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THE PENNSYLVANIA STATE UNIVERSITY Department of Engineering Science and Mechanics

Engineering Mechanics 212 — Exam 2 Thursday, July 11, 2013

Problem 1 Problem 2 Problem 3 Total

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X I am registered as a student in Penn State’s E MCH 212 during Summer 2013.

X I am the person taking this exam whose name appears at the top of this page.

X I did not receive any help from other parties while taking the exam, did not talk to anybody during the exam about the exam, and I did not talk to anybody about the exam content on the date of the exam after I saw the exam.

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Signature: 10 pts will be deducted from your total score if you do not sign this form.

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� Always use proper notation for vectors. Failure to do so will result in a substantial reduction in credit for that problem.

� You must draw FBD(s) for every kinetics problem. Define all component systems used.

� Be neat and show all of your work.

� If you have questions while you are taking the exam, I can be reached at (814) 883-4308 between the hours of 10:00 a.m. and 8:00 p.m. EDT.

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Problem 1 (34 pts)

The mass m compresses the linear elastic spring, whose constant is k, a distance ı0. The mass is released from rest and it slides along the horizontal surface with negligible friction until it encounters the bottom of rod OB. The mass attaches to B via a slot in the mass, and the rod and mass begin swinging upward in the vertical plane. Neglecting the mass of the rod, determine the initial compression of the spring so that the rod and mass reach the opposite vertical position with zero tension or compression in the rod.

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Problem 2 (33 pts)

The box B of mass mB is attached the cart C of mass mC via the linear elastic spring of constant k. The spring is compressed a amount ı when the system is released from rest. Determine the velocity of the box relative to the cart at the instant the spring becomes uncompressed. Use mB D 10 kg, mC D 25 kg, k D 150 N=m, and ı D 0:5 m. Neglect the mass of the spring and of the wheels.

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Problem 3 (33 pts)

Disc B is moving at speed v�B in the direction shown when it encounters disc A, which is at rest. If the coefficient of restitution of the impact is e and the mass of A is twice that of B, determine the post-impact velocities of A and B. The discs lie in the horizontal plane. Express your answers in the given component system.

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