How far can a stack of identical books (of mass m and unit length) extend without tipping over? The stack will not tip over if the (n + 1)st book is placed at the bottom of the stack with its right edge located at or before the center of mass of the first n books (Figure 6). Let c_n be the center of mass of the first n books, measured along the x-axis, where we take the positive x-axis to the left of the origin as in Figure 7. Recall that if an object of mass m₁ has center of mass at x₁ and a second object of m₂ has center of mass x₂, then the center of mass of the system has x-coordinate

Transcribed Image Text:

m1x1 + m2x2 m₁ + m2