I used this forum to get a lot of help with the first problem on my quarterly, but there are still 2 more problems and nobody in my class knows how to do them. I was hoping somebody here would. Here are the problems 1. A particle of mass m moves in a conservative force field described by the potential energy function U(r) = a(r/b +b/r), where a and b are positive constants and r is teh distance from the origin. The graph of U(r) has the following shape. a. In terms of the constants a and b, determine the following. i. The position ro (the 0 is subscript) at which the potential energy is a minimum ii. The minimum potential energy Uo (also subscript) b. Sketch the net force on the particle as a function of r on the graph below, considering a force directed away from the origin to be positive, and a force directed toward the origin to be negative. The particle is released from rest at r = ro/2 c. In terms of Uo and m, determine the speed of the particle when it is at r=ro. d. Write the equation or equations that could be used to determine where, if ever, the particle will again come to rest. It is not necessary to solve for this position. e. Briefly and qualitatively describe the motion of the particle over a long period of time. The first graph is like a swoosh. On the right it has Uo and U and on the bottom it shows r, 2r, 3r, and 4r. Dashed lines connect to meet at a point from Uo and r to get to the lowest point of the swoosh. The graph it says to draw on is just F on the y axis and r on the x axis. 2. Two stars, A and B are in circular orbits of radii ra and rb, respectively, about their common center of mass at point P, as shown above. Each star has the same period of revolution T. Determine expressions for the following three quantities in terms of ra, rb, T, and fundamental constants. a. The centripetal acceleration of star A b. The mass Mb of star B c. The mass Ma of star A Determine expressions for the following two quantities in terms of Ma, Mb, ra, rb, T, and fundamental constants. d. The moment of inertia of teh two-star system about its center of mass. e. The angular momentum of the system about the center of mass. The picture is 2 circles, one inside the other. B is on the outer circle to the right, rb is on the inner circle to the right, P is in the center, A is on the inner circle to the left, and ra is between P and A. I know it's a lot. I'm sorry I just really really need help. If you know how to do any part of either of these questions, help would be REALLY appreciated!