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Midterm Exam I Solutions

# Midterm Exam I Solutions - 1 Physics 40B Spring 2008...

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Unformatted text preview: 1 Physics 40B Spring 2008 Midterm I April 17, 2008 Name_______ Solutions________ Signature______________________ I. D. Number: XXX-XX-_________ Closed Book and Notes All books, backpacks etc. on floor All cell phones off and out of sight No Extra paper allowed—Show all work on test papers All calculators are okay Tear off back formula sheet if convenient 2 Problem 1 (30 points): The famous Bell Tower in Pisa, Italy, started to lean in 1173 AD, when construction began. The tilt has currently reached 5.5º. Assume that the Tower of Pisa is a uniform hollow cylinder of radius R = 9.8 m, height h = 60 m, and mass M = 1.3 x 10 7 kg. The center-of-mass is located at a height of h/2 , along the cylinder’s central axis. The tower is leaning to the right in the figure so that the center-of-mass point is shifted by a distance d to the right. We will assume that the ground exerts only two upward normal forces. The normal force F NL acts on the left wall and the normal force F NR acts on the right wall. Part A (10 points): If the Tower wasn’t leaning (tilt = 0º), what would be the values of F NL and F NR ? Use g = 9.8 m/s 2 . ∑ F y = 0 F NL + F NR = Mg With the tower in a vertical position, because of symmetry, one can also say that F NL = F NR . Therefore, F NR = F NL = 1/2Mg = ( 0.5)(1.3 x 10 7 kg)(9.8 m/s 2 ) = 6.37 x 10 7 N That F NL = F NR can easily be shown by applying the torque equation to any axis of rotation. No points are deducted for not showing this is true....
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Midterm Exam I Solutions - 1 Physics 40B Spring 2008...

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