X3.6d 205PHYS-205(6) (Kaldon-40534) Name ______________________________________________WMU-Fall 2000 Exam 3 - 100,000 points + 20,000 ¶ points11/16/2000•Rev.6State Any Assumptions You Need To Make – Show All Work – Circle Any Final AnswersUse Your Time Wisely – Work on What You Can – Be Sure to Write Down EquationsFeel Free to Ask Any Questions¶2a ¶2b ¶2c ¶2e“And Now We Take You To Palm Beach County, Florida…” (50,000 points)1.) (a) Suppose you suddenly have 400,000 computer punch card ballots to run through a countingmachine. Each card ( m = 0.000454 kg ) has to move 20.0 cm (0.200 m) in 1.00 seconds. A spinningdrive wheel of 6.00 cm diameter (0.0600 m) moves the cards along. Find the angular velocity, w, of thedrive wheel.(b) The solid drive wheel has a mass of 50.0 grams (0.0500 kg). Find the rotational kinetic energy of thedrive wheel. If you did not get an answer to (a), use w = 20.0 rad/sec.(c) Suddenly a card jams in the machine and the system automatically stops. Find the angular accelerationa to bring the drive wheel to a stop in a single rotation. If you did not get an answer to (a), use w0 = 20.0rad/sec.Physics 205 / Exam 3 Fall 2000 Page 2(d) One of the problems with the ballots in parts of Florida is chads – the small bits of the cards that aresupposed to be punched out. If you just push ona region of the card, you may stretch the materialas shown in the illustration – let us assume thatthis is a tension force problem, with T = 10.0 N.Consider a card that is 0.100 mm = 0.000100 mthick, where the size of the stretched region isL0 = 2.00 mm = 0.00200 m and 2.00 L0 deep.The material is depressed by d = 0.250 mm =0.000250 m. Find the Young’s Modulus, Ym, of the card material.(e) A U.S. flag hangs from a bracket wall. The flag and pole provide a positive torque, t = 30.0 N ·m,about a pivot point at the end of the bracket. To keep the flag from falling, a force perpendicular to theflagpole is applied 7.00 cm from the pivot point. Determine if this force is F1 or F2, and then find themagnitude of this force.Physics 205 / Exam 3 Fall 2000 Page 3So You Think You’ve Got Star Problems? When I Was A Kid… (50,000 points)2.) ¶(a) A plate of mass m = 6.00 kg has dimensions a = 1.50 m and b = 0.720 m.Find the center of mass coordinate xcm by integrating xMxdmcm=z1.¶(b) A plate of mass m = 6.00 kg has dimensions a = 1.50 m and b = 0.720 m.Find the moment of inertia I of the plate about an axis along the left edge as shown,by integrating Irdm=z2 .Physics 205 / Exam 3 Fall 2000 Page 4¶(c) A simple harmonic oscillator has an acceleration given as at m s t() . / cos( )= 1002wbg. Find x(t).(d) Bob weighs 981 N on the surface of the Earth. What would his weight be on the planet Mercury?MM = 3.18 × 10 23 kg , RM = 2.43× 10 6 m , g = 9.81 m/s² , G = 6.67 × 10-11 N·m²/kg².¶(e) A torque rt to tighten a bolt consists of a force being applied at a distance from the axis of rotation.As the bolt gets tighter, it gets harder and harder to turn the bolt, so the torque as a function of angle isgiven by tq= C , where C is some constant with appropriate units. If the total work done by applyingthis torque through two complete revolutions is 1500. J, then find