While making holiday decorations for your home, you alternately string together cranberries (each identical with mass mc = 2.83 g), and pieces of popcorn (each identical and with mass mp = 0.37 g). You start with a cranberry and then string on a piece of popcorn a distance d = 1.89 cm along the string. You continue the pattern of 1 cranberry, 1 piece of popcorn, each equidistant. Fortunately, you are using is the special massless string that your physics instructor gave you for your outstanding inquiry skills. For this problem, treat the cranberries and pieces of popcorn as point masses. Let the position of the first cranberry be x = 0.

Part (a) If you have attached only 1 cranberry and 1 piece of popcorn, determine the position of the center of mass (in cm) with respect to the first cranberry.

Part (b) Find the position of the center of mass (in cm) with respect to the first cranberry if you have used 2 cranberries and 1 piece of popcorn.

Part (c) Find the position of the center of mass (in cm) with respect to the first cranberry if you have used 2 cranberries and 2 pieces of popcorn.

Part (d) Find the position of the center of mass (in cm) with respect to the first cranberry if you have used 3 cranberries and 2 pieces of popcorn.

Part (e) Determine an expression for the position of the center of mass with respect to the first cranberry if you have used an integral number n cranberries and (n -1) pieces of popcorn.