exam3ws03sol - [:l Last name initial Winter 2003 Last Name...

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Unformatted text preview: [:l Last name initial Winter 2003 Last Name Physics 175 Exam #3 First Name ID # anus for each question are indicated in parentheses, Show. your work for. solutions to questions that require calculations. Explain from where you start to solve the problem and show your math flowing from it for full credit. Surround your result in a box and don ’t forget to include the units for your result. If you need more space to finish a question, write BPP (Back of the Previous Page) at the end of the space provided and then complete your work on the back of the previous page. For multiple choice questions, circle the letter which you believe to be correct (or best). In all problems, take the gravitational acceleration g = 10 m/s2. Problem 1 (15 points) A uniform rod (length = 2.4 m) of negligible mass has a 1.0-kg point mass attached to one end and a 2.0- kg point mass attached to the other end. The rod is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through a point 1.0 m from the 2.0-kg mass. The rod is released from rest when it is horizontal. What is the angular velocity of the rod at the instant the 2.0—kg mass passes through its lowest point? l :7 Epfifigkb g3 ©:§L:w2+ mm‘gbu’alwz%& Z :5) : NZRCl’ ;> m2: ' o D ' z I \ V631 m : 002+ 3‘02 l l Problem 2 (5 points) A box with its center-of-mass off-center as indicated by the black dot, is placed on an inclined plane. In which of the four orientations shown, if any, does the box tip over? Problem 3 (5 points) A girl stands on the edge of a merry-go-round which is initially rotating without friction at constant angular speed. If she walks radially inward toward the center of the merry-go—round, which of the following best describes what happens to the system during this process? a) the angular momentum and the moment of inertia of the system both decrease and the angular speed increases b) the angular momentum increases While the moment of inertia and the angular speed both remain constant c) the angular speed, the angular momentum, and the moment of inertia all decrease the moment of inertia decreases, the angular speed increases, and the angular momentum remains constant e) the angular speed decreases while the moment of inertia and the angular momentum remain constant Problem 4 (5 points) As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it? a) To your left b) To your right c Up Down Problem 5 (10 points) True or false: , 2T) a) The moment of inertia of a solid object is a quantity represented by a vector ‘HACXL '2? b) A constant torque must be applied to a body in order for the body to maintain rotational motion Thigh '2? c) A pitcher throws a ball past a stationary batter. If the ball has no spin and is thrown straight, then the ball has no angular momentum with respect to the batter. 3?ch 2f (1) The angle between a particle’s linear momentum p and its angular momentum L is always 900. TKV we/ 2? e) If the net torque on a body is zero, the angular momentum must be zero. :Foflsgt. , Problem 6 (15 points) A flagpole consists of an 80 kg rod of length L = 2 m with a 10 kg mass attached to the end. The pole is hinged at the bottom and is kept in equilibrium by a horizontal cable as shown. a) Draw all the forces acting on the pole. b) Find the tension in the horizontal cable. Take sin3 00 = 0.5, and cos30° = 0.8. ZFGlfO % «Hg limbo dmgkw‘fio + D + \ lcgiu38~0 c) Suppose the horizontal cable breaks. What will be the initial magnitude of the angular acceleration of the flagpole about the hinged point? The moment of inertia for the rod and mass m attached to it is 400 kg m2. 2"; $1.34 ;> Tleimmfiflfifigi(madmmglcméo:fiLol Whem W? m \e Medea tBTto‘ :7 1 04 “Allhsgi ‘+ maleBD 5L! mg“; go \0 z+\0\0 "prng will M “9me —-«> M m Problem 7 (5 points) The object shown below has mass m and velocity v. The direction of its angular momentum vector with respect to an axis perpendicular to the page through point 0 is: a) downwards v b to the right — — _ _ _ _ _ _ _ fl é into the page (1) out of the page . e) counterclockwise. O Problem 8 (10 points) The figure at right shows a uniform rod of length L = 1 m and mass M = 0.3 kg pivoted at the top. The rod which is initially at rest is struck by a particle of mass m = 0.1 kg and speed V = 18.45 m/s at a point d = 0.8 m below the pivot. Assume that the collision is perfectly inelastic. Find the angular speed with which the system starts rotating immediately after collision. The moment of inertia of the rod with respect to the pivot is 1/3 MLZ. LL=L¥ LL 2 LT; fl.” = Neda» O 3 tr 5 ‘9 mwizlwda~étfi§.w.g :-W¥& '2. m (l 2—} l n L J W omwwm ,>{W_geg<i \ 0N0fi+é0%fi PM t‘- Problem 9 (5 points) A sphere rolling on a horizontal flat surface slows down because of V Qobl \ “H a) friction force eformation of the surface Bonus guestion (10 points) Calculate the center of mass of a semicircular hoop with the origin at the center of curvature and the y axis on the hoop’s line of symmetry. c) gravitational force ...
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This note was uploaded on 04/30/2008 for the course PHYS 2760 taught by Professor Kozstin during the Spring '08 term at Missouri (Mizzou).

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exam3ws03sol - [:l Last name initial Winter 2003 Last Name...

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