Physics_114_Practice_Final_Exam

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PHYSICS 114 FINAL EXAM Name (Print): PID: Honor Pledge: On my honor, I have neither given nor received unauthorized aid on this examination. Signature: Do not open the exam until told to do so. You will have 3 hours to complete the examination. NO CELL PHONES, TEXT MSG, etc. ALLOWED AT ANY TIME. Before the exam begins: • Print and sign your name, and write your student PID number in the spaces above. During the exam • When the exam begins, print your name on each page. Do this first when you are told to open your exam. • If you are confused about a question, raise your hand and ask for an explanation. • If you cannot do one part of a problem, move on to the next part. • This is a closed book examination. All equations and constants are provided. • You may use a calculator, but not a computer, or other Internet-connected devices (smart-phones, iPads, etc.). • Please write neatly and legibly. Do not use scratch paper; it will be ignored. • Show your work in enough detail so that the grader can follow your reasoning and your method of solution. Circle your answers, and state units if appropriate. End of exam: • Out of respect to other students, please remain seated for the last 10 minutes of the exam. At the end of the exam, please remain seated until all exams have been collected. PHYS 114
Physics 114, Final Exam 2 1. At the train station, you notice a large horizontal bumper at the end of the train track. a. [4 pts] If you assume that the bumper can sustain a maximum compression of 0.8 m and it has a spring constant of 500,000 N/m, what would be the fastest train that the bumper can stop? Assume the train has a mass of 10 4 kg. Ignore friction between the train and the tracks. Show your work. b. [4 pts] Using the speed you found in part a, what is the magnitude of the average force felt by the train while the bumper is being compressed 0.8 m? Ignore friction between the train and the tracks. Show your work.
Physics 114, Final Exam 3 c. [5 pts] If the resilience of the bumper is 0.03, with what speed would the train bounce off the bumper? Use your result from part a as the train’s initial speed. Ignore friction between the train and the tracks. Show your work.
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Physics 114, Final Exam 4 2. [6 pts] A 500-N person steps on a scale in an elevator. The elevator goes down. During the elevator ride, the person notices the following readings on the scale at different times: 347 N, 500 N, and 653 N. For each of the time intervals described below, identify which of the three scale readings (347 N, 500 N, or 653 N) the person saw. • the time interval during which the elevator speeds up: • the time interval during which the elevator moved at a constant speed between floors: • the time interval during which the elevator slowed down: Explain the reasoning you used to arrive at your answers.
Physics 114, Final Exam 5 3. An object with a mass m = 3.0 kg is confined to a potential energy well shown on the right. It is released from rest at point C. a. [2 pts] What is the possible range of the object (maximum and minimum distance in m)? No explanation is necessary to receive full credit. b. [4 pts] What is the maximum speed of the object? c. [2 pts] While moving from point C to D, is there a force on the object, and if so, which way is it pointing? d. [4 pts] In order to reach point A, what must be the minimum speed of the object at point C?
Physics 114, Final Exam 6 4. [4 pts] The system at right consists of three blocks, A, B, and C. Blocks A and B have mass m ; block C has mass 2 m . Ignore air resistance. The system is lowered with acceleration g /3 downward (one third the acceleration it would have in free fall). Rank all the forces exerted on the blocks A and B, from largest to smallest. Explain your reasoning. 5. [5 pts] The dinosaur Pachycephalosaurus wyomingensis had a thick skull with which it could ram other dinosaurs. If a 488-kg Pachycephalosaurus running at 6.7 m/s rammed into another animal and came to a complete stop in 0.015 s (the stopping time for collisions between NFL football players), what would be the magnitude of the force that animal would experience? Show your work.
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Physics 114, Final Exam 7 Wallabies are marsupial mammals native to Australia that are famous for their ability to hop. In the next 4 questions, you will examine various aspects of physics that allow a 10.5-kg red- necked wallaby ( Macropus rufogriseus ) to efficiently hop. Note: Questions 5, 6, 7, and 8 are independent of each other, so you may do them in any order. 6. [4 pts] The gastrocnemius is an important muscle in the wallaby’s leg. For the 10.5-kg red-necked wallaby, scientists measured the force experienced by this muscle as it stretched and relaxed during a hop. Below is a graph of this force versus the change in the length of the muscle. The dashed red lines outline a triangle whose area we will use to approximate the area under the loading curve. The solid blue lines outline a triangle whose area we will use to approximate the area under the unloading curve. Determine the resilience of the wallaby’s gastrocnemius muscle. Show your work. A red-necked wallaby 0 10 20 length change (mm) 100 400 300 200 force (N) 0
Physics 114, Final Exam 8 7. Wallabies can use energy stored in their tendons to help them jump efficiently. a. [4 pts] The gastrocnemius muscle exerts a maximum force of 480 N on the gastrocnemius tendon. The tendon has an equilibrium length of 250 mm, a cross-sectional area of 8.9 mm 2 , and a Young’s modulus of 1.2 x 10 9 N/m 2 . Determine the change in the tendon’s length when it is loaded with a 480 N force. Assume the tendon is in the linear regime. Show your work. b. [2 pts] How much elastic potential energy is stored in a gastrocnemius tendon when a 480 N force stretches it by the amount you calculated in part (a)? The spring constant for the tendon is k = 43,000 N/m. Show your work. c. [8 pts] The elastic potential energy stored in the wallaby’s tendons can be converted to other forms of energy. Since the wallaby has two legs (and, therefore, two gastrocnemius tendons), the total amount of elastic potential energy stored by both of its gastrocnemius tendons is twice the amount you calculated in part (b). The wallaby also has two plantaris tendons which together store a total of 13.4 J of elastic potential energy. When the 10.5-kg red-necked wallaby hops off the ground, the active contraction of its leg muscles does +46 J of work on the wallaby. Assuming the wallaby starts from rest, what is its maximum height it will reach above the ground at the top of its hop? Show your work.
Physics 114, Final Exam 9 The figure at right shows the leg and foot bones of the 10.5-kg red-necked wallaby. Two forces are shown: The normal force that the ground exerts on the foot ( N GF ) and the tension force that all of the tendons (not just the gastrocnemius tendons mentioned in question 6) exert on the foot ( T TF ). R is the perpendicular distance (a.k.a. moment arm) between the ankle joint and N GF and r is the perpendicular distance (moment arm) between T TF and the ankle joint. Questions 7 and 8 refer to this figure. 8. [4 pts] Biologists have found that r (in mm) scales with body mass M (in kg) according to the relationship r = 10.7 M 0.46 . Complete the following sentence: This relationship would appear as a straight line on a ___ ( choose one: linear, semilog, log-log ) graph and on that graph it would have a slope of ___ and a y-intercept of ___. Show your work for determining the slope and y - intercept. 9. [5 pts] R (in mm) scales with body mass M (in kg) according to the relationship R = 44.7 M 0.97 . Imagine that the 10.5-kg red-necked wallaby is standing still and that each foot supports half of its weight. What is the magnitude of T TF ? Show your work. N GF R r
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Physics 114, Final Exam 10 10. [8 pts] A student was asked to draw a PV diagram and the corresponding energy bar chart for an isothermal process that takes an ideal gas from point B to point A. Point A is at a higher pressure but smaller volume than point B. The number of particles in the gas did not change during this process. The student made four errors in their PV diagram and energy bar chart. Identify all four errors and explain why they are wrong. volume pressure B A energy E th,i W on Q E th,f Q = 0 J
Physics 114, Final Exam 11 11. Diffusion of aerosolized virus particles in air can be treated as diffusion in an ideal gas, as long as the size of the particles is smaller than the mean free path of molecules of air (about 100 nm). At 300 K, the diffusion coefficient for 10-nm virus particles is 7.1×10 -4 cm 2 /s. Assume 3D diffusion. a. [2 pts] How long does it take for the 10-nm particles to diffuse 1.0 m? Show your work. b. [2 pts] Based on your answer to (a), do you expect the transmission of this virus to occur via a diffusion process? Explain. c. [6 pts] If the temperature is to increase by 50 ℃ , how long does it take for the same particles to diffuse 1.0 m? Assume the volume also increases so that the pressure does not change. Show your work.
Physics 114, Final Exam 12 12. Pole vaulting is one of the most athletically complex and demanding sports. The graph illustrates the horizontal ( v x ) and vertical ( v y ) velocity components of a world class pole vaulter performing a vault. The 85-kg athlete has a center-of-mass (COM) 1.1 m above the ground and used a 3 kg fiberglass pole. a. [8 pts] Sketch a graph of the athlete’s x -acceleration versus time for the time period of 6.0 s to 10.0 s, and a separate graph of the athlete’s y -acceleration versus time for the same time period. On each graph, clearly label the quantitative values of the acceleration. b. [4 pts] Determine the maximum magnitude of the athlete’s acceleration and identify the time window when it occurred. Show your work.
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Physics 114, Final Exam 13 c. [4 pts] What is the highest point above the ground reached by the athlete’s COM? Show your work. 13. [4 pts] 0.0040 mol of gas follows the isothermal trajectory shown in the figure at right. a. What is the final temperature? b. How does the magnitude of the work done on the gas compare to the magnitude of the heat exchange with the gas? Explain your reasoning.
Physics 114, Final Exam 14 The same experiment is conducted on two systems. Each system consists of a block and a spring; the only difference between them is the spring constant of the springs. Each block is initially at rest at point P , and each spring is initially at its equilibrium length. Each block is pulled to the right by a rope that exerts a constant force of the same magnitude F 0 . Block 1 is pulled from point P to point R . Let system 1 consist of the block and spring from experiment 1. Let system 2 consist of the block and spring from experiment 2. k 2 < k 1 . Both springs have negligible mass, and both surfaces are frictionless. 14. [4 pts] As block 1 moves from point P to point Q , does the total energy of system 1 increase, decrease, or remain the same? Explain. 15. [4 pts] Is the absolute value of the change in total energy of system 1 greater than, less than, or equal to the absolute value of the change in total energy of system 2 as each block travels from P to Q ?
Physics 114, Final Exam 15 16. [4 pts] Brad Daugherty, a former basketball player who played for UNC and the Cleveland Cavaliers, is 7.0 feet (2.13 m) tall. What is Brad Daugherty’s maximum walking speed? Assume that his center of mass can be found by multiplying his height by 0.56. Show your work.
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Physics 114, Final Exam 16 17. The pV diagram at right represents the changes two different ideal gases take to get from the same initial state ( P = 3 Pa, V = 3 m 3 ) to the same final state ( P = 1 Pa, V = 1 m 3 ). Both contain 0.08 mol of particles. a. [5 pts] Determine the initial and final temperatures of the gas represented by the solid blue line and the initial and final temperatures of the gas represented by the dashed red line. b. [10 pts] Complete the first law bar chart for the gas represented by the solid blue line. Make sure the bar chart is quantitatively correct. 0 1 2 3 4 0 1 2 3 4 pressure (Pa) volume (m 3 ) -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 Energy (J) E th,i W Q E th,f
Physics 114, Final Exam 17 c. [10 pts] Complete the first law bar chart for the gas represented by the dashed red line. Make sure the bar chart is quantitatively correct. -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 Energy (J) E th,i W Q E th,f
Physics 114, Final Exam 18 18. [2 pts] The graph at right shows a simplified plot of the net force on a grasshopper as it jumps. Assuming the grasshopper begins at rest and jumps straight upward, determine the speed of the grasshopper at the instant it leaves the ground
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Physics 114, Final Exam 19 19. The famous basketball player Michael Jordan once jumped off the court and spent an amazing 0.92 s in the air before landing on the ground. The graphs below represent the x - and y -components of his velocity during his jump. a. [5 pts] Jordan traveled a horizontal distance of 1.08 m during this jump. Determine his initial x - velocity, initial y -velocity, and the magnitude of his initial velocity. Show your work. b. [3 pts] What was Jordan’s maximum height above the ground? Show your work. 0.46 0.92 time (s) v y 0.46 0.92 time (s) v x
Physics 114, Final Exam 20 20. Imagine an 80-kg person is standing, at rest, on one leg. The hip abductor muscle exerts a force ( F MP ) on the pelvis that makes an angle of 20 0 with respect to the vertical. The femur exerts a force on the pelvis at the location of the black dot (but note that this force is not shown on the diagram at right). The weight of the person ( W EP ) points straight down. a. [7 pts] Use the above information and the diagram at right to determine the magnitude of F MP . Show your work. b. [6 pts] What is the magnitude of the force that the femur exerts on the pelvis? Show your work. 2.0 inches 4.0 inches F MP W EP 20 0
Physics 114, Final Exam 21 21. [4 pts] The graphs below shows the force applied to the Achilles tendon as a function of its change in length for three different human walking speeds: 0.75 m/s, 1.00 m/s, and 1.25 m/s. The arrows at the top of each curve show that the tendon follows the left side of the curve as it stretches out and then the right side as it relaxes. Based on these graphs, does the resilience of the human Achilles tendon increase, decrease, or stay the same as walking speed increases? Explain your reasoning.
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Physics 114, Final Exam 22 22. The graph at right shows the stress- strain curves for the Achilles tendons of rats. Data from two groups of rats are shown: the diabetic group (DG; dashed line) and the control group (CG; solid line). Note that the authors used a comma where we would normally use a decimal point. Also, strains are listed as percentages, so 60,000% is actually 60.000% = 0.60). a. [3 pts] At a stress of 5500 N/m 2 (5,500 MPa on the graph), is the Young’s modulus for the CG’s Achilles greater than, less than, or equal to that of the DG? Explain your reasoning. b. [4 pts] The unstretched length of a rat’s Achilles tendon 5.5 mm. If an Achilles tendon from a diabetic rat and an Achilles tendon from a non-diabetic rat are both stretched by a stress of 4000 N/m 2 (4,000 MPa on the graph), which rat (diabetic or non-diabetic) will end up with a longer Achilles tendon and by how much? Show your work.
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Physics 114, Final Exam 23 23. A child, starting from rest, sleds down a snow-covered hill. The hill makes an angle of 25 o with respect to the horizontal and the top is 8.0 m above the bottom. The coefficient of kinetic friction between the sled and the snowy hill is 0.05 and the total mass of the child and sled is 35 kg. a. [5 pts] Treat the child and sled as a single object and draw their free-body diagram. Label the types of forces (e.g., normal, friction, weight, etc.) and use appropriate subscripts to indicate the object exerting the force and the object feeling the force. The lengths of your arrows should be qualitatively correct (e.g., if two forces have the same magnitude, then their arrows should be the same length). No explanation is necessary to receive full credit. b. [7 pts] What is the magnitude of the acceleration experienced by the sled and child as they travel down the hill? Show your work. 25 o 8.0 m
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Physics 114, Final Exam 24 c. [7 pts] Use work-energy principles to calculate the speed of the child and sled at the bottom of the hill. You may use any system you wish. Show your work.
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Physics 114, Final Exam 25 24. The plot at right shows the cumulative number of COVID-19 cases in Canada from February 27 to April 2, 2020. a. [2 pts] Determine how many COVID-19 cases there were in Canada on February 27 (labeled as day 0). Show your work. b. [2 pts] Determine how many COVID-19 cases there were in Canada just 35 days later, on April 2. Show your work. c. [4 pts] Find the mathematical relationship between the cumulative number of COVID-19 cases N COVID and t , the time in days. There should be no logarithms in your final result. Show your work. d. [2 pts] Based on the relationship between N COVID and t from part c, how many days would it take, if no restrictive measures had been taken, to reach 330 million cases (which happens to be equal to the population of the United States)? Show your work.
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Physics 114, Final Exam 26 25. A person is using a rope to pull a 60-kg crate up an incline. The incline makes an angle of 35 o with respect to the horizontal. The coefficient of kinetic friction between the crate and the incline is 0.25. The crate accelerates up the incline at 0.5 m/s 2 . a. [4 pts] Draw the crate’s FBD. Make sure to label the forces appropriately using the proper subscripts and that the lengths of your arrows are qualitatively correct (e.g., if two forces have the same magnitude, then their arrows should have the same length). No explanation is necessary to receive full credit. b. [6 pts] What is the magnitude of the tension force that the rope exerts on the crate? Show your work. 35 o
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Physics 114, Final Exam 27 26. A 2.0-kg mass is attached to a spring of spring constant k = 7.0 N/m. The mass is oscillating back- and-forth on a horizontal plane between the positions x = -15 cm and +15 cm (note that x = 0 corresponds to the position at which the spring is at its equilibrium length). The plane is frictionless, so there is no damping. The mass is at x = -6.0 m at t = 0 s and is headed toward x = +15 cm. a. [2 pts] What is the amplitude of this oscillatory motion? Explain/show your work. b. [2 pts] What is the period of this oscillatory motion? Explain/show your work. c. [3 pts] What is the phase constant (in radians) of this oscillatory motion? Explain/show your work. d. [3 pts] Write down an equation for the position x of the mass as a function of time.
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Physics 114, Final Exam 28 27. A 2500-kg rocket is sent up in the atmosphere carrying an instrument to study the outer Earth’s atmosphere. While the engine is firing, the rocket speeds up with a constant acceleration. After the engine shuts off, the rocket is in free fall. The rocket’s motion is entirely in the vertical direction. Define vectors that point up to be positive and vectors that point down to be negative. a. [4 pts] Draw a qualitatively correct velocity-time diagram for the motion of the rocket, from the instant it is launched until the instant it reaches its maximum height. You do not need to put any numbers on your graph in order to receive full credit. b. [3 pts] Knowing that the rocket reaches a maximum speed of 500 m/s, how far upward did it travel after the engine shut off? Show your work. c. [3 pts] If it took 600 s to reach the 500 m/s speed, what was the highest altitude reached by the rocket? Show your work.
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Physics 114, Final Exam 29 28. The PV diagram at right shows two different processes (Process A in blue and Process B in red) that a gas can take. Note that both processes have the same initial point and the same final point. Process A is an isothermal process. a. [4 pts] Sketch a first-law bar chart for Process A. You are not required to calculate any numbers, but your chart should be qualitatively correct. The dark black line represents 0; above this line are positive values of energy and below the line are negative values of energy. b. [5 pts] Is the heat added to the gas in Process B greater than, less than, or equal to the heat added to the gas in Process A? Explain your reasoning. Volume Pressure Process B E th,i W on Q E th,f Energy
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Physics 114, Final Exam 30 29. A 4.5-kg cat is on a horizontal, uniform beam that is 0.75 m above a roof. The cable that helps attach the beam to a building makes an angle of 25 o with respect to the beam. The cat is walking with a constant speed of 1.0 m/s away from the building. The beam has a mass of 18 kg and a length of 3.0 m. a. [10 pts] The cable will break when the tension force exceeds 300 N. How far from the building can the cat walk before the cable breaks? Show your work. b. [4 pts] The cable breaks as the cat is walking, causing the cat to fall. Use work-energy principles to determine the speed of the cat the instant before it reaches the roof. Ignore air resistance. Show your work. 25 o building beam
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Physics 114, Final Exam 31 30. Two objects of different mass are dropped, object A (blue circle on the left) is dropped straight down (with zero initial speed), and object B (red circle on the right) is shot off to the right with a constant horizontal speed. Define velocity components that point up or to the right to be positive and components that point down or to the left to be negative. A velocity is 0 m/s when it crosses the time axis. a. [4 pts] Sketch qualitatively correct graphs for the x - and y -components of object A’s velocity as a function of time. You do not need to put any numbers on your graph nor do you need to provide any explanation in order to receive full credit. b. [4 pts] Sketch qualitatively correct graphs for the x - and y -components of object B’s velocity as a function of time. You do not need to put any numbers on your graph nor do you need to provide any explanation in order to receive full credit. c. [3 pts] Based on your graphs, which object will reach the ground first (or do they reach the ground at the same time)? Explain your reasoning using the velocity vs. time diagrams you just drew. A B
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Physics 114, Final Exam 32 d. [4 pts] Which object will hit the ground with greater speed (or will they have the same speed)? Explain. 31. The figure at right is the position versus time graph of a 150 g baseball right before and right after being hit by a baseball bat. a. [5 pts] Calculate the change in momentum of the ball. Show your work. b. [3 pts] Knowing that the contact time between the baseball and the bat is 1 ms, calculate the magnitude of the average force exerted on the ball by the bat. Show your work.
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Physics 114, Final Exam 33 g = 9.8 m/s 2 k B = R/N A = 1.38 x 10 -23 J/K 1 in. = 2.54 cm R = 8.31 J/mol-K 1 ft. = 0.305 m N A = 6.02 x 10 23 mol -1 1 mi. = 1609 m 1 atm = 1.01 x 10 5 Pa �𝑆𝑆 ⃗ � = 𝑘𝑘 | 𝑥𝑥 ⃗ | r C circle π 2 =
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