Question

Problem 2 (25 points) – show detailed steps The collar has a mass of 0.6 kg. It is released from rest at point A and moves down along the frictionless vertical rod. Neglect the size of the collar and the diameter of the rod. The spring has a natural length of 1.5 m and a spring constant of k = 30 N/m. Solve the following: a) Draw a free body diagram of the collar at a typical position 2 m between A and C. (4 pts) b) Explicitly specify the condition under which the collar achieves the maximum vertical displacement s. (4 pts) c) Use work and energy methods (either the principle of work and energy or conservation of energy, whichever fits the best) to determine the maximum displacement s. (17 pts) (You should at least build a correct equation for s. You are not required to solve the equation for a specific value of s) k = 30 N/m S wa C

Answer 1

FBP → spring force Normal reaction no Potential mgas mg Condition for maximum vertical displacement is the total change in energy should be converted to spring energy ③ Change in Potential energy =) 0- 6x9.81 xS >) 5.886(5) spring energy stored as £ Kxe? x- expansion of spring X final length - initial length 72²5² 1.5 so 블 (30) (17753-115) 2 S 1275² 1.588615) = equation is 1.588615) = 2 1.130) (12+52-1-5) 15(tu 4+5+ -1.5)? Requred equation 1.5888 (5)