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LAHS Physics – Semester 1 Final Review Information Your Semester 1 Physics Final has two parts as follows: Part I - Multiple Choice Questions - (Individually, 50 minutes) Part II - Free Response Questions - (Assigned pairs announced 1st Mon of Dec, 50 minutes) Your Semester grade will be calculated as follows: Quarter 1 percentage = 40% of grade Quarter 2 percentage = 40% of grade Semester 1 Final – Part I = 10% of grade Semester 1 Final – Part II = 10% of grade It is highly recommend that you study/review in small groups well ahead of your scheduled Final, preferably with your assigned partner so that you can work out collaboration and cooperation details ahead of time. Arrange for tutoring help with your teacher or tutors at the Tutorial Center. If you happen to miss any part of the Final for any reason, expect to do the make-up exam(s) ALONE. Part I - Multiple Choice Questions The first 50 minutes of your written final on your scheduled 100-minute period will be a Multiple Choice section. You will do this part by yourself. The questions are conceptual and quick mathematical problems with the purpose of assessing how well you understand the concepts discussed throughout the semester. It is a scantron exam with no partial credit for wrong answers. If you don't know the answer, you are encouraged to guess. There is no penalty for guessing unlike some other types of exams. Part II - Free Response Questions The purpose of the Free Response Section of the Final is to assess your ability to solve problems. You will do this part with your assigned partner. This packet includes a set of review problems for you to study. On the Monday of Finals Week, 6 of these review problems will be announced as problems for you to prepare at home a perfect solution for grading. Then at the beginning of the last 50 minutes of the Final, you will be asked to submit only one of the 6 perfect solutions. This problem will be randomly chosen for each period and could be different for every Physics class. This one problem counts as one of the Free Response solutions to be graded. For the in class portion of the Free Response part of the Final, you will be asked to write your perfect solution to one of the remaining review problems in this packet not previously announced on the Monday of Finals Week. The numbers given in the problem will be changed slightly for the real test, but the wording and pictures (if any) will not be changed. In short, you will have seen all the free response problems on the test prior to taking the test if you study what is recommended. You will be assigned to a partner ahead of time and if you choose to do so, you may collaborate and cooperate to write your perfect solution during the Final. Each person in the pair will be required to turn-in their own solutions to the single problem. You will be given a clean equation sheet to use during the exam so that everyone has equal resources. Generally, points for each free response problem will be awarded for the following: Clear diagram or free body diagram with all given data indicated Writing the correct equation(s) to be used in solution Correct mathematical manipulations and algebraic substitutions A clearly boxed correct answer with correct units A complete sentence explaining your resultant numerical answer LAHS PHYSICS SEMESTER 1 FINAL EQUATIONS sin ø = opp/hyp cos ø = adj/hyp tan ø = opp/adj a 2 + b 2 = c2 x v v a v v o at x x o v o t 2 at 2 1 t t x x o vt 2 at 2 v 2 v o 2a(x x o ) x x o 2 (v o v)t 1 2 1 a = -g g = 9.8 m/s2 x x o v ox t (v o cos o )t y y o (v o sin o )t 2 gt 2 1 v y (v o sin o ) 2 2g(y y o ) v y v o sin gt 2 F = ma W = mg fs sN fk kN 2r v2 mv 2 v= ac Fc = t r r m1 m2 Nm2 F=G G 6.67x10 11 r2 kg2 Moon mass = 7.35x1022 kg Earth mass = 5.98x1024 kg Sun mass = 1.99x1030 kg Moon radius = 1.74x106 m Equatorial Earth radius = 6.37x106 m Sun radius = 6.95x108 m Distance from center of Sun to center of Earth = 1.5x1011 m Distance from center of Moon to center of Earth = 3.85x10 8 m W W = Fdcos W KE net K = 2 mv2 1 PE mgh P t Semester 1 Final Review Problems Kinematics 1. Police detectives, examining the scene of a reckless driving incident, measure the skid marks of a car, which came to a stop just before colliding into a Wal-Mart to be 50 meters. It is known that the coefficient of kinetic friction k = 0.89 between the specific brand of rubber tires on the car and the road. The speed limit in the area is 20 m/s (about 45 mph). Assume the skid marks are straight and use Newton’s laws and 1-D kinematics to determine if the driver of the skidding car was speeding before she began skidding? 2. A medical relief airplane climbs to an altitude of 200 m and flies at a constant cruising velocity of 80 m/s. The copilot steps to the back of the plane and opens the cargo door. She wants to drop a medical supply package to a landing site at a remote village. a. Neglecting air resistance, use 2-D kinematics to determine how far (horizontally) before the plane flies over the village must the package be dropped? b. To prevent the 15 kg supply package from getting damaged, the villagers set up an airbag at the landing site. The airbag is capable of stopping the supply package in 0.4 s and stands 5 meters above the ground. Use kinematics to determine the velocity of the package just before it hits the airbag. 200 m Airbag Range 3. A skydiver jumps out of a helicopter hovering at 2500 m above the ground. She free falls for 15 seconds before opening her parachute. Assume the parachute opens instantly and allows her to travel at a constant velocity of 12 m/s downwards until she reaches the ground. a. How much distance does she cover during the initial free fall? b. How much time does it take her to reach the ground? c. At the same time she jumps from the helicopter, her shoe comes off. How much time does it take her free falling shoe to hit the ground assuming no air friction? d. What would the final velocity of the shoe be just before it hits the ground? 4. Consider a projectile with an initial velocity vector of 34 m/s @ 25o above the +x-axis. The projectile is shot from ground level on a planet different than Earth where the acceleration of gravity isn’t known. The Range of this projectile is 180 m and it comes to rest at the same level at which it was shot: yo = yf = 0 meters. Use kinematics to solve the following: a. Calculate the hang-time of the projectile. b. Calculate the acceleration of gravity on this planet. c. If the planet's radius was the same as the Earth's, what does the result in part B imply about the mass of the planet? 5. An archer shoots an arrow from the top of a building at a speed of 28 m/s. The building is 40 meters tall. Ignoring air resistance, find the speed with which the arrow strikes the ground when the arrow is fired (a) horizontally (b) vertically straight up, and (c) vertically straight down. You must use kinematics and the quadratic formula to solve this problem. 6. An LAHS quarterback just about at the sideline and is 20 meters (or about 22 yards) from the goal line pylon (orange marker at the goal line) that is in front of him. He throws the line drive ball with a velocity of 24 m/s at an initial angle of 10 above the horizontal. His receiver runs at a constant speed 6 m/s following the goal line starting 6 meters (about 6.6 yards) away from the pylon at the same time the quarterback releases the ball toward the pylon. Assuming no- one interferes with the play, the receiver is essentially a point mass and if caught, the ball is caught at the same height that quarterback throws the ball, determine if the receiver reaches ball in time to catch it at the pylon. Newton’s Laws Problems 7. Consider a 65 kg clown with an initial velocity of 10.0 m/s sliding up a rough circus slide inclined 38 above the horizontal and measuring 16.5 m along the diagonal. The coefficient of friction between the slide and the clown is k = 0.25. Use Newton’s laws of motion to predict the highest point the clown will slide to. vo k h 8. A kinetic artist wants to build a life size double mass system in equilibrium, on an incline plane. The initial design consists of m1 = 35.0 kg connected to m2 = 17.5 kg by a thin, cable wrapped over a pulley. The artist hires you to predict the exact angle at which the system will maintain static equilibrium without any help from friction. Use Newton’s laws to correctly calculate the angle that maintains static equilibrium and get paid $750. m2 m1 9. Earlier this morning I saw Ms. Satterwhite, massing in at a liberal 82 kg, skate boarding through the quad. Suddenly, she flipped his board upside-down and skidded the wooden board scraping along the concrete for 4.2 m then stopped. If the coefficient of kinetic friction between the skateboard and the concrete quad is 0.73, use Newton’s laws to predict the skidding skateboard’s initial velocity just before it began to skid. 10. A physics student is wants to be “stuck” to the interior wall of an amusement park ride called the ROTOR. If the radius of the rotating cylinder is 4.2 m and the coefficient of static friction between the student and the rotor’s inner R wall is 0.56, predict the minimum safe speed at which the Rotor’s floor can be removed without the student sliding down the wall. 11. A model airplane is tied to a string and 15 propelled by a small electric motor in a perfect horizontal circle with a circumference of 23 m at constant speed. The plane isn’t really flying. Predict the time it takes for the plane to r complete one complete revolution. 12. Consider a circus clown weighing 720 N. The coefficient of static friction between the clown’s feet and the ground is 0.48. She pulls vertically downward on a rope that passes around three frictionless pulleys and then tied around her feet. What is the minimum pulling force that the clown must exert to yank her feet out from under herself? Gravity and Energy Problems 13. Assuming you are at the equator and your mass is 68 Kg, will you weigh more when the moon is on your side of the earth or when the moon is on the far side of the earth? How much more (in Newtons)? (Assume the moon, earth and you are in a straight line in each case.) G = 6.673 x 10-11 Nm2/kg2 Equatorial radius of earth = 6.38 x 106 m Mean radius of moon = 1.74 x 106 m Mass of earth = 5.98 x 1024 kg Mass of moon = 7.35 x 1022 kg Mean distance between the moon’s center and the earth’s center = 3.85 x 10 8 m 14. A space traveler whose mass is 90kg leaves earth. What are his weight and mass (a) on earth and (b) in interplanetary space where there are no nearby planetary objects? 15. Synchronous communications satellites are placed in a circular orbit that is 3.59 x 10 7 m above the surface of the earth. What is the magnitude of the acceleration due to gravity at this distance? 16. Your mass is 70 kg and you weigh 46.5 N more on planet Atrodox than on planet Xenor. Both planets have the same radius of 1.33 x 107 m. What is the difference MA – MX in the masses of these planets? 17. If your weight has decreased by half, what is your altitude above the earth’s surface? 18. A motorcycle is trying to leap across a canyon. Using the principle of Work-Energy Theorem, NOT Newton’s Laws or Kinematics, to find the speed with which the cycle will strike the ground on the other side. The cycle takes off horizontally from a cliff on one side of the canyon at a speed of 40 m/s and at a height of 75 m. The cycle lands at a height of 50 m. Neglect air resistance. 19. A fighter jet is launched from an aircraft carrier with the aid of its own engines and a steam- powered catapult. The thrust of its engines is 2.3 x 105 N. In being launched from rest it moves through a distance of 87 m and has a kinetic energy of 4.5 x 10 7 J at lift-off. What is the work done on the jet by the catapult? If the mass of the jet is 100,000 kg, what is its velocity? 20. An archer shoots an arrow from the top of a building at a speed of 28 m/s. The building is 40 m tall. Ignoring air resistance, find the speed with which the arrow strikes the ground when the arrow is fires (a) horizontally (b) vertically straight up, and (c) vertically straight down. You must use the Work-Energy Theorem, NOT Newton’s Laws or Kinematics. 21. The President, upon learning of his victory in the recent election, threw the 0.75 kg mug he was holding at the time straight up into the air with an initial speed of 18.0 m/s. (a) How high would it go if there was no air friction? (b) If the mug rises to a maximum height of only 11.8 m, determine the magnitude of the average force due to air resistance. You must use the Work-Energy Theorem, NOT Newton’s Laws or Kinematics. Answers: (You should double check with at least 3 other students too because these answers were given by students and may not necessarily be correct.) 1. 29.53 m/s 2. a) 511 m b) 101 m/s 3. a) 1102.5 m b) 107 s c) 22.58 s d) 221m/s 2 4. a) 5.8 s b) 4.9 m/s c) half mass of Earth 5. all same 39.6 m/s 6. No 7. 3.9 m 8. 30 degrees 9. 7.8 m/s 10. 8.6 m/s 11. 1.99 s 12. 234 N 13. 0.0044 N 14. a) 90 kg, 882 N b) 90 kg, 0 N 2 15. 0.223 m/s 24 16. 1.76x10 kg 6 17. 2.64x10 m 18. 45.7 m/s 7 19. 30 m/s, 2.5x10 J 20. 39.6 m/s all same 21. a) 16.5 m b) 2.95 N