The reactions on the bent rod.

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Chapter 5, Problem 25P

To determine

The reactions on the bent rod.

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Problem 1 (30 Points) Consider the following 2 scenarios. In scenario 1, a mass m slides on a cylindrical surface of radius R. In scenario 2, a mass m hangs at the end of a thin massless rod of length R. In both scenarios, there is no friction either on the surface (scenario 1), or at the pivot point of the pendulum (scenario 2). Also in both scenarios, there is one generalized coordinate, . R Scenario 1 R m R g Scenario 2 m HINT: In both scenarios, it is much easier to choose your datum for potential energy as the center of the bowl (scenario 1), or the pivot point of the pendulum (scenario 2). Part I a) Determine the Lagrangian for each system. DO NOT FIND THE EQUATIONS OF MOTION (5 points) b) What can you say about the systems based on the Lagrangian? (2 points) c) Solve for the equations of motion for both systems. (8 points) Part II Now, for scenario 1, introduce an additional coordinate and treat it as a nonholonomic system to determine the normal force acting on the mass. a)…