Exam2_F23

Physics E1ax Exam 2 November 7-14, 2023 Name: • When you upload your pdf to Gradescope, you must match each question to the location in your pdf . Instructions are here. If you skip this step, there will be a 5 point penalty applied to your exam. • You will only receive credit for work that we can tell you did, which means that you must show all your work and provide justifications for your work in the form of equations and/or words. • This is exam is open book, so you may use any of your personal notes from class or resources on Canvas, but absolutely no collaboration with others is allowed. All work must be your own. The Harvard Extension School states: “Harvard Exten- sion School expects students to understand and maintain high standards of academic integrity. Breaches of academic integrity are subject to review by the Administrative Board and may be grounds for disciplinary action, up to and including requirement to withdraw from the Extension School and suspension of registration privileges.” See their website for examples. • The use of Artificial Intelligence (AI) tools such as Chat GPT or similar for assistance of any kind on this exam is strictly forbidden . Suspected violations of this policy will be treated as instances of plagiarism and a breach of academic integrity. Agreement of Academic Integrity: I agree to uphold a high standard of academic integrity. I understand that the work I submit for this exam must be my own, and that violation of any of the rules above are subject to review and disciplinary action by the Administrative Board. Signature:

Physics E1ax Exam 2 - Page 2 of 8 November 7-14, 2023 Question Points Score 1 5 2 5 3 5 4 5 5 5 6 20 7 20 8 15 9 20 Total: 100

Physics E1ax Exam 2 - Page 4 of 8 November 7-14, 2023 3. (5 points) A box sits on a level floor at position A . A piglet pushes it to position B , where the box ends up at rest. The piglet then pushes it back to the box’s original spot (position A ), leaving it at rest again. Which of the following are true for the boxes’ journey from position A to position B and back to A ? Select all that apply. (a) The net work done on the box is zero. (b) The work done on the box by the piglet is zero. (c) The work done on the box by the piglet is positive. (d) The work done on the box by friction is zero. (e) The work done on the box by friction is negative. 4. (5 points) Two objects with different masses speeding towards each other collide and stick to-gether after the collision. The system (composed of the two masses, only) was completely isolated. Select all that apply. (a) Momentum was conserved but mechanical energy was not conserved. (b) The internal energy of the system decreased during the collision. (c) The internal energy of the system increased during the collision. (d) The kinetic energy of the system after the collision is equal to the sum of the kinetic energies of both masses before the collison. (e) During the collision, the two masses received equal (magnitude) and opposite (di- rection) impulses. 5. (5 points) Miranda is choosing between three masses ( m 1 = 1 kg, m 2 = 2 kg, m 3 = 3 kg) to hang on three springs ( k 1 = 200 N/m, k 2 = 400 N/m, k 3 = 600 N/m). Which mass and spring combination would produce the longest period of oscillation? Select only one answer. (a) m 1 and k 1 (b) m 1 and k 3 (c) m 2 and k 3 (d) m 3 and k 2 (e) m 3 and k 1

Physics E1ax Exam 2 - Page 5 of 8 November 7-14, 2023 6. Marvin the tiny mammoth is roaming a glacier when he encounters a deep ravine that he cannot cross. Fortunately, the glacier is shaped as shown below. The bottom of the big hill is a circular segment of radius R . After Marvin takes a few careful measurements, he climbs the big hill to height h , and, starting from rest, slides down the frictionless hill and shoots across the ravine, just barely making it across. Marvin has mass m . You may neglect friction and drag in this problem. (a) (10 points) What is the magnitude and direction of the normal force when Marvin reaches the bottom of the jump (the point marked A) in the figure? Your answer may be expressed in terms of any of the variables given in the problem and any physical constants. (b) (5 points) What is Marvin’s speed when he first becomes airborne (point B in thefigure)? Your answer may be expressed in terms of any of the variables given in theproblem and any physical constants. (c) (5 points) How high up the hill did Marvin start? Your answer may be expressed in terms of any of the variables given in the problem (except h ) and any physical constants. In other words, find h in terms of the other known variables and physical constants given that Marvin just barely makes it across the ravine. Total for Question 6: 20

Physics E1ax Exam 2 - Page 7 of 8 November 7-14, 2023 8. (15 points) After a long day of playing and catching bugs outside, a mama cat drags her basket of sleepy kittens to bed. She drags the basket up a hill at over a total distance of 8 meters starting from rest. The hill makes an angle of 20 degrees with the horizontal, and the coefficient of kinetic friction is µ k = 0 . 3. When she reaches the top, the basket of kittens is moving at a speed of 0.5 m/s. How much work did the mama cat do on the basket of kittens? The kittens and basket have a mass m = 3 kg. I 20

Physics E1ax Exam 2 - Page 8 of 8 November 7-14, 2023 9. You place a mass m = 2 kg on a frictionless horizontal surface, and attach it to a wall with a spring as shown below. The spring has spring constant k = 1000 N/m. The mass sits at x = 0 in equilibrium. At time t = 0, you give the mass a whack, sending it moving to the right with an instantaneous velocity of v 0 = 3 m/s at x = 0, and the mass begins to undergo simple harmonic motion. (a) (5 points) Calculate the amplitude (maximum displacement from equilibrium) of the motion. (b) (5 points) What is the oscillation frequency, ω , of the mass? (c) (5 points) What is the maximum acceleration of the mass as it oscillates? (d) (5 points) Calculate the kinetic energy of the oscillator when it is at half its max- imum displacement from equilibrium. Total for Question 9: 20