The setup is shown below. It consists of a ruler (L = 50cm long) and a small slab of lead setting on top of the ruler. The slab of lead has width t 0.026m, (equal to the width of the ruler), thickness s = 0.0017m, and length k (a variable to be determined). The left end of the lead slab is to remain flush with the end of the ruler (x = 50cm). Imagine that we have many pieces of lead, all of different lengths k (but t and s remain the same). Lead Ruler Coff Lead L Ruler The Challenge: What value of length of lead slab (k) - looking for an actual number gives the most extreme value of the balance point of the ruler/lead system. In other words, what value of k for the lead forces the balance point the furthest to the left this point being Xcofg (the center of gravity or balance point) of the entire system (lead and ruler)? Important locations (where x is measured from right hand end of ruler, as shown in the figure) XLead location of the center of mass of the Lead slab (variable) XCofg location of the center of gravity (balance point) of whole system (Lead slab and Ruler combined) (variable) XRuler location of the center of mass of the Ruler (constant: 0.25m) Density of lead= 8770kg/m³ Mass of ruler 0.0672kg Keep the following in mind: the s and t dimensions of the lead slab remain constant. The left end of the lead slab must stay flush with the left end of the ruler. The center of mass of the ruler, XRuler, is constant and is located at L/2. Wondering where to begin? The balance point of ruler plus lead slab (xcofg) is given by XCofg = (m1XRuler +m2XLead)/M (Look this up in your text book) = Where mi mass of ruler (constant), m2 mass of lead slab (variable: depends on size of k), XRuler constant = 0.25m. XLead position of the center of the lead slab (a variable depending on size of k) and M = m1 + m2.