal. Do these forces cause the lever to rotate about the pivot? If so, in which direction?

Transcribed Image Text:

Figure 12.7 The TH 8/3 pivot 45 f/3 1/3