Get Discount Coupons for your Coaching institute and FREE Study Material at Force System
|
|
- Justina Barton
- 5 years ago
- Views:
Transcription
1 Get Discount Coupons for your Coaching institute and FEE Study Material at Mechanics Force System When a member of forces simultaneously acting on the body, it is known as force system. A force system is a collection of forces acting at specified locations. Thus, the set of forces can be shown on any free body diagram makes-up a force system. Truss It is a rigid structure composed of number of straight members pin jointed to each other. It can sustain static or dynamic load without any relative motion to each other. Types of Truss. Plane Truss It is defined as a truss in which members are essentially lies in a single plane.. igid Truss igid means there is no deformation take place due to internal strain in members. 3. Simple Truss This type of trusses built a basic triangle by adding different members are known as simple truss. Classification of a Truss (based on joints) Truss can be classified on the basis of joints (j) and members (m) in the structure. It can be easily understood with the help of following hierarchical approach. D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:35 AM Get Discount Coupons for your Coaching institute and FEE Study Material at
2 Get Discount Coupons for your Coaching institute and FEE Study Material at Handbook Mechanical Engineering Truss Perfect Truss m = j 3 Imperfect Truss (unstable truss) n j 3 where m number of members and j number of joints Key Points edundant Truss m > = j 3 Analysis of a Framed Structure (Section Method). This method is used when the forces in the few members of a truss is required to found out in a truss structure. To find out force in AC, BC and BD First cut a section which passes through AC, BC and BD members. Find out reaction at point A and B Deficient Truss m < = j 3 m = 6, j = 4 m = 4, j = 4 6 > < > 5 4 < 5 Classification of truss A C F B D Framed structure using section method Find out forces FCA, FCB and F DB in membersca, CBand DB respectively by taking moment about A and B. E D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:35 AM Get Discount Coupons for your Coaching institute and FEE Study Material at
3 Get Discount Coupons for your Coaching institute and FEE Study Material at Mechanics 3. Analytical Method In this method, the free body diagram of each joint is separately analysed to find magnitude of stresses in the truss members. Lami s Theorem Friction Force It is resistant force which acts in opposite direction at the surface in body which tend to move or its move. Normal force mg If mg F, the body will not move. mg F the body will tend to move. mg F the body will move. Angle of Friction Q It is defined as the angle between normal reaction and resultant reaction when the body is in condition of just sliding. esultant mg tan reaction φ mg (Q mg mg ) F F µmg P tan coefficient of friction γ β Three concurrent forces P, Q and α µ F mg Friction force on a body mg Angle of friction due to resultant reaction D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:35 AM 3 Get Discount Coupons for your Coaching institute and FEE Study Material at 3
4 Get Discount Coupons for your Coaching institute and FEE Study Material at 4 Handbook Mechanical Engineering Angle of epose ( ) It is defined as angle of inclined plane with horizontal at which body is in condition of just sliding. Angle of friction is equal to angle of repose. Plane Motion When all parts of the body move in a parallel planes then a rigid body said to perform plane motion. Key Points Straight Line Motion It defines the three equations with the relationship between velocity, acceleration, time and distance travelled by the body. In straight line motion, acceleration is constant. v u at s ut at v u as where, u initial velocity v final velocity a acceleration of body t time s distance travelled by body Distance travelled in nth second sn u a ( n ) w sin α α α w cos α w Angle of epose ( ) µ D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:35 AM 4 Get Discount Coupons for your Coaching institute and FEE Study Material at 4
5 Get Discount Coupons for your Coaching institute and FEE Study Material at Mechanics 5 Projectile Motion Projectile motion defines that motion in which velocity has two components, one in horizontal direction and other one in vertical direction. Horizontal component of velocity is constant during the flight of the body as no acceleration in horizontal direction. Let the block of mass is projected at angle from horizontal direction Maximum height h where, u initial velocity Key Points max u sin g u Time of flight T sin g ange u sin g otational Motion with Uniform Acceleration Uniform acceleration occurs when the speed of an object changes at a constant rate. The acceleration is the same over time. So, the rotation motion with uniform acceleration can be defined as the motion of a body with the same acceleration θ over time. Let the rod of block rotated about a point in horizontal plane with angular otational motion velocity. Angular velocity d (change in angular displacement per unit time) dt Angular acceleration d dt where angle between displacement. d dt θ u h max range Projectile motion D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:35 AM 5 Get Discount Coupons for your Coaching institute and FEE Study Material at 5
6 Get Discount Coupons for your Coaching institute and FEE Study Material at 6 Handbook Mechanical Engineering In case of angular velocity, the various equations with the relationships between velocity, displacement and acceleration are as follows. t 0 0 t 0t t where 0 initial angular velocity final angular velocity angular acceleration angular displacement Angular displacement in nth second n 0 ( n ) 0 elation between Linear and Angular Quantities There are following relations between linear and angular quantities in rotational motion. e r e t e r and e t are radial and tangential unit vector. Linear velocity v r e t Linear acceleration (Net) Tangential acceleration a a r e r dv dt e t t Centripetal acceleration ar r v r Net acceleration a a a where a r centripetal acceleration a t tangential acceleration dv (rate of change of speed) dt r t v d v r dt Y O e t θ e r Position of radial and tangential vectors X ( Q v r ) D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:35 AM 6 Get Discount Coupons for your Coaching institute and FEE Study Material at 6
7 Get Discount Coupons for your Coaching institute and FEE Study Material at Mechanics 7 Centre of Mass of Continuous Body Centre of mass of continuous body can be defined as Centre of mass about x, x Centre of mass about y, y Centre of mass about z, z CM CM CM xdm dm y dm dm z dm dm x dm M y dm M z dm CM of uniform rectangular, square or circular plate lies at its centre. CM of semicircular ring CM of semicircular disc CM of hemispherical shell CM of solid hemisphere O O O Law of Conservation of Linear Momentum CM CM CM The product of mass and velocity of a particle is defined as its linear momentum (p). p mv p Km M π 4 3π 3 8 D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:35 AM 7 Get Discount Coupons for your Coaching institute and FEE Study Material at 7
8 Get Discount Coupons for your Coaching institute and FEE Study Material at 8 Handbook Mechanical Engineering p F d dt where, K kinetic energy of the particle F net external force applied to body P momentum ocket Propulsion Let m 0 be the mass of the rocket at time t 0, m its mass at any time t and v its velocity at that moment. Initially, let us suppose that the velocity of the rocket is u. u u At t = 0 v =u m=m 0 Thrust force on the rocket F v t r dm dt dm where, rate at which mass is ejecting dt v r relative velocity of ejecting mass (exhaust velocity) Weight of the rocket w mg Net force on the rocket Fnet Ft w v Net acceleration of the rocket F a m d v vr dm g dt m dt where, m 0 mass of rocket at time t 0 m mass of rocket at time t m0 v u gt vr ln m r At t= t m =m v =v exhaust velocity =v r ocket propulsion dm mg dt D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:35 AM 8 Get Discount Coupons for your Coaching institute and FEE Study Material at 8
9 Get Discount Coupons for your Coaching institute and FEE Study Material at Mechanics 9 Impulse The product of constant force F and time t for which it acts is called the impulse (J) of the force and this is equal to the change in linear momentum which it produces. Impulse J F t p pf pi where, F constant force P linear momentum Instantaneous Impulse e.g., bat and ball contact Key Points Collision J F dt p p p A Collision is an isolated event in which two or more moving bodies exert forces on each other for a relatively short time. Collision between two bodies may be classified in two ways Head-on collision Oblique collision. Head-on Collision Let the two balls of masses m and m collide directly with each other with velocities v and v in direction as shown in figure. After collision the velocity become v and v along the same line. m v m v Before collision m em v m m v m em m m v f m m v v After collision i D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:35 AM 9 Get Discount Coupons for your Coaching institute and FEE Study Material at 9
10 Get Discount Coupons for your Coaching institute and FEE Study Material at 0 Handbook Mechanical Engineering m em v m m v m em m m v where, m mass of body m mass of body v velocity of body v velocity of body v velocity of body after collision v velocity of body after collision where e coefficient restitution Separation speed e Approach speed v v e v v In case of head-on elastic collision e In case of head-on inelastic collision 0 e In case of head-on perfectly inelastic collision e 0 If e is coefficient of restitution between ball and ground, then after nth collision with the floor, the speed of ball will n remain e v and it will go upto a height e h. n 0 v e v e gh n n n h e h Oblique Collision 0 n 0 In case of oblique collision linear momentum of individual particle do change along the common normal direction. No component of impulse act along common tangent direction. So, linear momentum or linear velocity remains unchanged along tangential direction. Net momentum of both the particle remain conserved before and after collision in any direction. v h O u = 0 O u = gh 0 Collision of a ball with floor Oblique collision y x D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:35 AM 0 Get Discount Coupons for your Coaching institute and FEE Study Material at 0
11 Get Discount Coupons for your Coaching institute and FEE Study Material at Mechanics Moment of Inertia Momentum of inertia can be defined as r distance of the body of mass, m from centre of axis. Very thin circular loop (ring) I m r I i i i r dm I M where, M mass of the body radius of the ring I moment of inertia Uniform circular loop I M M Uniform solid cylinder I A Uniform circular loop A Uniform solid cylinder A Thin circular ring D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:35 AM Get Discount Coupons for your Coaching institute and FEE Study Material at
12 Get Discount Coupons for your Coaching institute and FEE Study Material at Handbook Mechanical Engineering Uniform solid sphere Uniform thin rod I M 5 (AA ) moment of inertia about the centre and perpendicular axis to the rod moment of inertia about the one corner point and perpendicular (BB ) axis to the rod. Ml I Very thin spherical shell Thin circular sheet M I 4 A A Uniform solid sphere l I Ml 3 A Uniform thin rod Thin sperical shell I M 3 Thin circular sheet D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:35 AM Get Discount Coupons for your Coaching institute and FEE Study Material at
13 Get Discount Coupons for your Coaching institute and FEE Study Material at Mechanics 3 Thin rectangular sheet Uniform right cone Uniform cone as a disc I M a b I 3 M 0 Suppose the given section is th part of the disc, then mass of disc will n be nm. O Inertia of the disc, Inertia of the section, I Idisc ( nm) section a A Thin rectangular sheet A M Uniform right cone A part of uniform cone as a disc b n I disc M D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:36 AM 3 Get Discount Coupons for your Coaching institute and FEE Study Material at 3
14 Get Discount Coupons for your Coaching institute and FEE Study Material at 4 Handbook Mechanical Engineering Torque and Angular Acceleration of a igid Body For a rigid body, net torque acting I where, angular acceleration of rigid body I moment of inertia about axis of rotation Kinetic energy of a rigid body rotating about fixed axis KE I Angular moment of a particle about same point L r p L m( r v) where L angular displacement ( angular velocity) Angular moment of a rigid body rotating about a fixed axis. L I A B Angular moment of a rigid body Angular moment of a rigid body in combined rotation and translation L LCM M ( r0 v0) Conservation of angular momentum d L dt dl r F v p dt r 0 O CM O ω Combined rotation and translation in a rigid body ω r P V 0 θ r p = mv Angular moment D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:36 AM 4 Get Discount Coupons for your Coaching institute and FEE Study Material at 4
15 Get Discount Coupons for your Coaching institute and FEE Study Material at Mechanics 5 Kinetic energy of rigid body in combined translational and rotational motion Uniform Pure olling K mvcm I CM Pure rolling means no relative motion or no slipping at point of contact between two bodies. If v v P Q v if v v p Q v if v v P CM Q v no slipping forward slipping backward slipping Accelerated Pure olling ω v ω v s = π Pure olling No slipping s Forward slipping s Backward slipping s A pure rolling is equivalent to pure translation and pure rotation. It follows a uniform rolling and accelerated pure rolling can be defined as ω F f Ma ( F f ) I P Q Uniform Pure olling v D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:36 AM 5 Get Discount Coupons for your Coaching institute and FEE Study Material at 5
16 Get Discount Coupons for your Coaching institute and FEE Study Material at 6 Handbook Mechanical Engineering α F C a F force acting on a body, f friction on that body Angular Impulse The angular impulse of a torque in a given time interval is defined as t t t t dt dt L L where, L and L are the angular momentum at time t and t respectively. Key Points f Accelerated pure rolling D:\Book Final\G5 Handbook Mechanical Engineering\Mechanical Engineering\Chap_0\Chap_.vp Thursday, October 4, 03 4:49:36 AM 6 Get Discount Coupons for your Coaching institute and FEE Study Material at 6
where G is called the universal gravitational constant.
UNIT-I BASICS & STATICS OF PARTICLES 1. What are the different laws of mechanics? First law: A body does not change its state of motion unless acted upon by a force or Every object in a state of uniform
More information2015 ENGINEERING MECHANICS
Set No - 1 I B. Tech I Semester Supplementary Examinations Aug. 2015 ENGINEERING MECHANICS (Common to CE, ME, CSE, PCE, IT, Chem E, Aero E, AME, Min E, PE, Metal E) Time: 3 hours Max. Marks: 70 Question
More informationLesson 7. Luis Anchordoqui. Physics 168. Tuesday, October 10, 17
Lesson 7 Physics 168 1 Eruption of a large volcano on Jupiter s moon When volcano erupts speed of effluence exceeds escape speed of Io and so a stream of particles is projected into space Material in stream
More informationMechanics II. Which of the following relations among the forces W, k, N, and F must be true?
Mechanics II 1. By applying a force F on a block, a person pulls a block along a rough surface at constant velocity v (see Figure below; directions, but not necessarily magnitudes, are indicated). Which
More informationRotational Kinematics and Dynamics. UCVTS AIT Physics
Rotational Kinematics and Dynamics UCVTS AIT Physics Angular Position Axis of rotation is the center of the disc Choose a fixed reference line Point P is at a fixed distance r from the origin Angular Position,
More informationHandout 6: Rotational motion and moment of inertia. Angular velocity and angular acceleration
1 Handout 6: Rotational motion and moment of inertia Angular velocity and angular acceleration In Figure 1, a particle b is rotating about an axis along a circular path with radius r. The radius sweeps
More informationHandout 7: Torque, angular momentum, rotational kinetic energy and rolling motion. Torque and angular momentum
Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion Torque and angular momentum In Figure, in order to turn a rod about a fixed hinge at one end, a force F is applied at a
More informationPhysics 5A Final Review Solutions
Physics A Final Review Solutions Eric Reichwein Department of Physics University of California, Santa Cruz November 6, 0. A stone is dropped into the water from a tower 44.m above the ground. Another stone
More informationThe... of a particle is defined as its change in position in some time interval.
Distance is the. of a path followed by a particle. Distance is a quantity. The... of a particle is defined as its change in position in some time interval. Displacement is a.. quantity. The... of a particle
More informationChapter 8- Rotational Motion
Chapter 8- Rotational Motion Assignment 8 Textbook (Giancoli, 6 th edition), Chapter 7-8: Due on Thursday, November 13, 2008 - Problem 28 - page 189 of the textbook - Problem 40 - page 190 of the textbook
More informationPLANAR KINETIC EQUATIONS OF MOTION (Section 17.2)
PLANAR KINETIC EQUATIONS OF MOTION (Section 17.2) We will limit our study of planar kinetics to rigid bodies that are symmetric with respect to a fixed reference plane. As discussed in Chapter 16, when
More informationjfpr% ekuo /kez iz.ksrk ln~xq# Jh j.knksm+nklth egkjkt
Phone : 0 903 903 7779, 98930 58881 Rotational Motion Page: 1 fo/u fopkjr Hkh# tu] ugha vkjehks dke] foifr ns[k NksM+s rqjar e/;e eu dj ';kea iq#"k flag ladyi dj] lgrs foifr vusd] ^cuk^ u NksM+s /;s; dks]
More informationK.GNANASEKARAN. M.E.,M.B.A.,(Ph.D)
DEPARTMENT OF MECHANICAL ENGG. Engineering Mechanics I YEAR 2th SEMESTER) Two Marks Question Bank UNIT-I Basics and statics of particles 1. Define Engineering Mechanics Engineering Mechanics is defined
More information2. a) Explain the equilibrium of i) Concurrent force system, and ii) General force system.
Code No: R21031 R10 SET - 1 II B. Tech I Semester Supplementary Examinations Dec 2013 ENGINEERING MECHANICS (Com to ME, AE, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions
More informationPLANAR KINETICS OF A RIGID BODY FORCE AND ACCELERATION
PLANAR KINETICS OF A RIGID BODY FORCE AND ACCELERATION I. Moment of Inertia: Since a body has a definite size and shape, an applied nonconcurrent force system may cause the body to both translate and rotate.
More informationKINGS COLLEGE OF ENGINEERING ENGINEERING MECHANICS QUESTION BANK UNIT I - PART-A
KINGS COLLEGE OF ENGINEERING ENGINEERING MECHANICS QUESTION BANK Sub. Code: CE1151 Sub. Name: Engg. Mechanics UNIT I - PART-A Sem / Year II / I 1.Distinguish the following system of forces with a suitable
More informationNov. 27, 2017 Momentum & Kinetic Energy in Collisions elastic collision inelastic collision. completely inelastic collision
Nov. 27, 2017 Momentum & Kinetic Energy in Collisions In our initial discussion of collisions, we looked at one object at a time, however we'll now look at the system of objects, with the assumption that
More informationPH1104/PH114S MECHANICS
PH04/PH4S MECHANICS SEMESTER I EXAMINATION 06-07 SOLUTION MULTIPLE-CHOICE QUESTIONS. (B) For freely falling bodies, the equation v = gh holds. v is proportional to h, therefore v v = h h = h h =.. (B).5i
More informationChapter 10. Rotation of a Rigid Object about a Fixed Axis
Chapter 10 Rotation of a Rigid Object about a Fixed Axis Angular Position Axis of rotation is the center of the disc Choose a fixed reference line. Point P is at a fixed distance r from the origin. A small
More informationMechanics Answers to Examples B (Momentum) - 1 David Apsley
TOPIC B: MOMENTUM ANSWERS SPRING 2019 (Full worked answers follow on later pages) Q1. (a) 2.26 m s 2 (b) 5.89 m s 2 Q2. 8.41 m s 2 and 4.20 m s 2 ; 841 N Q3. (a) 1.70 m s 1 (b) 1.86 s Q4. (a) 1 s (b) 1.5
More informationUNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics
UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics Physics 111.6 MIDTERM TEST #2 November 15, 2001 Time: 90 minutes NAME: STUDENT NO.: (Last) Please Print (Given) LECTURE SECTION
More informationPhysics for Scientists and Engineers 4th Edition, 2017
A Correlation of Physics for Scientists and Engineers 4th Edition, 2017 To the AP Physics C: Mechanics Course Descriptions AP is a trademark registered and/or owned by the College Board, which was not
More informationConnection between angular and linear speed
Connection between angular and linear speed If a point-like object is in motion on a circular path of radius R at an instantaneous speed v, then its instantaneous angular speed ω is v = ω R Example: A
More informationKinematics (special case) Dynamics gravity, tension, elastic, normal, friction. Energy: kinetic, potential gravity, spring + work (friction)
Kinematics (special case) a = constant 1D motion 2D projectile Uniform circular Dynamics gravity, tension, elastic, normal, friction Motion with a = constant Newton s Laws F = m a F 12 = F 21 Time & Position
More information2007 Problem Topic Comment 1 Kinematics Position-time equation Kinematics 7 2 Kinematics Velocity-time graph Dynamics 6 3 Kinematics Average velocity
2007 Problem Topic Comment 1 Kinematics Position-time equation Kinematics 7 2 Kinematics Velocity-time graph Dynamics 6 3 Kinematics Average velocity Energy 7 4 Kinematics Free fall Collisions 3 5 Dynamics
More informationDEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS OPTION B-1A: ROTATIONAL DYNAMICS Essential Idea: The basic laws of mechanics have an extension when equivalent principles are applied to rotation. Actual
More informationPhysics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/1
Physics 201 p. 1/1 Physics 201 Professor P. Q. Hung 311B, Physics Building Physics 201 p. 2/1 Rotational Kinematics and Energy Rotational Kinetic Energy, Moment of Inertia All elements inside the rigid
More informationUniform Circular Motion:-Circular motion is said to the uniform if the speed of the particle (along the circular path) remains constant.
Circular Motion:- Uniform Circular Motion:-Circular motion is said to the uniform if the speed of the particle (along the circular path) remains constant. Angular Displacement:- Scalar form:-?s = r?θ Vector
More informationEF 151 Final Exam, Fall, 2011 Page 1 of 11
EF 5 Final Exam, Fall, 0 Page of Instructions Do not open or turn over the exam until instructed to do so. Name, and section will be written on the st page of the exam after time starts. Do not leave your
More informationE 490 FE Exam Prep. Engineering Mechanics
E 490 FE Exam Prep Engineering Mechanics 2008 E 490 Course Topics Statics Newton s Laws of Motion Resultant Force Systems Moment of Forces and Couples Equilibrium Pulley Systems Trusses Centroid of an
More informationparticle p = m v F ext = d P = M d v cm dt
Lecture 11: Momentum and Collisions; Introduction to Rotation 1 REVIEW: (Chapter 8) LINEAR MOMENTUM and COLLISIONS The first new physical quantity introduced in Chapter 8 is Linear Momentum Linear Momentum
More informationISBN :
ISBN : 978-81-909042-4-7 - www.airwalkpublications.com ANNA UNIVERSITY - R2013 GE6253 ENGINEERING MECHANICS UNIT I: BASICS AND STATICS OF PARTICLES 12 Introduction Units and Dimensions Laws of Mechanics
More information6-1. Conservation law of mechanical energy
6-1. Conservation law of mechanical energy 1. Purpose Investigate the mechanical energy conservation law and energy loss, by studying the kinetic and rotational energy of a marble wheel that is moving
More informationPHYS 1114, Lecture 33, April 10 Contents:
PHYS 1114, Lecture 33, April 10 Contents: 1 This class is o cially cancelled, and has been replaced by the common exam Tuesday, April 11, 5:30 PM. A review and Q&A session is scheduled instead during class
More informationAPPLIED MATHEMATICS AM 02
AM SYLLABUS (2013) APPLIED MATHEMATICS AM 02 SYLLABUS Applied Mathematics AM 02 Syllabus (Available in September) Paper I (3 hrs)+paper II (3 hrs) Applied Mathematics (Mechanics) Aims A course based on
More informationROTATORY MOTION. ii) iii) iv) W = v) Power = vi) Torque ( vii) Angular momentum (L) = Iω similar to P = mv 1 Iω. similar to F = ma
OTATOY MOTION Synopsis : CICULA MOTION :. In translatory motion, every particle travels the same distance along parallel paths, which may be straight or curved. Every particle of the body has the same
More informationDepartment of Physics
Department of Physics PHYS101-051 FINAL EXAM Test Code: 100 Tuesday, 4 January 006 in Building 54 Exam Duration: 3 hrs (from 1:30pm to 3:30pm) Name: Student Number: Section Number: Page 1 1. A car starts
More informationCenter of Gravity. The location of the center of gravity is defined by: n mgx. APSC 111 Review Page 7
Center of Gravity We have said that for rigid bodies, all of the forces act at the centre of mass. This is a normally a very good approximation, but strictly speaking, the forces act at the centre of gravity,
More informationQ1. For a completely inelastic two-body collision the kinetic energy of the objects after the collision is the same as:
Coordinator: Dr.. Naqvi Monday, January 05, 015 Page: 1 Q1. For a completely inelastic two-body collision the kinetic energy of the objects after the collision is the same as: ) (1/) MV, where M is the
More information8.012 Physics I: Classical Mechanics Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical Mechanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE
More information3. Kinetics of Particles
3. Kinetics of Particles 3.1 Force, Mass and Acceleration 3.3 Impulse and Momentum 3.4 Impact 1 3.1 Force, Mass and Acceleration We draw two important conclusions from the results of the experiments. First,
More information= o + t = ot + ½ t 2 = o + 2
Chapters 8-9 Rotational Kinematics and Dynamics Rotational motion Rotational motion refers to the motion of an object or system that spins about an axis. The axis of rotation is the line about which the
More informationVALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR DEPARTMENT OF MECHANICAL ENGINEERING
VALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR 603203 DEPARTMENT OF MECHANICAL ENGINEERING BRANCH: MECHANICAL YEAR / SEMESTER: I / II UNIT 1 PART- A 1. State Newton's three laws of motion? 2.
More informationChapter Rotational Motion
26 Chapter Rotational Motion 1. Initial angular velocity of a circular disc of mass M is ω 1. Then two small spheres of mass m are attached gently to diametrically opposite points on the edge of the disc.
More informationWork and kinetic Energy
Work and kinetic Energy Problem 66. M=4.5kg r = 0.05m I = 0.003kgm 2 Q: What is the velocity of mass m after it dropped a distance h? (No friction) h m=0.6kg mg Work and kinetic Energy Problem 66. M=4.5kg
More informationA) 4.0 m/s B) 5.0 m/s C) 0 m/s D) 3.0 m/s E) 2.0 m/s. Ans: Q2.
Coordinator: Dr. W. Al-Basheer Thursday, July 30, 2015 Page: 1 Q1. A constant force F ( 7.0ˆ i 2.0 ˆj ) N acts on a 2.0 kg block, initially at rest, on a frictionless horizontal surface. If the force causes
More informationMechanics Topic B (Momentum) - 1 David Apsley
TOPIC B: MOMENTUM SPRING 2019 1. Newton s laws of motion 2. Equivalent forms of the equation of motion 2.1 orce, impulse and energy 2.2 Derivation of the equations of motion for particles 2.3 Examples
More informationVideo Lecture #2 Introductory Conservation of Momentum Problem using Unit Vectors
AP Physics C Video Lecture Notes Chapter 09-10 Thank You, Emily Rencsok, for these notes. Video Lecture #1 Introduction to Momentum and Derivation of Conservation of Momentum Video Lecture #2 Introductory
More informationMechanics Topic D (Rotation) - 1 David Apsley
TOPIC D: ROTATION SPRING 2019 1. Angular kinematics 1.1 Angular velocity and angular acceleration 1.2 Constant-angular-acceleration formulae 1.3 Displacement, velocity and acceleration in circular motion
More informationKinetics of Particles: Work and Energy
Kinetics of Particles: Work and Energy Total work done is given by: Modifying this eqn to account for the potential energy terms: U 1-2 + (-ΔV g ) + (-ΔV e ) = ΔT T U 1-2 is work of all external forces
More informationPHYS 111 HOMEWORK #11
PHYS 111 HOMEWORK #11 Due date: You have a choice here. You can submit this assignment on Tuesday, December and receive a 0 % bonus, or you can submit this for normal credit on Thursday, 4 December. If
More informationis acting on a body of mass m = 3.0 kg and changes its velocity from an initial
PHYS 101 second major Exam Term 102 (Zero Version) Q1. A 15.0-kg block is pulled over a rough, horizontal surface by a constant force of 70.0 N acting at an angle of 20.0 above the horizontal. The block
More informationAPPLIED MATHEMATICS HIGHER LEVEL
L.42 PRE-LEAVING CERTIFICATE EXAMINATION, 203 APPLIED MATHEMATICS HIGHER LEVEL TIME : 2½ HOURS Six questions to be answered. All questions carry equal marks. A Formulae and Tables booklet may be used during
More information. d. v A v B. e. none of these.
General Physics I Exam 3 - Chs. 7,8,9 - Momentum, Rotation, Equilibrium Oct. 28, 2009 Name Rec. Instr. Rec. Time For full credit, make your work clear to the grader. Show the formulas you use, the essential
More informationRIGID BODY MOTION (Section 16.1)
RIGID BODY MOTION (Section 16.1) There are cases where an object cannot be treated as a particle. In these cases the size or shape of the body must be considered. Rotation of the body about its center
More informationDistance travelled time taken and if the particle is a distance s(t) along the x-axis, then its instantaneous speed is:
Chapter 1 Kinematics 1.1 Basic ideas r(t) is the position of a particle; r = r is the distance to the origin. If r = x i + y j + z k = (x, y, z), then r = r = x 2 + y 2 + z 2. v(t) is the velocity; v =
More informationDelve AP Physics C Practice Exam #1 Multiple Choice Section
Delve AP Physics C Practice Exam #1 Multiple Choice Section 1. Jerk is defined as the rate of change of acceleration with respect to time. What are the SI units of jerk? a) m/s b) m/s 2 c) m/s 3 d) m/s
More informationAngular Motion, General Notes
Angular Motion, General Notes! When a rigid object rotates about a fixed axis in a given time interval, every portion on the object rotates through the same angle in a given time interval and has the same
More informationVersion A (01) Question. Points
Question Version A (01) Version B (02) 1 a a 3 2 a a 3 3 b a 3 4 a a 3 5 b b 3 6 b b 3 7 b b 3 8 a b 3 9 a a 3 10 b b 3 11 b b 8 12 e e 8 13 a a 4 14 c c 8 15 c c 8 16 a a 4 17 d d 8 18 d d 8 19 a a 4
More informationWrite your name legibly on the top right hand corner of this paper
NAME Phys 631 Summer 2007 Quiz 2 Tuesday July 24, 2007 Instructor R. A. Lindgren 9:00 am 12:00 am Write your name legibly on the top right hand corner of this paper No Books or Notes allowed Calculator
More informationTranslational vs Rotational. m x. Connection Δ = = = = = = Δ = = = = = = Δ =Δ = = = = = 2 / 1/2. Work
Translational vs Rotational / / 1/ Δ m x v dx dt a dv dt F ma p mv KE mv Work Fd / / 1/ θ ω θ α ω τ α ω ω τθ Δ I d dt d dt I L I KE I Work / θ ω α τ Δ Δ c t s r v r a v r a r Fr L pr Connection Translational
More informationPhysics Fall Mechanics, Thermodynamics, Waves, Fluids. Lecture 20: Rotational Motion. Slide 20-1
Physics 1501 Fall 2008 Mechanics, Thermodynamics, Waves, Fluids Lecture 20: Rotational Motion Slide 20-1 Recap: center of mass, linear momentum A composite system behaves as though its mass is concentrated
More informationpaths 1, 2 and 3 respectively in the gravitational field of a point mass m,
58. particles of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a c is varying with time t as a c = k 2 rt 2 where k is a constant. The power delivered
More informationChap10. Rotation of a Rigid Object about a Fixed Axis
Chap10. Rotation of a Rigid Object about a Fixed Axis Level : AP Physics Teacher : Kim 10.1 Angular Displacement, Velocity, and Acceleration - A rigid object rotating about a fixed axis through O perpendicular
More informationRotational Motion About a Fixed Axis
Rotational Motion About a Fixed Axis Vocabulary rigid body axis of rotation radian average angular velocity instantaneous angular average angular Instantaneous angular frequency velocity acceleration acceleration
More informationMoments of Inertia (7 pages; 23/3/18)
Moments of Inertia (7 pages; 3/3/8) () Suppose that an object rotates about a fixed axis AB with angular velocity θ. Considering the object to be made up of particles, suppose that particle i (with mass
More informationAngular velocity and angular acceleration CHAPTER 9 ROTATION. Angular velocity and angular acceleration. ! equations of rotational motion
Angular velocity and angular acceleration CHAPTER 9 ROTATION! r i ds i dθ θ i Angular velocity and angular acceleration! equations of rotational motion Torque and Moment of Inertia! Newton s nd Law for
More informationz F 3 = = = m 1 F 1 m 2 F 2 m 3 - Linear Momentum dp dt F net = d P net = d p 1 dt d p n dt - Conservation of Linear Momentum Δ P = 0
F 1 m 2 F 2 x m 1 O z F 3 m 3 y Ma com = F net F F F net, x net, y net, z = = = Ma Ma Ma com, x com, y com, z p = mv - Linear Momentum F net = dp dt F net = d P dt = d p 1 dt +...+ d p n dt Δ P = 0 - Conservation
More informationRolling, Torque & Angular Momentum
PHYS 101 Previous Exam Problems CHAPTER 11 Rolling, Torque & Angular Momentum Rolling motion Torque Angular momentum Conservation of angular momentum 1. A uniform hoop (ring) is rolling smoothly from the
More information1.1. Rotational Kinematics Description Of Motion Of A Rotating Body
PHY 19- PHYSICS III 1. Moment Of Inertia 1.1. Rotational Kinematics Description Of Motion Of A Rotating Body 1.1.1. Linear Kinematics Consider the case of linear kinematics; it concerns the description
More informationAfternoon Section. Physics 1210 Exam 2 November 8, ! v = d! r dt. a avg. = v2. ) T 2! w = m g! f s. = v at v 2 1.
Name Physics 1210 Exam 2 November 8, 2012 Afternoon Section Please write directly on the exam and attach other sheets of work if necessary. Calculators are allowed. No notes or books may be used. Multiple-choice
More informationAdvanced Higher Mathematics of Mechanics
Advanced Higher Mathematics of Mechanics Course Outline (2016-2017) Block 1: Change of timetable to summer holiday Assessment Standard Assessment 1 Applying skills to motion in a straight line (Linear
More informationPhys101 Second Major-173 Zero Version Coordinator: Dr. M. Al-Kuhaili Thursday, August 02, 2018 Page: 1. = 159 kw
Coordinator: Dr. M. Al-Kuhaili Thursday, August 2, 218 Page: 1 Q1. A car, of mass 23 kg, reaches a speed of 29. m/s in 6.1 s starting from rest. What is the average power used by the engine during the
More informationChapter 8: Momentum, Impulse, & Collisions. Newton s second law in terms of momentum:
linear momentum: Chapter 8: Momentum, Impulse, & Collisions Newton s second law in terms of momentum: impulse: Under what SPECIFIC condition is linear momentum conserved? (The answer does not involve collisions.)
More informationPART A. 4cm 1 =1.4 1 =1.5. 5cm
PART A Straight Objective Type This section contains 30 multiple choice questions. Each question has 4 choices (1), (), (3) and (4) for its answer, out of which ONLY ONE is correct. 1. The apparent depth
More informationReview of Linear Momentum And Rotational Motion
Physics 7B-1 (A/B) Professor Cebra Winter 2010 Lecture 7 Review of Linear Momentum And Rotational Motion Slide 1 of 29 Physics 7B Lecture 7 17-Feb-2010 Slide 2 of 29 The Definition of Impulse Recall that
More informationPhysics 207: Lecture 24. Announcements. No labs next week, May 2 5 Exam 3 review session: Wed, May 4 from 8:00 9:30 pm; here.
Physics 07: Lecture 4 Announcements No labs next week, May 5 Exam 3 review session: Wed, May 4 from 8:00 9:30 pm; here Today s Agenda ecap: otational dynamics and torque Work and energy with example Many
More information= y(x, t) =A cos (!t + kx)
A harmonic wave propagates horizontally along a taut string of length L = 8.0 m and mass M = 0.23 kg. The vertical displacement of the string along its length is given by y(x, t) = 0. m cos(.5 t + 0.8
More informationAP Physics C Mechanics Objectives
AP Physics C Mechanics Objectives I. KINEMATICS A. Motion in One Dimension 1. The relationships among position, velocity and acceleration a. Given a graph of position vs. time, identify or sketch a graph
More informationPSI AP Physics I Rotational Motion
PSI AP Physics I Rotational Motion Multiple-Choice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from
More informationPC 1141 : AY 2012 /13
NUS Physics Society Past Year Paper Solutions PC 1141 : AY 2012 /13 Compiled by: NUS Physics Society Past Year Solution Team Yeo Zhen Yuan Ryan Goh Published on: November 17, 2015 1. An egg of mass 0.050
More informationChapter 9 Notes. x cm =
Chapter 9 Notes Chapter 8 begins the discussion of rigid bodies, a system of particles with fixed relative positions. Previously we have dealt with translation of a particle: if a rigid body does not rotate
More informationAP PHYSICS 1 Learning Objectives Arranged Topically
AP PHYSICS 1 Learning Objectives Arranged Topically with o Big Ideas o Enduring Understandings o Essential Knowledges o Learning Objectives o Science Practices o Correlation to Knight Textbook Chapters
More informationLAWS OF MOTION Newtons laws of motion. (i) First law: Law of inertia. Every body continues to be in its state of rest or of uniform motion in a
LAWS OF MOTION Newtons laws of motion. (i) First law: Law of inertia. Every body continues to be in its state of rest or of uniform motion in a straight line unless compelled to change that state by an
More informationRotation. Kinematics Rigid Bodies Kinetic Energy. Torque Rolling. featuring moments of Inertia
Rotation Kinematics Rigid Bodies Kinetic Energy featuring moments of Inertia Torque Rolling Angular Motion We think about rotation in the same basic way we do about linear motion How far does it go? How
More informationPHYSICS 221, FALL 2011 EXAM #2 SOLUTIONS WEDNESDAY, NOVEMBER 2, 2011
PHYSICS 1, FALL 011 EXAM SOLUTIONS WEDNESDAY, NOVEMBER, 011 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively. In this
More informationSt. Joseph s Anglo-Chinese School
Time allowed:.5 hours Take g = 0 ms - if necessary. St. Joseph s Anglo-Chinese School 008 009 First Term Examination Form 6 ASL Physics Section A (40%) Answer ALL questions in this section. Write your
More information( m/s) 2 4(4.9 m/s 2 )( 52.7 m)
Version 072 idterm 2 OConnor (05141) 1 This print-out should have 18 questions ultiple-choice questions may continue on the next column or page find all choices before answering V1:1, V2:1, V3:3, V4:5,
More information( m/s) 2 4(4.9 m/s 2 )( 53.2 m)
Version 074 idterm 2 OConnor (05141) 1 This print-out should have 18 questions ultiple-choice questions may continue on the next column or page find all choices before answering V1:1, V2:1, V3:3, V4:5,
More informationChapter 12: Rotation of Rigid Bodies. Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics
Chapter 1: Rotation of Rigid Bodies Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics Translational vs Rotational / / 1/ m x v dx dt a dv dt F ma p mv KE mv Work Fd P Fv / / 1/ I
More informationFALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003
FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003 NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 14 pages. Make sure none are missing 2. There is
More information2015 ENGINEERING MECHANICS
Set No - 1 I B.Tech I Semester Regular/Supple. Examinations Nov./Dec. 2015 ENGINEERING MECHANICS (Common to CE, ME, CSE, PCE, IT, Chem. E, Aero E, AME, Min E, PE, Metal E, Textile Engg.) Time: 3 hours
More informationPractice Problems for Exam 2 Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 Fall Term 008 Practice Problems for Exam Solutions Part I Concept Questions: Circle your answer. 1) A spring-loaded toy dart gun
More informationEngineering Mechanics
2019 MPROVEMENT Mechanical Engineering Engineering Mechanics Answer Key of Objective & Conventional Questions 1 System of forces, Centoriod, MOI 1. (c) 2. (b) 3. (a) 4. (c) 5. (b) 6. (c) 7. (b) 8. (b)
More information5/2/2015 7:42 AM. Chapter 17. Plane Motion of Rigid Bodies: Energy and Momentum Methods. Mohammad Suliman Abuhaiba, Ph.D., PE
5//05 7:4 AM Chapter 7 Plane Motion of Rigid Bodies: Energy and Momentum Methods 5//05 7:4 AM Chapter Outline Principle of Work and Energy for a Rigid Body Work of Forces Acting on a Rigid Body Kinetic
More informationConcept Question: Normal Force
Concept Question: Normal Force Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is 1. larger than 2. identical
More informationSolution. will lead to a positive torque, while the bigger cat will give a negative torque. So,
Physics 18 Fall 009 Midterm s For midterm, you may use one sheet of notes with whatever you want to put on it, front and back Please sit every or seat, and please don t cheat! If something isn t clear,
More informationLecture D20-2D Rigid Body Dynamics: Impulse and Momentum
J Peraire 1607 Dynamics Fall 004 Version 11 Lecture D0 - D Rigid Body Dynamics: Impulse and Momentum In lecture D9, we saw the principle of impulse and momentum applied to particle motion This principle
More informationPhysics 2514 Lecture 26
Physics 2514 Lecture 26 P. Gutierrez Department of Physics & Astronomy University of Oklahoma Physics 2514 p. 1/12 Review We have defined the following using Newton s second law of motion ( F net = d p
More informationWiley Plus. Final Assignment (5) Is Due Today: Before 11 pm!
Wiley Plus Final Assignment (5) Is Due Today: Before 11 pm! Final Exam Review December 9, 009 3 What about vector subtraction? Suppose you are given the vector relation A B C RULE: The resultant vector
More information