phy136h-j17

NAME (PRINT): Last/Surname First /Given Name STUDENT #: SIGNATURE: UNIVERSITY OF TORONTO MISSISSAUGA JUNE 2017 FINAL EXAMINATION PHY136H5F Introductory Physics | Marc De Benedetti Duration - 2 hours Aids: Non-Programmable Calculators; One double-sided, 8-1/2 x 11 hand-written sheet The University of Toronto Mississauga and you, as a student, share a commitment to academic integrity. You are reminded that you may be charged with an academic offence for possessing any unauthorized aids during the writing of an exam. Clear, sealable, plastic bags have been provided for all electronic devices with storage, including but not limited to: cell phones, SMART devices, tablets, laptops, calculators, and MP3 players. Please turn off all devices, seal them in the bag provided, and place the bag under your desk for the duration of the examination. You will not be able to touch the bag or its contents until the exam is over. If, during an exam, any of these items are found on your person or in the area of your desk other than in the clear, sealable, plastic bag, you may be charged with an academic offence. A typical penalty for an academic offence may cause you fo fail the course. Please note, once this exam has begun, you CANNOT re-write it. Notes to Students The Exam constitutes 35% of the whole mark of PHY136HSE. There are 3 pages near the back for scrap work. They will not be marked. Marks may be deducted for unclear or disorganized solutions. The provided formula sheet is the very last page. You may detach it. Let the mark allocation indicate the level of difficulty. OO0 O000O0 The exam is written on 18 pages, including the cover page Mark Answers to Multiple Choice M/C (14) Short Answer (/8) 1 2 3 4 5 6 | 7 Full Solution (/24) Challenge (/4) Total (/50) Page 1 of 18

Section 1: Multiple choice. Write your answer to each question in the chart on the COVER PAGE in capital letters. [2 marks each] C- 1. Two identical billiard balls traveling at the same speed have a head-on collision and rebound. If the balls had twice the mass, but maintained the same size and speed, the rebound would occur: a) at a higher speed b) at a slower speed c) at the same speed \é 2. You are lying in bed and want to shut your bedroom door. You have a bouncy “superball” and a blob of clay, both with the same mass. Which one would be more effective to throw at your door to close it? a) The superball b) The blob of clay c) Both are the same d) Neither will work {_ 3. The solid dot shown in the figure (left side of the beam) is a pivot point. The board can rotate about the pivot. Which force shown exerts the largest torque, in magnitude, on the board? a) The (a) force b) The (5) force (e) 500N ¢) The (c) force d) The (d) force . |t () 800 N e) The (e) force fi é é (B)S00N (c)S00N (a) 1000 N Page 3 of 18

Section 2: Answer only. Please provide a numerical answer in the box provided, with the correct units when appropriate. Some questions may ask specifically for a formula/expression. Only the answer in the box will be marked. 8. [2 marks] There is a spring attached to a wall. A physics student pushes a block against the spring, thus compressing the spring until the spring has a total of 60 J of stored energy. Afier the block is released it slides along a frictionless floor, eventually colliding head-on elastically with the stationary Giancoli physics textbook. If the block has the same mass as the textbook, what is the kinetic energy of the textbook after the collision? (No, you don’t need mass, before you ask, and recall the chart from lecture to predict direction of final velocity) 1 9. [2 marks] The variable g pendulum lab asks you to plot 72 vs cosé. If the T =om [ ety equation of the period is geosé what would the slope be (as an expression)? slope = Page 5 of 18

10. [4 marks] In the Standing Waves on a String lab, we ask you to plot (f2)? n? fo=2./E vs 4L7 . For reference, the standing wave equation is 2LV e Ifa physics student measures their slope to be 10 = 1, what is their experimental value for the linear mass density # (both magnitude and uncertainty)? Page 6 of 18

a) [6 marks] Determine an expression for the final translational velocity of the hollow sphere when it reaches the bottom of the incline, just before the collision. b) [2 marks] Assuming that the speed of the hollow sphere just before impact is v, calculate the resulting speed, v/, after the collision. Your answer may be in terms of v. Page 8 of 18

¢) [4 marks] At this point, the chunk of mass starts to move across the rough floor with speed v'(determined in part (b)). What is the speed, v2, of the chunk of mass when it has reached the end of the table, after having travelled a distance d. Your answer should be in terms of v’ (do not use your derived formula from part b). d) [4 marks] If the height of the table is & = 50 cm, and the speed at the end of the table is ¥2 = 4 m/s, how far will the chunk land from the base of the table? Page 9 of 18

b) [2 marks] Part of a forensic scientist’s job is to quantify uncertainty in their findings. Using the formula for the muzzle speed listed in part (a), determine the uncertainty in the muzzle velocity. For time purposes, assume that the M /51 uncertainty in the first term is Al V29h) = & 1 s, Clearly state your final muzzle velocity along with its uncertainty. Bonus: |3 marks] With this value, and using the table below, state whether the police would be able to identify which gun was used. If so, which gun was used, if not, why not? - 10-mm Winchester 381 Colt45 280 CCI-Speer 297 Remington 260 Page 11 of 18

Section 5: Find and explain the mistake in the solution. Clearly circle/indicate the issues and concisely explain each mistake using words in bullet form. 14. [4 marks] What is the beat frequency if middle C (262 Hz) and C* (277 Hz) are played together? What if each is played two octaves lower (each frequency reduced by a factor of 4)? gbu‘\ 2 5~ 5 o= -an = 15 ¥z o\.)fln_ best SM"L"QN\B e -G “1?. b) §w -15-5] - \ g‘l’g“’\ - %L—%i\ e .—m \ el - Y !-S:‘l‘%s v~>ofl\\3 S dien s Yhak +\>é ore- U"d\”\a,\.‘i . 2 e & S Ven S vndhuwa, o, % Th be ?g‘l’ ua s AM&& Page 12 of 18

Uneertainty Propagation Add/Subtraction 2=ty Az = /Az? + Ay? FRITOT z=uzy 3 Multiplication Az = [zy| /(A?) N (%)z ivisi z==2 Aon? . [ Ag? Division v Ay — lfl /(Gz) + (_yy) Power z=2x" Az = |njz" Az Maultiplication by g=cr Az = c|Az a constant™ Standard Deviation Zavg Az = (or just use EXCEL’s STDEV function) Some Rotational Inertias Hoop or thin cplindrical shell Ty =MR? Sulid cylinder o disk Tex= % MR2 Long thin rod with rotation axis tirough center Tang = 1L2 M2 Solid sphere [ & 2 Iom=% M2 i 7 Hollow cylinder Iow= éM(R;E + R Rectangular plate Tew = g5 M(a2+ 40 Long thin rod with rotation axis through cud 1= % ML2 Thin spherical shelt 2 ap low=§ MR Page 18 of 18