Problem 6: A child's toy consists of a m = 42 g monkey suspended from a spring of negligible mass and spring constant k. When the toy monkey is first hung on the spring and the system reaches equilibrium, the spring has stretched a distance of x = 16.1 cm, as shown in the diagram. This toy is so adorable you pull the monkey down an additional d = 4.1 cm from equilibrium and release it from rest, and smile with delight as it bounces playfully up and down. Unstretched Position Equilibrium Stretched Position Part (a) Using the given information, determine the spring constant, k, in Newtons per meter, of the spring. Numeric : A numeric value is expected and not an expression. k = Part (b) Select the free-body diagram that best represents the forces acting on the monkey as you are pulling it down, immediately before you let go. SchematicChoice : F. F. AF, spring spring spring F F. F gravity F applied applied F, A F. spring -spring F. Fopplied spring F E. gravity F. gravit gravity applied Part (c) Calculate the potential energy, Epottom, in joules, stored in the stretched spring immediately before you release it. Numeric : A numeric value is expected and not an expression. Epottom = Part (d) Assume that the system has zero gravitational potential energy at the lowest point of the motion. Derive an expression for the total mechanical energy, Eequilibrium of the system as the monkey passes through the equilibrium position in terms of m, x, d, g, k, and the speed of the monkey, ve- Expression: Eequilibrium = Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, a, d, g, h,max, i, j, k, m, P, t, ve, X Part (e) Calculate the speed of the monkey, ve, in meters per second, as it passes through equilibrium. Numeric : A numeric value is expected and not an expression. Ve = Part (f) Derive an expression for the total mechanical energy of the system as the monkey reaches the top of the motion, Eop; in terms of m, x, d, k, the maximum height above the bottom of the motion, har, and the variables available in the palette. Expression : Etop = Select from the variables below to write your expression. Note that all variables may not be required. a. B, 0, a, d, g, hmax, i, j, k, m, P, t, ve, x Part (g) Calculate the maximum displacement, h, in centimeters, above the equilibrium position, that the monkey reaches. Numeric : A numeric value is expected and not an expression. h =