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Download Midterm 1 Solutions | Introductory Solid Mechanics | TAM 251 and more Exams Applied Solid Mechanics in PDF only on Docsity!
| TAM 251. Midterm J. Wednesday 9 March 2011 ¢ NAME: DISCUSSION SECTION # INSTRUCTIONS: This is a closed-book, closed-note exam. You have 45 minutes to com- plete it. Answer the questions in the space provided. THE REVERSE SIDE OF THE PAGES WILL NOT BE GRADED; use them for scratch calculations if you wish. The value of each and every question (“a”, “b”, “c”, et cetera) is the same: 4 points. BOX YOUR ANSWERS! PROBLEM 1 Consider the problem shown in the figure below, where Tg is an applied torque, and 6.4 and @p are the small angles of rotation of the gears. bar of torsional stiffness k, bar of torsional stiffness ko gears of radius R< H Ta 05 (a) Write the equation that relates ¢, to é4 (where ¢; is the twist angle of bar 1). Also write the equation that relates ¢2 to 64 (where dp is the twist angle of bar 2). G,- -@r-0° By @ fr * g-~ te Ps hz Da (> (b) Show that the ratio J; /T2 depends only on the ratio ky /k2 (where T; and T2 are respectively the internal torque in bar ] and the internal torque in bar 2). T= Rd, -@ > 1h 5 Rds RCH ) =) Le TR -O TG mb kt) [% (c) Make suitable free-body diagrams and use the diagrams to obtain the equation of equilib- rium that relates Tg to T; and To. Is this a statically determined problem? ar las (e) r | fj _ Zm-0 =) Tae d, @ ne R Ds a a ly A fig | y _ | © Irae | 
