PHYS101_2022_Final

PHYS 101 Final Dec 20 th 2022 Reproduction forbidden Page 1 of 14 PHYS 101 Introductory Physics – Mechanics (all sections) Final Exam – December 20, 2022 6:00-9:00 pm Instructor: Prof. Lilian Childress Associate Examiner: Prof. Jack Sankey Materials allowed: Calculator (any kind), one page formula sheet (both sides, printed w/annotations), dictionary (any kind). Instructions: • Answer ONLY on these sheets IN THE SPACE ALLOTTED. • NO EXTRA SHEETS are allowed (there is one page of extra work space at the end; make sure you indicate IN THE QUESTION if you will be making use of the extra work space for that question). • Do NOT write on the QR codes in the upper corners. • Write legibly and dark enough for a scan to be readable; put final answers in boxes provided. • Show your work and explain your reasoning. Correct answers without sufficient explanation/sketches/work to follow their logic will not receive full credit. • The exam is 68 pts: 28 pts conceptual (7 questions) + 40 pts quantitative (6 multi-part problems). There are 3 additional bonus points (only attempt if you have extra time!). • If you’re stuck because you need, e.g., part (a) to answer part (c), you can o give part (a) a variable name and find part (c) in terms of it (full credit possible), o explain how you would find part (c) if you knew part (a) (partial credit)

PHYS 101 Final Dec 20 th 2022 Reproduction forbidden Page 2 of 14 1. [4 pts] While riding at constant horizontal velocity ! !"#$ on your bike, you toss your keys vertically up in the air (as viewed in your reference frame) with speed ! % . If you don’t move your hand after tossing the keys, will they land right back in your hand or in front of or behind your hand? (Neglect air resistance.) Explain your answer from the perspective of an observer on the ground – what is the keys’ launch velocity in the ground frame, and how does that explain where they land? 2. [4 pts] Two satellites are in uniform circular orbits around earth; one has a mass of 100 kg, and orbits at a height of 200 km above earth’s surface, while the other has ten times the mass (1000 kg) and ten times the orbital altitude (2000 km). Which satellite experiences the larger centripetal acceleration (or are they equal, or can you not tell)? Explain. since the bike as a horizontal velocity V Bike and you are on the bike so you have the same Velocity when you throw the Keys in the air it means that they have a vertical velocity indeed but also the horizontal velocity Vaine So it you don't more youre hand the Keys should fall right back in it Ac V so the bigger the radius distance from Earth the less centripetal acceleration The Orbit with 100 kg 200km above surface will have a langer centripetal acceleration

PHYS 101 Final Dec 20 th 2022 Reproduction forbidden Page 4 of 14 5. [4 pts] A sinusoidal wave is propagating along a stretched string that is tied to a much heavier (per unit length) rope. When the wave reaches the heavier rope, it is partially transmitted. How does the wavelength # & of the transmitted wave compare to the wavelength # " of the incident wave? (Larger, smaller, the same, or can you not tell?) Explain your answer. 6. [4 pts] A child is sitting cross-legged (i.e. with their legs in close to them) in a spinning chair. If the child suddenly sticks their legs out horizontally in front of them (i.e. away from the center of the spinning chair), without touching the ground, will their angular speed increase, decrease, or stay the same? Explain your answer. FI it the mass of the string increases the velocity decreases it Velocity is smaller the wanelenght will also decrease so it'll be shorter Angular speed would decrease

PHYS 101 Final Dec 20 th 2022 Reproduction forbidden Page 5 of 14 7. [4 pts] Two identical hockey pucks are sliding on the ice with the same speed, moving at equal and opposite angles $ to a line on the ice. The hockey pucks collide and each emerges at angle % < $ with respect to the line as illustrated. Is this an elastic collision, an inelastic collision, or do you not have enough information to tell? Explain your answer. Perfectly inelastic collision conservation of momentum Vi USO VOS Vi VA SO kinetic energy was lost

PHYS 101 Final Dec 20 th 2022 Reproduction forbidden Page 7 of 14 9. A bullet of mass ’ = 50.0 g is fired with an initial velocity of 300. m/s at a stationary block of wood (mass , = 0.750 kg), and lodges in the block. The block of wood is attached to an effectively massless spring of spring constant . = 500. N/m, which is oriented along the same axis as the bullet’s velocity and starts at its equilibrium position. (a) [2 pts] What is the speed of the block+bullet immediately after the collision? (b) [2 pts] What is the maximum displacement of the spring from equilibrium? Answer Answer conservation of momentum MbVb M BVB Mb MB V 50 1300 50 750 15000 800N 18,75 78,75 KE PEspring 1mV 14 2 110.871947572 50071 2 0.75M 0.75M

PHYS 101 Final Dec 20 th 2022 Reproduction forbidden Page 8 of 14 (c) [2 pts] Sketch the displacement and velocity of the block as a function of time after the collision (choose a duration that makes the long-term behaviour clear, and assume the bullet’s initial velocity is in the positive direction). Make sure that the / = 0 point (the collision) is clearly indicated on both graphs. (d) [3 pts] At time / = 0.200 s after the collision, what is the displacement of the block from its original position? Answer V N V Asinff t sin 2

PHYS 101 Final Dec 20 th 2022 Reproduction forbidden Page 10 of 14 11. A child is recklessly whirling a ball of mass ’ = 0.100 kg on a string of length 6 = 0.500 m in a vertical circle (i.e. the circle is in a vertical plane), maintaining the ball at constant speed throughout. When the ball is at the very top of the circle, at a distance of 1.5 0m from the ground and right above the child’s head, the tension in the string is 20.0 N. (a) [3 pts] What is the speed of the ball? (b) [3 pts] If the child releases the ball when it is exactly at the top of the circle, how far from the child will the ball land (measured horizontally on the ground from the child’s location)? Answer Answer M 0.7kg Fc mV L 0.5M 20 0.9 19,009 0.9 V2 T 20 015 v 90,24 90,24 MIS 165M 24mg

PHYS 101 Final Dec 20 th 2022 Reproduction forbidden Page 11 of 14 12. Magnesium fluoride ( MgF ' ) is a transparent solid with an index of refraction of 1.38, and can be deposited in very thin layers to create coatings. (a) [4 pts] Suppose that you want to create an anti-reflection coating on a piece of glass (index of refraction 1.45) using a thin layer of MgF ' , choosing a thickness such that reflections off the top and bottom surface of the MgF ' interfere destructively. If you are designing the coating for light of wavelength 532 nm (in vacuum) at normal incidence (i.e. incident perpendicular to the surface), what are the three smallest thicknesses you could choose for your coating? (b) Bonus point [+1]: which of those three thicknesses would give you the widest bandwidth anti-reflection coating – that is, the largest range of wavelengths on either side of 532 nm before you get to a wavelength whose reflections off the two MgF ' surfaces interfere constructively? Explain or derive your answer. Answer

PHYS 101 Final Dec 20 th 2022 Reproduction forbidden Page 13 of 14 (c) [2 pts] The string on the right (with length 6 ' ) resonates in its fundamental mode at 240.2 Hz. If you pluck both strings at the same time, such that they each resonate in their fundamental mode, at what frequency will the intensity of the emitted sound wave modulate (i.e. get louder and softer, a phenomenon known as beating)? (d) [+ 1 bonus point]: Discuss the significant figures appropriate for your answer to (c). Note: you will not lose points for sig figs in (c). (e)[+ 1 bonus point]: Stare off into space for a moment and write something. Happy holidays! -Prof. Childress Answer fb f1 f2 Fb 240.93 240.2 fb 0,735676 01742

PHYS 101 Final Dec 20 th 2022 Reproduction forbidden Page 14 of 14 EXTRA WORKSPACE (below): You must CLEARLY INDICATE IN THE QUESTION if you are putting work for it in this space, AND clearly indicate here which question you are working on. We will not grade work here unless you reference the extra workspace in the question AND indicate the question number here.