vertical extent of free-loat frame near earth note: this exercise makes use of elementary calculus and the newtonian theory of gravitation a paragraph in section 2.3 says: as another example, drop the same antique [20-meter- long] railway coach from rest in a vertical orientation, with the lower end of the coach inicially 315 meters from the surface of earth (figure 2-5, right). again release two tiny ball bearings from rest at opposite ends of the coach. in this case, during the time of fall [8 seconds], the ball bearings move apart by a distance of two millimeters because of the greater gravitational acceleration of the one nearer earth, as newton would put it. this is twice the change that occurs for horizontal separation. demonstrate this 2-millimeter increase in separation. the following outline may be useful. take the gravi- tational acceleration at the surface of earth to bego- 9.8 meters/second" and the radius of earth to be 637 × 106 meters. more generally, the gravitational acceleration g of a particle of mass m a distance r from the center of earth (mass m) is given by the expression a take the differential of this equation for g to obtain an approximate algebraic expression for ag the change in g, for a small change ar in height. b now use ay-agr® to find an algebraic expression for increase in distance δy between ball bearings in a fall that lasts for time t c substitute numbers given in the quotation above to verify the 2-millimeter change in separation during fall.