A uniform rod of length 2 m and of mass 34 kg is suspended by two vertical strings - Leaving Cert Applied Maths - Question 7 - 2009

To find the length of the section ab:

1. Consider the moments about point c: The weight of the 3.4 kg mass will create a moment about point c. The equation for moments can be written as:

   $F_1(1.5) = 3.48g(34)(0.8)$
   To ensure balance, the upward moments must equal the downward moments:

   $20.74g(1.5 - x) = 3.48g(1 + 34)(0.8)$

   Solving this gives:

   $x = 1.15 ext{ m}$

2. Consider the moments about point d: Similarly, treating moments about point d:

   $F_1(1.5) = 3.48g(34)(0.7)$

   Which leads to:

   $17g(1.5 - x) = 3.48g(34)(0.7)$

   Thus, solving results in:

   $x = 1 ext{ m}$

3. Determine the length of ab: By considering distances, we find:

   $|ab| = 0.15 ext{ m or } 15 ext{ cm}$