Simple Harmonic Motion - Classical Mechanics - Solved Exam, Exams of Classical Mechanics

Download Simple Harmonic Motion - Classical Mechanics - Solved Exam and more Exams Classical Mechanics in PDF only on Docsity! HYSICS 218 FINAL EXAM Spring, 2005 Name: , (A bud Pfs Signature: Student ID: E-mail: Section Number: « You have the full class period to complete the exam. « Formulae are provided on the last page. You may NOT use any other formula sheet. * When calculating numerical values, be sure to keep track of units, « You may use this exam or come up front for scratch paper. ¢ Be sure to put a box around your final answers and clearly indicate your work to your grader, » All work must be shown to get credit for the answer marked. If the answer marked does not obviously follow from the shown work, even if the answer is correct, you will not get credit for the answer. ° Clearly erase any unwanted marks, No credit will be given if we can’t figure out which answer you are choosing, or which answer you want us to consider. * Partial credit can be given only if your work is clearly explained and labeled. Put your initials here after reading the above instructions: Part 1. Conceptual Questions (5 pts each) Circle the correct answer 1. A ball is thrown up in the air. At the highest point the ball reaches, {a) its acceleration is zero (b) its acceleration is horizontal Qe acceleralion is vertically down d) its acceleration is vertically up 2. If an object is in simple harmonic motion, its: (a) Velocity is proportional to its displacement. ¢(b) Acceleration is proportional to its displacement. ¢) Kinetic energy is proportional to its displacement. (d) Period is proportional to its displacement. {e) Frequency is proportional to its displacement. 3. Haley’s comet has an elliptical orbit around the sun, as shown in the figure at right. At which point in its orbit does it have its greatest angular momentum with respect to the Sun’s center? (Neglect the effect of the planets). (a) Point A (b} Point B {c) Point C aoe (@) Point D eo (e) tts angular momentum is the same everywhere. i ‘ od? A Ban co y SB eB ee 4. Tn the problem above, at which point in its orbit does it have its grcatost angular velocity? fa)} Point A “%) Point B (ce) Point C (dd) Point D (e) Tis angular velocity is the same everywhere. 5, When a car moves in a circle with constant speed, its acceleration is: @ constant in magnitude and pointing towards the center (6) constant in magnitude and pointing away from the center (ec) zero (d) constant in magnitude and direction (ec) none of these Problem 3: Going up a plane (35 points) A disk with uniform density and M and radius R is rolling without slipping with constant speed V along a flat horizontal surface. It then goes up an inclined plane of angle 6 as shown in the figure. Assume the acceleration due to gravily is given by g Cgiae7€L/2)MR?) a) (10 pis) How high up the inclined plane will the ball go’? In other words, what is the height # in the figure? b)} (10 pts) Draw the forec diagram of the disk as it is going up the ramp. ¢) (10 pts) Write down Newton’s 2™ law equations (lincar and angular) of motion as the disk is going up the ramp @) (5 pts) What is the acceleration as the disk gocs up the ramp? ae Problem 4: A Bullet and a Block (30 points) A bullet of mass #1 and velocity V, plows into a block of wood at rest with mass M which is part of a pendulum and stays inside the block. Assume that the acceleration due to gravity is g. a) (5 pts) What is the velocity of the block/bullet pair after the collision? b) (7 pts) How much work is done on the block during the collision? c) (8 pts) How much energy is converted from mechanical to non-mechanical energy? {i.e., sound, heat cic.) d) (10 pts) How high, 4, does the block of wood go? 2) (Ses) Wed g Hae gortod aA asa Rabin 7 Ye Uz Ye (mith) & ; ap kG a 2%) Gali. uve, £ Boy hme sa 2 al z a net é ‘ £ ho ey 5) U.. Aes £CAMD UG - O afi mw yh | oe Peblecie ~ URE OB . [4 hay i t iw ~ if A ou dagiten htt o) fue Meade u Part 5: (30 points) x You are 4 siunt artisi on a motorbike jumps from a ramp to the top of a building. & is the vertical distance from the top of the ramp ic the top of the building. The ramp is a distance d away from the buildi ‘The initial velocity is unknown, however the spectators notice that it just so happens that ye ch the top of the building at the maximum height point during the flight, barely missing the building. {n this problem you should ignore air friction. AU your answers should be in terms of the variables giver. ‘The acceleration of geavity pointing down (g is a positive aumber), a (5 pts) What mus: be y-component of the initial velocity so that you just bercly reach the top of the building? 1) (0 pis) How much ime does it as as pts) What is the mz #7 credit, you must show for you to get there? milude and angle of the initial veloci er work that produces your answ: y? Again, to receive full, or even partial, oS