As defined in Chapter 7, gravitational potential energy is ?U = ?mgy and is positive for a body of mass m above the earth’s surface (which is at y ? = 0). But in this chapter, gravitational potential energy is ?U = ??Gm?E?m?/?r?. which is negative for a body of mass m above the earth’s surface (which is at r ? = ? ?E). How can you reconcile these seemingly incompatible descriptions of gravitational potential energy?
Solution 10DQ Introduction We have to discuss why there is this apparent anomaly in the sign of gravitational potential. Step 1 The gravitational energy is given by GmEm U = r Now at the surface of the earth the= R E, the potential energy is given by Gm E U s RE And the potential energy at a height y is given by Since y R ,Ewe are we are neglecting the higher order term in the binomial distribution as the terms will be very small. Hence we have Now, we know that acceleration due to gravity is given by So the above equation becomes So we can see that the change in energy while going up is positive. Now the actual potential energy stored in some mass m in some height is the change in potential energy going from surface to that height. Since the change in positive, hence the energy stored is positive.
