Question
cylinder of mass m rolls down the inclined surface AB without friction. If both cylinder and prism are at rest initially, what will be the relative velocity vr and absolute velocity v0 of the cylinder's center O after its height decreased by h. Ans. vr = Hints: 1. You may use conservation of momentum principle for the system cylinder-prism to relate velocities of prism and of cylinder's center (absolute vo and relative vrel) When you apply conservation of energy relation do NOT forget to account for kinetic energy of the cylinder's rotation. Solutions are to be brought in at the Exam # 4, by 9:50 AM on 10/11/12. M-6A. A cord is wrapped around spool of inner and outer radii r and R respectively. The spool of mass m and radius of gyration kG rests on a flat rough horizontal surface and does not slip whenever it is in rolling motion. Force F is applied to the cord inclined by angle 6 to the surface. Derive formula for resulting horizontal acceleration ax of the spool's mass center. Explain in words meaning of positive and negative values of ax. M-6B. Planetary mechanism consists of three gears each of mass M and radius r and arm OA which may be regarded as a uniform bar of mass m. The gear 1 is fixed whereas gears 2 and 3 may be regarded as uniform solid disks. Find kinetic energy T of the whole system for the case where the arm rotates in horizontal plane with constant angular velocity omega. Ans. T = omega 2r2/3. (33M + 8w) M-6 C. A gymnast A and a weight B - each of mass M- are attached to a cord/pulley set as shown. The whole system is originally at equilibrium. Then the gymnast starts climbing along the cord with velocity vr relative to the cord. What will be the resulting velocity vc of the cord with attached weight B if the pulley may be regarded as a thin solid disk of mass m and outer radius R? You may obtain the solution using conservation of angular momentum principle. M- 6 D. A right triangular prism ABD with inclination angle 30 degree and mass m can slide without friction along smooth horizontal surface. A uniform solid cylinder of mass m rolls down the inclined surface AB without friction. If both cylinder and prism are at rest initially, what will be the relative velocity vr and absolute velocity v0 of the cylinder's center O after its height decreased by h. Ans. vr = Hints: 1. You may use conservation of momentum principle for the system cylinder-prism to relate velocities of prism and of cylinder's center (absolute v0 and relative vrel) When you apply conservation of energy relation do NOT forget to account for kinetic energy of the cylinder's rotation. Solutions are to be brought in at the Exam # 4, by 9:50 AM on 10/11/12.
Explanation / Answer
The pictures are inverted...please post again with upright pictures.
