Question

3. A piece of thin-walled pipe and a spring are lying on their sides on a level table. The spring is kept compressed and the pipe is placed against one end of it such that when the spring is ļet go, it will push against the pipe and start it rolling without slipping on the table (i.e., the length of the spring is perpendicular to the length of the pipe; the other end of the spring is fixed). If the pipe has total mass 0.2 kg and radius 0.05 m, and the spring has spring constant 10 N/m and is compressed to a length that is 0.1m shorter than its equilibrium length, determine the pipe's speed once it has lost contact with the spring. Submit your answer in the following form: • Referring to the numbered equation list attached to the end of the exam, list only the equation numbers relevant for this problem. • Give your numerical answer for the relevant moment of inertia of the pipe. . Give the numerical factor by which one has to multiply the angular speed of the pipe to obtain the speed of the pipe. • Give your numerical answer for the speed of the pipe.

Answer 1

solution Given 0.2 kg man of pipe (m) radies of pipe (4) 0.65 m moment Inutia (I) I MRZ – x 0,2x10.0572 2.5x10.4 kg. m2 when pipe lost contact with the spring, the entire spring potential enugy gets converted ento rotational kinetic energy of pipe acording of conservation mechanical energy haw - taw2 3442 2. (10) (001)² (2.5x10th) w2 w marads Anguloy speed of pipe BORS riadis hineau speed of pipe (u) = ow 0:05 x 20 1 m/s