MAT 127 Midterm: S07mt2sol
31 Jan 2019
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April 4, 2007: (25 pts) let m denote the mass of the earth. Newtons on an object of mass m which is r meters away from the center of the earth. (treat g, m, m as constants in this problem. ) Let re denote the radius of the earth (a constant). Find the work required to move the object from the surface of the earth (r = re) to a point in nitely far from earth (r = ). (ignore the gravitational pull of other astronomical bodies. ) A correct solution must involve taking a limit! The work is the integral of the force. W = z t (cid:2) gmmr 1(cid:12)(cid:12) t re re. Gmm r2 dr = lim t z t re. Joules: (25 pts) find the volume of the solid obtained by rotating the shaded region around the x-axis. (begin by deciding whether to use dx or dy. )
