Exam text n1

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APPLIED MECHANICS Study Track on Chemical Engineering July 22nd, 2015 Exercise n.1 (only for students who have not got a positive score about kinematic and dynamic yet) The mechanical system illustrated in Fig. 1 moves in a vertical plane. A hydraulic actuator (represented by means of: the slotted link hinged at point O to a fixed frame, the piston having barycentre A and the massless link AB) moves the link CD, hinged at point C to the ground. The slotted link, whose barycentre is G 1, has a mass m1 and a mass moment of inertia J G1. The piston has a mass m 2 and a mass moment of inertia J A. The link CD, whose barycentre is G 3, has a mass m 3 and a mass moment of inertia J D, evaluated about an axis passing through point D. The absolute velocity and acceler ation of point G3, at the current time , are v and a respectively (see Fig. 1). An unknown horizontal resistance force, F , is applied to point D. The kinetic friction coefficient between piston and slotted link BC is f k. The pressure of the fluid contained in the hydraulic actuator is p. All the geometrical parameters are assumed to be known . You are asked to describe the procedure to: 1 evaluate the velocity and acceleration of the barycentre G1; 2 evaluate the magnitude of the resistance force F applied to point D; 3 evaluate the external reactions at points O and C; 4 write the expression of the kinetic energy of the system. N.B.: You are asked to write the equations that allow one to calculate any unknown kinematic and mechanical parameter that is cited in the expressions of your solution procedure. If the kinematic analysis is carried out using a mobile reference frame it is mandatory to indicate the origin of the frame and its type of motion. S tudents who only passed a previous test about kinematics…