ME 274 Fall 2009 Examination No 3 PROBLEM NO 1 Name Given A uniform rectangular plate of mass m is able to move on a smooth HORIZONTAL plane with corner A of the plate being constrained to move within a smooth guide in the plane of motion The plate is initially at rest with edge AB aligned with the guide for A A force P is applied at corner D Find Determine the initial angular acceleration of the plate Write your answer as a vector Use the following parameters in your analysis m 200kg b 4 meters h 3meters 36 87 and P 800 N A E b P h B D smooth guide for pin A HORIZONTAL PLANE ME 274 Fall 2009 Examination No 3 PROBLEM NO 2 Name Given Block B with mass M is being transported up the slope by using two cylindrical rollers A and D each having a mass m and radius r as shown A constant force F is applied on the block and the system starts at rest Assume that there is no slip at all surfaces Find The speed of block B when the block has moved a distance d up the hill Use the following parameters d 2 m m 5 kg M 50 kg r 0 5m 30o F 400 N M B F A m r no slip m r D no slip ME 274 Fall 2009 Examination No 3 PROBLEM NO 3 Name Given A homogeneous drum of mass m and x outer radius R rolls without slipping on a rough horizontal surface A spring of stiffness k is attached between the R m k center O of the drum and ground such that the spring remains horizontal at all O time Block A of mass 2m is g connected to an inextensible cable that no slip is wrapped around the outer radius of the drum as shown in the figure Let x represent the motion of O measured positively to the right with the spring being unstretched when x 0 Assume that the cable does not go slack at any time Find 2m A For this problem a Draw individual free body diagrams of the disk and of block A b Derive the single differential equation of motion EOM for the system in terms of the coordinate x its time derivatives and at most the following parameters g m and k c What is the natural frequency of the system O A