Name PSU Email ID Section THE PENNSYLVANIA STATE UNIVERSITY Department of Engineering Science and Mechanics Engineering Mechanics 212 Exam 3 Wednesday April 13 2022 Problem 1 Problem 2 Problem 3 Problem 4 Total General Instructions Please read them The exam goes from 8 00 9 30 p m it is 90 minutes long You may remove the equation sheet from the front of the exam but leave the rest of the exam stapled together If you need extra space write on the back of the page Calculators are permitted during the exam You may not use a smart phone as a calculator De ne all component systems used and use proper vector notation both of these are worth points Be neat and show all of your work Determining your section Section 1 9 05 9 55 a m Section 2 10 10 11 00 a m Section 3 1 25 2 15 p m Section 4 2 30 3 20 p m Section 5 3 35 4 25 p m Section H 11 15 a m 12 05 p m Good luck Problem 1 25 pts A disk of mass m and the linear elastic spring of constant k and unstretched length 0 move in the horizontal plane One end of the spring is attached to the disk and the other end is pinned to a xed support At the instant shown the mass is moving with speed v1 in the direction indicated If in the ensuing motion the spring stretches to a maximum length equal to 2 0 determine the corresponding speed v2 as a function of v1 and the required spring constant k as a function of m v1 and 0 Neglect the mass of the spring and friction between the mass and the horizontal surface Use sin 30 D cos 60 D 1 2 and cos 30 D sin 60 D p3 2 Problem 2 25 pts Disks E and F roll without slipping on the at surface The two disks are pin connected at their periphery by the bar BC At the instant shown A and B are at the same height C is at the top of F and disk E is rotating in the direction shown with constant angular speed E At this instant determine the angular velocities and angular accelerations of bar BC and disk F as a function of E Problem 3 25 pts At the instant shown point B of the 4 bar linkage is moving with constant speed v0 Determine as functions of v0 and L the angular velocities and angular accelerations of bars AB BC and CD at this instant Problem 4 25 pts The cart B of mass 3m is at rest when the ball of mass m strikes it while moving with speed v0 in the direction shown The linear elastic spring of constant k that is between the cart and the wall is undeformed when the cart is hit by the ball If the coef cient of restitution for the impact is e and the cart moves without friction determine the maximum compression of the spring as a function of v0 e k and m Use sin 30 D cos 60 D 1 2 and cos 30 D sin 60 D p3 2