...Lab # 111 “Projectile Motion” Objectives : The purpose of this lab is to understand projectile motion in two dimensions and apply linear motion equations to solve the problem. Also to predict where a given size bullet to be placed in horizontal direction to leaving table. In addition to that measure the range of projectile leaving table at an angle, and use the value to predict where the projectile bullet to strike at floor. Theory : To predict where bullet will land on the floor when lunched from the mini launcher from a table at an angle, but to do that first we need to determine the velocity of the bullet and to determine by launching the bullet horizontally from the table and measuring the vertical and horizontal distances through distance that the bullet travels. Then the initial velocity can be used to calculate where the bullet will land when the bullet lunched from the mini launcher at an angle. Horizontally lunched bullet at θ=0 off a table with an initial speed, vo, the horizontal distance travelled by the bullet and the vertical distance of the bullet drop in time t describe: x= v0t (1) y=v0yt+12gt2 (2) Now we can determine the initial velocity of the bullet by measuring x and y. where y = 0, therefore, the time of the bullet can be found by equation: t= 2yg, Where g = 9.8 (3) Now, to guess the range of the bullet, x, at and angle, θ, above horizontal, we guess the time of the bullet using vertical motion equation: 12gt2-(v0sinθ)t-H=0...
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...There are two important motion characteristics which are true of free-falling objects: Free-falling objects do not encounter air resistance. All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s2 19 Examples of objects in free fall include skydivers, an object dropped from the top of a cliff, an apple falling from a tree etc. (www.howstuffworks.com) A projectile is any object which once projected or dropped continues in motion by its own inertia ( the property of matter by which it retains its velocity so long as it is not acted upon by an external force) and is influenced only by the downward force of gravity. By definition, a projectile has only one force acting upon it - the force of gravity. There are a variety of examples of projectiles. An object dropped from rest is a projectile. An object which is thrown vertically upward is also a projectile. And an object which is thrown upward at an angle to the horizontal is also a projectile. Projectile motion is simply the motion of an object in a plane (two dimensions) under the influence of gravity. The trajectory describes an arc. The equations of motion describe the components of such motion and are useful to analyze projectile motion. In textbook problems, the initial velocity of an object is typically given, and the subsequent motion is described with equations of motion. The method used in this lab will be to determine the initial velocity of a projectile from range-fall measurements...
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... COLLAGE OF ENGINEERING PHYSICS 101 LABORATORY REPORT NUMBER OF LAB SESSION: 2 EXPERIMENTS: 1- The Relationship between Time of Flight and Initial Velocity 2- Projectile Motion 3- Projectile Range versus Angle AUTHOR OF THIS REPORTS: FULL NAME: RANA AKMAN STUDENT NO: 140201038 LAB SECTION: OTHER EXPERIMENTER: FULL NAME: EDA HAZAL RAŞİT STUDENT NO: 140203009 EXPERIMENT PERFORMED ON: 30/09/2015 REPORT SUBMITTED ON: 07/10/2015 EXPERIMENT 1: The Relationship between Time of Flight and Initial Velocity Equipments: 1. Projectile launcher 2. Time-of-Flight Accessory 3. Xplorer GLX (as timing device) 4. Yellow Nylon Ball (2.5 cm diameter, 10 g) 5. Photogate 6. Photogate bracket 7. Carbon paper 8. White paper 9. Measuring tape 10. Duct tape Purpose: Purpose of this experiment is to Procedure: I have equipment to measured the fall time and I have different ball. This lesson was my first LAB so I didn’t know anything about equipments and teacher have thought equipments. After...
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...Name Pishoy Shehata Projectile Motion Go to http://phet.colorado.edu/simulations/sims.php?sim=Projectile_Motion and click on Run Now. Pre Lab Reflections: What are the ● What forces are at play on a body under fall ? Under free fall, the only force acting upon an object is the force of gravity. But realistically, there is also the force of friction from the air (Air Resistance) that opposes the force of gravity. ● Make a prediction of which angle results in maximum range. Activity: Open the sim, projectile motion. Familiarize yourself with the variables shown there. Ensure the air resistance check box remains unchecked. Using the mouse set the angle of projection(i) to 5 deg. Alternatively enter the value in directly. Set the initial speed to a value U=15m/s . Click on Fire to start the projectile and record the corresponding value of the range R. Repeat with values i= 10,15,20,25,30,35,40,45,50,60,70,75,80,85. Draw a graph of Range (R) against Angle of projection (i) You may want your lay out to appear like in the table. U=……… Angle (i) 5 10 15 20 30 35 40 45 50 55 60 65 Range(m) 9.7 12.2 14.9 17.5 21.8 23.2 24.0 24.1 23.6 22.4 20.6 18.1 70 75 80 85 15.2 11.65 7.81 3.92 From your graph, o Describe the shape of the graph obtained. Comment. o The graph has a maximum point and it opens downwards (nshaped) o Determine using the graph the angle for maximum range. o Maximum range is at 45 degrees Post activity discussion:...
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...Name ____Anjad itayem______________ Projectile Motion Go to http://phet.colorado.edu/simulations/sims.php?sim=Projectile_Motion and click on Run Now. Pre Lab Reflections: What are the • What forces are at play on a body under fall ? gravity and air resistance • Make a prediction of which angle results in maximum range. My prediction is that angel of 70 degrees will be the mazimum range Activity: - Open the sim, projectile motion. - Familiarize yourself with the variables shown there. - Ensure the air resistance check box remains unchecked. - Using the mouse set the angle of projection(i) to 5 deg. Alternatively enter the value in directly. - Set the initial speed to a value U=15m/s . - Click on Fire to start the projectile and record the corresponding value of the range R. - Repeat with values i= 10,15,20,25,30,35,40,45,50,60,70,75,80,85. - Draw a graph of Range (R) against Angle of projection (i) You may want your lay out to appear like in the table. U=……… |Angle (i) |Range(m) | |5 |9.7 | |10 |12.2 | |15 |14.9 | |20 |17.5 | |30 |21.8 | |35 |23.2 ...
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...Experiment 4 Projectile Motion Introduction We examined projectile motion by observing a ball rolling down then leaving the ramp, thus becoming a projectile with a horizontal initial velocity. We measured the horizontal initial velocity using the photogate and computer. We measured the horizontal and vertical distances that the projectile traveled from the end of the ramp to when it hit the floor my using a meter stick to measure Experimental Set-Up In our experiment, we used the following: ramp, photogate, steal ball, plumb bob, meter stick, and vernier caliper. Experimental Procedure 1.At the edge of our lab table, we prepared the ramp. 2.Exactly below the launch point, we marked a point on the floor by using the plumb bob. 3.We determined the vertical distance that the ball fell (mm) from when it was launched from the ramp and fell on the floor. We then entered this in our data table. 4.We positioned a piece of paper on the floor to where the ball would land. We put the carbon paper above the paper and taped them to the floor. 5.We fixed the photogate so the ball rolled out and the light beam was blocked and unblocked. The photogate was plugged into the LabPro Dig/Sonic1 port. 6.We opened up the One Gate Timing from the Logger Pro folder. 7.We measured the diameter of the ball with the vernier caliper and recorded it in the computer so that it could calculate the ball’s launch velocity. 8.We launched the ball from a specific height from the ramp so that the ball...
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... 1.09! 1.101! 1.010! 1.03! 1.165! 1.131! .96! 1.25! 1.302! Average!=1.024! Average!=1.175! Average!=1.152! 1.34! 1.343! 1.002! 1.39! 1.295! .9316! 1.42! 1.268! .8927! 1.29! 1.395! 1.082! 1.33! .90! .90! .90! .90! .90! ! Average!=2.029! 1.06! .60! .60! .60! .60! .60! ! 11! 12! 13! 14! 15! Angle/of/incline/=///35/ /o! Distance/(x)! –//m! ! 6! 7! 8! 9! 10! ! ! m! 1.353! 1.018! Average!=1.354! Average!=1.331! www.HOLscience.com 1! Average!=.9852! ©Hands-On Labs, Inc. ! Experiment AccelerAtion! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Questions A. Newton’s/first/law/says/a/body/at/rest/will/remain/at/rest/unless/acted/upon/by/an/outside/ force,/ and/ a/ body/ in/ motion/will/ continue/in/ motion/at/ the/ same/ speed/ and/ in/ the/ same/ direction/unless/acted/upon/by/an/outside/force./What/forces/were/acting/on/the/marble/as/ it/traveled/down/the/ramp?/ Gravitational! forces! are! acting! upon! the! marble! in! an! attempt! to! normalize! the! potential! energy!built!up!by!it’s!elevation.!This!is!spent!in!the!form!of!kinetic!energy!as!the!marble!rolls! down!the!ramp.! B. Did/the/velocity/of/the/marble/increase/as/it/traveled/down/the/ramp?/...
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...AP Physics Lab Reports 1. All lab reporting will be done on binder paper or graph paper as the lab is being conducted. You may use the front and back of each page. If you want to delete something, simply cross it out. All work should be neat and legible. 2. Prepare as much as possible prior to the actual lab day (such as title, problem or purpose, materials, and background information) ---just to give you more time to work with the equipment. 3. October 12, 2014 Jamie Smith P1 Partners: Roy Rogers Dale Evans October 12, 2014 Jamie Smith P1 Partners: Roy Rogers Dale Evans In the upper corner of the first page of each lab, write your name, the date, period, and names of lab partner(s). Example: 4. Give your lab a title. (Creativity is appreciated, but a subtitle should be more descriptive of the procedure.) Example: “Shooting Hoops” (Projectile Motion to a Raised Target) 5. State the problem or purpose of the lab. Example: Purpose: To determine the air drag coefficient for a falling coffee filter. 6. List the materials needed. 7. Provide a brief description of the procedure and/or diagram of the set-up. A labeled diagram is often the quickest and easiest way to do this. 8. Provide a background with necessary equations, derivations of equations, safety comments, and notes about procedure that will reduce error….anything that is important in preparing, setting up...
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...Lab #4: Kinematics - Velocity and Acceleration Introduction: The purpose of this lab is to discover and understand the relationships between position, velocity, and acceleration. Additionally, constant/uniform acceleration due to the force of gravity will be examined to find possible mathematical relationships to position and velocity. Velocity and acceleration are changes in position and velocity, respectively, with regards to time. This change can be shown mathematically in calculus derivatives: EQ 1. EQ 2. As dt decreases in value, the instantaneous velocity and acceleration can also be found. Furthermore, if constant acceleration is established, two basic relations between distance, velocity, and the constant acceleration can be found: EQ 3. EQ 4. In any environment near Earth, the acceleration in the vertical direction is constant at a value of g=9.8m/s2 towards the center of Earth or often written as g=-9.8m/s2. In such an environment there is no natural acceleration in the horizontal direction, thus the horizontal motion is analyzed independently of the vertical motion. Thus it can be established that the general form of a position curve for a projectile would follow an inverse parabola shape and the maximum height occurs when vertical velocity is zero. By calculus derivation, it can also be found that the velocity graph would display a linear line with a negative slope. Procedure: This lab consists of two separate but related experiments...
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...Experiment 6: Blackwood Ballistic Pendulum September 18, 2013 Jamal Wright Zachary Floyd Christopher Wilson Experiment 6 Blackwood Ballistic Pendulum Jamal Wright, Zachary Floyd, Christopher Wilson Abstract Our goal of this experiment is to determine muzzle velocity by two methods: 1) employing uniform linear motion relations, the kinematic equations; 2) using the principles of conservation of energy and momentum. In this paper, we aim to validate the law of conservation of momentum. We do so by comparing results from two experiments conducted with a single ballistic launcher/pendulum apparatus. Hypothesis: The initial velocity of a ballistic pendulum can be determined using the law of conservation of momentum. Momentum should be conserved, based on the law of conservation of energy. If momentum is conserved, the velocity found using the law of conservation of momentum equation should equal the velocity found using projectile motion. Due to the law of conservation of momentum, the total momentum before the pendulum is swung equals the net momentum after the pendulum is swung. Introduction/Purpose The ballistic pendulum is a device where a ball is shot into and captured by a pendulum. The pendulum is initially at rest but acquires energy from the collision with the ball. Using conservation of energy it is possible to find the initial velocity of the ball. In this ball-pendulum system we cannot use the conservation of mechanical energy to relate the quantities...
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...1 UNIT 1 Living Things and Their Environment DRAFT April 29, 2014 Photo Credit: http://www.flyingfourchette.com/2013/05/25/around-ubud/ 2 UNIT 1: Living Things and Their Environment Introduction At this point, students have already learned in Grade 8 how the body breaks down food into forms that can be absorbed through the digestive system and then transported to each cell, which was on the other hand discussed in Grade 7 to be the basic unit of life. The learners have also discovered that cells divide to produce new cells by mitosis and meiosis. They have understood that meiosis is an early step in sexual reproduction that leads to variation. Students have been introduced to genetics to be able to appreciate evolutionary differences among species. Learners have also found out that biodiversity is the collective variety of species living in an ecosystem, and by studying the ecosystem; they have come across the various cycling of materials and energy transformation. DRAFT April 29, 2014 All modules in Grade 9 Unit 1-Living Things and Their Environment present student-centered activities that will allow the learners to discover and develop concepts that they may consider useful to their everyday life. At the end of each lesson, key concepts are provided for the students to grasp ideas and information that they will remember even after they have left school. Instructional activities are designed to build up the students’ knowledge, understanding, skills, and ability to transfer...
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...Dashain Vacation Home Assignment-2069 Grade XI, Science Note: Home assignments of each subject should be done in different copies/papers. English 1. Write an essay on ‘Dashain and its significance in Hindu Religion’. 2. Prepare a report on ‘Global Warming, its consequences and solutions’. 3. Write an article on ‘Importance of Media’. 4. Write on ‘English for Global education’. Mathematics 1. Find the angle between the pair of straight lines x2 -2secAxy +y2= 0. 2. Evaluate: limx→∞ 3x2-2x+5x3 3. Prove that: A-B=B-A 4. Define lower triangular matrix with an example. 5. Find the equation of circle concentric with the circle x2+ y2 – 6x + 12y + 15 = 0 and having the area twice the area of the given circle. 6. For any two real numbers x and y, prove that |x+y| ≤ |x| + |y|. 7. What do you mean by tautology of compound statement? Give an example of it. 8. For any positive constant ‘a’ and for any real number ‘x’ , prove that |x| < a ⇒ -a < x < a. 10. Prove that the tangent to the circle x2+y2=5 at the point (1,-2) also touches the circle x2 + y2 - 8x + 6y + 20 = 0 and find the point of contact. 11. If P is the length of perpendicular dropped from the origin of the line xa + yb = 1 prove that 1a2 + 1b2 = 1 p2. 12. Find the equation of the circle with centre at (4, -1) and passing through the origin. 13. Evaluate; limx→osin(x-a)x-a 14. Define absolute value of a real number. Rewrite the following relation without using...
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...SENIOR SECONDARY COURSE PHYSICS 1 (CORE MODULES) Coordinators Dr. Oum Prakash Sharma Sh. R.S. Dass NATIONAL INSTITUTE OF OPEN SCHOOLING A-25, INSTITUTIONAL AREA, SECTOR-62, NOIDA-201301 (UP) COURSE DESIGN COMMITTEE CHAIRMAN Prof. S.C. Garg Former Pro-Vice Chancellor IGNOU, Maidan Garhi, Delhi MEMBERS Prof. A.R. Verma Former Director, National Physical Laboratory, Delhi, 160, Deepali Enclave Pitampura, Delhi-34 Dr. Naresh Kumar Reader (Rtd.) Deptt. of Physics Hindu College, D.U. Dr. Oum Prakash Sharma Asstt. Director (Academic) NIOS, Delhi Prof. L.S. Kothari Prof. of Physics (Retd.) Delhi University 71, Vaishali, Delhi-11008 Dr. Vajayshree Prof. of Physics IGNOU, Maidan Garhi Delhi Sh. R.S. Dass Vice Principal (Rtd.) BRMVB, Sr. Sec. School Lajpat Nagar, New Delhi-110024 Dr. G.S. Singh Prof. of Physics IIT Roorkee Sh. K.S. Upadhyaya Principal Jawahar Navodaya Vidyalaya Rohilla Mohammadabad (U.P.) Dr. V.B. Bhatia Prof. of Physics (Retd.) Delhi University 215, Sector-21, Faridabad COURSE DEVELOPMENT TEAM CHAIRMAN Prof. S.C. Garg Former Pro-Vice Chancellor IGNOU, Delhi MEMBERS Prof. V.B. Bhatia 215, Sector-21, Faridabad Prof. B.B. Tripathi Prof. of Physics (Retd.), IIT Delhi 9-A, Awadhpuri, Sarvodaya Nagar Lucknow-226016 Sh. K.S. Upadhyaya Principal Navodaya Vidyalaya Rohilla Mohammadabad, (U.P.) Dr. V.P. Shrivastava Reader (Physics) D.E.S.M., NCERT, Delhi EDITORS TEAM CHAIRMAN Prof. S.C. Garg Former Pro-Vice Chancellor IGNOU, Delhi MEMBERS Prof. B.B. Tripathi Prof...
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...PHYSIC AL CONSTANTS CONSTANT Speed of light Elementary charge Electron mass Proton mass Gravitational constant Permeability constant Permittivity constant Boltzmann’s constant Universal gas constant Stefan–Boltzmann constant Planck’s constant Avogadro’s number Bohr radius SYMBOL c e me mp G m0 P0 k R s h 15 2p"2 NA a0 THREE-FIGURE VALUE 3.003108 m/s 1.60310219 C 9.11310231 kg 1.67310227 kg 6.67310211 N # m2/kg 2 1.2631026 N/A2 1H/m2 8.85310212 C 2/N # m2 1F/m2 1.38310223 J/K 8.31 J/K # mol 5.6731028 W/m2 # K4 6.63310234 J # s 6.0231023 mol21 5.29310211 m BEST KNOWN VALUE* 299 792 458 m/s (exact) 1.602 176 4871402 310219 C 9.109 382 151452 310231 kg 1.672 621 6371832 310227 kg 6.674 281672 310211 N # m2/kg 2 4p31027 (exact) 1/m0c2 (exact) 1.380 65041242 310223 J/K 8.314 4721152 J/K # mol 5.670 4001402 31028 W/m2 # K4 6.626 068 961332 310234 J # s 6.022 141 791302 31023 mol21 5.291 772 08591362 310211 m *Parentheses indicate uncertainties in last decimal places. Source: U.S. National Institute of Standards and Technology, 2007 values SI PREFIXES POWER 1024 1021 1018 1015 1012 109 106 103 102 101 100 1021 1022 1023 1026 1029 10212 10215 10218 10221 10224 THE GREEK ALPHABET PREFIX yotta zetta exa peta tera giga mega kilo hecto deca — deci centi milli micro nano pico femto atto zepto yocto SYMBOL Y Z E P T G M k h da — d c m μ n p f a z y Alpha ...
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...CHAPTER 0 Contents Preface v vii Problems Solved in Student Solutions Manual 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Matrices, Vectors, and Vector Calculus Newtonian Mechanics—Single Particle Oscillations 79 127 1 29 Nonlinear Oscillations and Chaos Gravitation 149 Some Methods in The Calculus of Variations 165 181 Hamilton’s Principle—Lagrangian and Hamiltonian Dynamics Central-Force Motion 233 277 333 Dynamics of a System of Particles Motion in a Noninertial Reference Frame Dynamics of Rigid Bodies Coupled Oscillations 397 435 461 353 Continuous Systems; Waves Special Theory of Relativity iii iv CONTENTS CHAPTER 0 Preface This Instructor’s Manual contains the solutions to all the end-of-chapter problems (but not the appendices) from Classical Dynamics of Particles and Systems, Fifth Edition, by Stephen T. Thornton and Jerry B. Marion. It is intended for use only by instructors using Classical Dynamics as a textbook, and it is not available to students in any form. A Student Solutions Manual containing solutions to about 25% of the end-of-chapter problems is available for sale to students. The problem numbers of those solutions in the Student Solutions Manual are listed on the next page. As a result of surveys received from users, I continue to add more worked out examples in the text and add additional problems. There are now 509 problems, a significant number over the 4th edition. The instructor will find a large...
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