APPLICATIONS. CEE 271: Applied Mechanics II, Dynamics Lecture 17: Ch.15, Sec.4 7. IMPACT (Section 15.4) APPLICATIONS (continued) IMPACT READING QUIZ
|
|
- Edgar Daniel
- 6 years ago
- Views:
Transcription
1 APPLICATIONS CEE 271: Applied Mechanics II, Dynamics Lecture 17: Ch.15, Sec.4 7 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Date: The quality of a tennis ball is measured by the height of its bounce. This can be quantified by the coefficient of restitution of the ball. If the height from which the ball is dropped and the height of its resulting bounce are known, how can we determine the coefficient of restitution of the ball? 1 / 34 4 / 34 IMPACT (Section 15.4) APPLICATIONS (continued) Today s objectives: Students will be able to 1 Understand and analyze the mechanics of impact. 2 Analyze the motion of bodies undergoing a collision, in both central and oblique cases of impact. In-class activities: Reading Quiz Applications Central Impact Coefficient of Restitution Oblique Impact Concept Quiz Group Problem Solving Attention Quiz In the game of billiards, it is important to be able to predict the trajectory and speed of a ball after it is struck by another ball. If we know the velocity of ball A before the impact, how can we determine the magnitude and direction of the velocity of ball B after the impact? What parameters do we need to know for this? 2 / 34 5 / 34 READING QUIZ 1 When the motion of one or both of the particles is at an angle to the line of impact, the impact is said to be (a) central impact. (b) oblique impact. (c) major impact. (d) None of the above. 2 The ratio of the restitution impulse to the deformation impulse is called (a) impulse ratio. (b) restitution coefficient. (c) energy ratio. (d) mechanical efficiency. IMPACT Impact occurs when two bodies collide during a very short time period, causing large impulsive forces to be exerted between the bodies. Common examples of impact are a hammer striking a nail or a bat striking a ball. The line of impact is a line through the mass centers of the colliding particles. In general, there are two types of impact: Central impact occurs when the directions of motion of the two colliding particles are along the line of impact. Oblique impact occurs when the direction of motion of one or both of the particles is at an angle to the line of impact. 3 / 34 6 / 34
2
3 PROCEDURE FOR ANALYSIS In most impact problems, the initial velocities of the particles and the coefficient of restitution, e, are known, with the final velocities to be determined. Define the x y axes. Typically, the x-axis is defined along the line of impact and the y-axis is in the plane of contact perpendicular to the x-axis. For both central and oblique impact problems, the following equations apply along the line of impact (x-dir.): Σm(v x ) 1 = Σm(v x ) 2 and e = [(v Bx ) 2 (v Ax ) 2 ]/[(v Ax ) 1 (v Bx ) 1 ] For oblique impact problems, the following equations are also required, applied perpendicular to the line of impact (y-dir.): m A (v Ay ) 1 = m A (v Ay ) 2 and m B (v By ) 1 = m B (v By ) 2 CONCEPT QUIZ 1 Two balls impact with a coefficient of restitution of Can one of the balls leave the impact with a kinetic energy greater than before the impact? (a) Yes (b) No (c) Impossible to tell (d) Don t pick this one! ANS: (a) 2 Under what condition is the energy lost during a collision maximum? (a) e = 1.0 (b) e = 0.0 (c) e = 1.0 (d) Collision is non-elastic. 13 / / 34 EXAMPLE GROUP PROBLEM SOLVING Top view Given: The ball strikes the smooth wall with a velocity (v b ) 1 = 20 m/s. The coefficient of restitution between the ball and the wall is e = Find: The velocity of the ball just after the impact. Given: A 2 kg crate B is released from rest, falls a distance h = 0.5 m, and strikes plate P (3 kg mass). The coefficient of restitution between B and P is e = 0.6, and the spring stiffness is k = 30N/m. Find: The velocity of crate B just after the collision. Plan: The collision is an oblique impact, with the line of impact perpendicular to the plane (through the relative centers of mass). Thus, the coefficient of restitution applies perpendicular to the wall and the momentum of the ball is conserved along the wall. Plan: 1 Determine the speed of the crate just before the collision using projectile motion or an energy method. 2 Analyze the collision as a central impact problem. 14 / / 34 EXAMPLE (Solution) Solve the impact problem by using x y axes defined along and perpendicular to the line of impact, respectively: The ball momentum is conserved in the y-dir: m(v b ) 1 sin30 = m(v b ) 2 sinθ (1) 10m/s = (v b ) 2 sinθ (2) The coefficient of restitution applies in the x-dir: e = 0.75 = [0 (v bx) 2 ] [(v bx ) 1 0] = [0 ( v b) 2 cosθ] [20cos30 0] (v b ) 2 cosθ = 12.99m/s (3) Using Eqs. (1) and (2) and solving for the velocity and θ yields: (v b ) 2 = ( ) 0.5 = 16.4m/s θ = tan 1 (10/12.99) = / 34 GROUP PROBLEM SOLVING (continued) Determine the speed of block B just before impact by using conservation of energy (why?). Define the gravitational datum at the initial position of the block (h 1 = 0) and note the block is released from rest (v 1 = 0): T 1 +V 1 = T 2 +V 2 (4) 1 2 m(v 1) 2 +mgh 1 = 1 2 m(v 2) 2 +mgh = 1 2 (2)(v 2) 2 +(2)(9.81)( 0.5) v 2 = 3.132m/s( ) (5) This is the speed of the block just before the collision. Plate (P) is at rest, velocity of zero, before the collision. 18 / 34
4
5
6 Again, EXAMPLE (Solution) = 0.5(v B ) 2 ( ) r B (6) Now use Conservation of Angular Momentum. (r A m s v A )sinφ A = r B m s v B sin90 r B v B = ( )(10000)sin70 or r B = ( ) v B (7) Solving the two equations of Eq. (6) and (7) for r B and v B yields r B = m (8) v B = 10.2km/s (9) ATTENTION QUIZ 1 A ball is traveling on a smooth surface in a 3 ft radius circle with a speed of 6ft/s. If the attached cord is pulled down with a constant speed of 2ft/s, which of the following principles can be applied to solve for the velocity of the ball when r = 2 ft? (a) Conservation of energy (b) Conservation of angular momentum (c) Conservation of linear momentum (d) Conservation of mass 2 If a particle moves in the z y plane, its angular momentum vector is in the (a) x direction. (c) z direction. (b) y direction. (d) z y direction. ANS: (a) 31 / / 34 GROUP PROBLEM SOLVING Given: The four 5 lb spheres are rigidly attached to the crossbar frame, which has a negligible weight. A moment acts on the shaft as shown, M = (0.5t+0.8) lb ft Find: The velocity of the spheres after 4 seconds, starting from rest. Plan: Apply the principle of angular impulse and momentum about the axis of rotation (z-axis). 32 / 34 GROUP PROBLEM SOLVING (Solution) Angular momentum: H Z = r mv reduces to a scalar equation. (H Z ) 1 = 0 and (H Z ) 2 = 4 (5/32.2)(0.6)v 2 = v 2 Angular impulse: t2 t 1 Mdt = t2 t 1 (0.5t+0.8)dt = [ (0.5/2)t t ] 4 0 (10) = 7.2lb ft s (11) Apply the principle of angular impulse and momentum = v 2 v 2 = 719.4ft/s 33 / 34
IMPACT Today s Objectives: In-Class Activities:
Today s Objectives: Students will be able to: 1. Understand and analyze the mechanics of impact. 2. Analyze the motion of bodies undergoing a collision, in both central and oblique cases of impact. IMPACT
More informationIMPACT (Section 15.4)
IMPACT (Section 15.4) Today s Objectives: Students will be able to: a) Understand and analyze the mechanics of impact. b) Analyze the motion of bodies undergoing a collision, in both central and oblique
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 17: Ch.15, Sec.2 4
1 / 38 CEE 271: Applied Mechanics II, Dynamics Lecture 17: Ch.15, Sec.2 4 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Tuesday, October 16, 2012 2 / 38 PRINCIPLE
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 14: Ch.15, Sec.1-3
1 / 20 CEE 271: Applied Mechanics II, Dynamics Lecture 14: Ch.15, Sec.1-3 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Thursday, October 4, 2012 PRINCIPLE OF LINEAR
More informationenergy by deforming and moving. Principle of Work And (c) Zero By substituting at = v(dv/ds) into Ft = mat, the result is
APPLICATIONS CEE 27: Applied Mechanics II, Dynamics Lecture : Ch.4, Sec. 4 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa A roller coaster makes use of gravitational
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 9: Ch.13, Sec.4-5
1 / 40 CEE 271: Applied Mechanics II, Dynamics Lecture 9: Ch.13, Sec.4-5 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa 2 / 40 EQUATIONS OF MOTION:RECTANGULAR COORDINATES
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 informationCEE 271: Applied Mechanics II, Dynamics Lecture 27: Ch.18, Sec.1 5
1 / 42 CEE 271: Applied Mechanics II, Dynamics Lecture 27: Ch.18, Sec.1 5 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Tuesday, November 27, 2012 2 / 42 KINETIC
More informationREADING QUIZ. CEE 271: Applied Mechanics II, Dynamics Lecture 27: Ch.18, Sec.1 5 APPLICATIONS KINETIC ENERGY, WORK, PRINCIPLE OF WORK AND ENERGY
READING QUIZ CEE 27: Applied Mechanics II, Dynamics Lecture 27: Ch.8, Sec. 5 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Date: Kinetic energy due to rotation
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 28: Ch.17, Sec.2 3
1 / 20 CEE 271: Applied Mechanics II, Dynamics Lecture 28: Ch.17, Sec.2 3 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Monday, November 1, 2011 2 / 20 PLANAR KINETIC
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 25: Ch.17, Sec.4-5
1 / 36 CEE 271: Applied Mechanics II, Dynamics Lecture 25: Ch.17, Sec.4-5 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Date: 2 / 36 EQUATIONS OF MOTION: ROTATION
More informationREADING QUIZ. CEE 271: Applied Mechanics II, Dynamics Lecture 21: Ch.16, Sec.1 4 APPLICATIONS. PLANAR RIGID BODY MOTION: TRANSLATION and ROTATION
READING QUIZ CEE 271: Applied Mechanics II, Dynamics Lecture 21: Ch.16, Sec.1 4 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Date: 1 If a rigid body is in translation
More informationChapter 15 Kinematics of a Particle: Impulse and Momentum. Lecture Notes for Section 15-5~7
Chapter 15 Kinematics of a Particle: Impulse and Momentum Lecture Notes for Section 15-5~7 ANGULAR MOMENTUM, MOMENT OF A FORCE AND PRINCIPLE OF ANGULAR IMPULSE AND MOMENTUM Today s Objectives: Students
More informationDynamics Kinetics of a particle Section 4: TJW Force-mass-acceleration: Example 1
Section 4: TJW Force-mass-acceleration: Example 1 The beam and attached hoisting mechanism have a combined mass of 1200 kg with center of mass at G. If the inertial acceleration a of a point P on the hoisting
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 24: Ch.17, Sec.1-3
1 / 38 CEE 271: Applied Mechanics II, Dynamics Lecture 24: Ch.17, Sec.1-3 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Tuesday, Nov. 13, 2012 2 / 38 MOMENT OF
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 informationChapter 4 Kinetics of Particle: Impulse and Momentum
Chapter 4 Kinetics of Particle: Impulse and Momentum Dr. Khairul Salleh Basaruddin Applied Mechanics Division School of Mechatronic Engineering Universiti Malaysia Perlis (UniMAP) khsalleh@unimap.edu.my
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 6: Ch.12, Sec.10
1 / 18 CEE 271: Applied Mechanics II, Dynamics Lecture 6: Ch.12, Sec.10 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Date: 2 / 18 RELATIVE-MOTION ANALYSIS OF TWO
More informationEQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES (Section 13.5)
EQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES (Section 13.5) Today s Objectives: Students will be able to apply the equation of motion using normal and tangential coordinates. APPLICATIONS Race
More informationName: Class: Date: d. none of the above
Name: Class: Date: H Phys quiz Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following is the cause of an acceleration? a. speed b. inertia
More informationChapter 15 Kinematics of a Particle: Impulse and Momentum. Lecture Notes for Section 15-2~3
Chapter 15 Kinematics of a Particle: Impulse and Momentum Lecture Notes for Section 15-2~3 PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM AND CONSERVATION OF LINEAR MOMENTUM FOR SYSTEMS OF PARTICLES Today s
More information3. How long must a 100 N net force act to produce a change in momentum of 200 kg m/s? (A) 0.25 s (B) 0.50 s (C) 1.0 s (D) 2.0 s (E) 4.
AP Physics Multiple Choice Practice Momentum and Impulse 1. A car of mass m, traveling at speed v, stops in time t when maximum braking force is applied. Assuming the braking force is independent of mass,
More informationSOLUTION. will destroy the integrity of the work and Anis not permitted
15 42. The block has a mass of 50 kg and rests on the surface of the cart having a mass of 75 kg. If the spring which is attached to the cart and not the block is compressed 0.2 m and the system is released
More informationPRINCIPLE OF LINEAR IMPULSE AND MOMENTUM FOR A SYSTEM OF PARTICLES AND CONSERVATION OF LINEAR MOMENTUM FOR A SYSTEM OF PARTICLES
PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM FOR A SYSTEM OF PARTICLES AND CONSERVATION OF LINEAR MOMENTUM FOR A SYSTEM OF PARTICLES Today s Objectives: Students will be able to: 1. Apply the principle of
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 33: Ch.19, Sec.1 2
1 / 36 CEE 271: Applied Mechanics II, Dynamics Lecture 33: Ch.19, Sec.1 2 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Thursday, December 6, 2012 2 / 36 LINEAR
More informationME 230 Kinematics and Dynamics
ME 230 Kinematics and Dynamics Wei-Chih Wang Department of Mechanical Engineering University of Washington Lecture 8 Kinetics of a particle: Work and Energy (Chapter 14) - 14.1-14.3 W. Wang 2 Kinetics
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 informationPLANAR KINETICS OF A RIGID BODY: WORK AND ENERGY Today s Objectives: Students will be able to: 1. Define the various ways a force and couple do work.
PLANAR KINETICS OF A RIGID BODY: WORK AND ENERGY Today s Objectives: Students will be able to: 1. Define the various ways a force and couple do work. In-Class Activities: 2. Apply the principle of work
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 5: Ch.12, Sec.9
1 / 20 CEE 271: Applied Mechanics II, Dynamics Lecture 5: Ch.12, Sec.9 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Date: 2 / 20 ABSOLUTE DEPENDENT MOTION ANALYSIS
More informationPRINCIPLE OF LINEAR IMPULSE AND MOMENTUM
PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM Today s Objectives: Students will be able to: 1. Calculate the linear momentum of a particle and linear impulse of a force. 2. Apply the principle of linear impulse
More informationCenter of Mass & Linear Momentum
PHYS 101 Previous Exam Problems CHAPTER 9 Center of Mass & Linear Momentum Center of mass Momentum of a particle Momentum of a system Impulse Conservation of momentum Elastic collisions Inelastic collisions
More informationPRINCIPLE OF LINEAR IMPULSE AND MOMENTUM AND CONSERVATION OF LINEAR MOMENTUM FOR SYSTEMS OF PARTICLES
PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM AND CONSERVATION OF LINEAR MOMENTUM FOR SYSTEMS OF PARTICLES Today s Objectives: Students will be able to: 1. Apply the principle of linear impulse and momentum
More informationEQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES
EQUATIONS OF MOTION: NORMAL AND TANGENTIAL COORDINATES Today s Objectives: Students will be able to: 1. Apply the equation of motion using normal and tangential coordinates. In-Class Activities: Check
More informationAP Mechanics Summer Assignment
2012-2013 AP Mechanics Summer Assignment To be completed in summer Submit for grade in September Name: Date: Equations: Kinematics (For #1 and #2 questions: use following equations only. Need to show derivation
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 informationPhysics Lecture 12 Momentum & Collisions
Physics 101 - Lecture 12 Momentum & Collisions Momentum is another quantity (like energy) that is tremendously useful because it s often conserved. In fact, there are two conserved quantities that we can
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 informationl1, l2, l3, ln l1 + l2 + l3 + ln
Work done by a constant force: Consider an object undergoes a displacement S along a straight line while acted on a force F that makes an angle θ with S as shown The work done W by the agent is the product
More informationN - W = 0. + F = m a ; N = W. Fs = 0.7W r. Ans. r = 9.32 m
91962_05_R1_p0479-0512 6/5/09 3:53 PM Page 479 R1 1. The ball is thrown horizontally with a speed of 8 m>s. Find the equation of the path, y = f(x), and then determine the ball s velocity and the normal
More informationExam Question 5: Work, Energy, Impacts and Collisions. June 18, Applied Mathematics: Lecture 5. Brendan Williamson.
Exam Question 5: Work, Energy, Impacts and June 18, 016 In this section we will continue our foray into forces acting on objects and objects acting on each other. We will first discuss the notion of energy,
More informationWORK, POWER AND ENERGY
WORK, POWER AND ENERGY Important Points:. Dot Product: a) Scalar product is defined as the product of the magnitudes of two vectors and the cosine of the angle between them. The dot product of two vectors
More informationPlease circle the name of your instructor: EB01: Beamish EB02: Fenrich EB03: Ruhl. EB04: Rahman EB05: Nedie EB06: Ropchan LAST NAME: FIRST NAME: ID#:
Faculty of Engineering and Department of Physics ENPH 131 Final Examination Saturday, April 20, 2013; 2:00 pm 4:30 pm Universiade Pavilion Section EB01 (BEAMISH): Rows 1, 3, 5(seats 1-45) Section EB02
More informationMOMENTUM. The world is wide, and I will not waste my life in friction when it could be turned into momentum. Frances E. Willard.
MOMENTUM The world is wide, and I will not waste my life in friction when it could be turned into momentum. Frances E. Willard Honors Physics CONSERVATION OF Energy Linear Momentum Angular Momentum Electric
More information(A) 10 m (B) 20 m (C) 25 m (D) 30 m (E) 40 m
PSI AP Physics C Work and Energy (Algebra Based) Multiple Choice Questions (use g = 10 m/s 2 ) 1. A student throws a ball upwards from the ground level where gravitational potential energy is zero. At
More informationEQUATIONS OF MOTION: CYLINDRICAL COORDINATES
Today s Objectives: Students will be able to: 1. Analyze the kinetics of a particle using cylindrical coordinates. EQUATIONS OF MOTION: CYLINDRICAL COORDINATES In-Class Activities: Check Homework Reading
More informationDynamics 4600:203 Homework 09 Due: April 04, 2008 Name:
Dynamics 4600:03 Homework 09 Due: April 04, 008 Name: Please denote your answers clearly, i.e., box in, star, etc., and write neatly. There are no points for small, messy, unreadable work... please use
More informationME 230 Kinematics and Dynamics
ME 230 Kinematics and Dynamics Wei-Chih Wang Department of Mechanical Engineering University of Washington Lecture 6: Particle Kinetics Kinetics of a particle (Chapter 13) - 13.4-13.6 Chapter 13: Objectives
More informationQ1. Which of the following is the correct combination of dimensions for energy?
Tuesday, June 15, 2010 Page: 1 Q1. Which of the following is the correct combination of dimensions for energy? A) ML 2 /T 2 B) LT 2 /M C) MLT D) M 2 L 3 T E) ML/T 2 Q2. Two cars are initially 150 kilometers
More informationPRINCIPLE OF LINEAR IMPULSE AND MOMENTUM (Section 15.1)
PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM (Section 15.1) Linear momentum: L = mv vector mv is called the linear momentum denoted as L (P in 1120) vector has the same direction as v. units of (kg m)/s or
More informationENGR-1100 Introduction to Engineering Analysis. Lecture 9
ENGR-1100 Introduction to Engineering Analysis Lecture 9 MOMENT OF A FORCE (SCALAR FORMULATION), CROSS PRODUCT, MOMENT OF A FORCE (VECTOR FORMULATION), & PRINCIPLE OF MOMENTS Today s Objectives : Students
More informationPRACTICE TEST for Midterm Exam
South Pasadena AP Physics PRACTICE TEST for Midterm Exam FORMULAS Name Period Date / / d = vt d = v o t + ½ at 2 d = v o + v 2 t v = v o + at v 2 = v 2 o + 2ad v = v x 2 + v y 2 = tan 1 v y v v x = v cos
More informationUNIVERSITY OF MANITOBA
PAGE NO.: 1 of 6 + Formula Sheet Equal marks for all questions. No marks are subtracted for wrong answers. Record all answers on the computer score sheet provided. USE PENCIL ONLY! Black pen will look
More informationFinal Review. If a car has 3,000kg-m/s of momentum, and a mass of 1,000kg. How fast is it moving? A ball that has momentum must also have energy.
Physics Name: Date: Period: Final Review Write the appropriate formulas with all units below. Impulse Momentum Conservation of Momentum Rank these in order from least to most momentum:.01kg mass moving
More informationPRINCIPLE OF LINEAR IMPULSE AND MOMENTUM AND CONSERVATION OF LINEAR MOMENTUM FOR SYSTEMS OF PARTICLES
PRINCIPLE OF LINEAR IMPULSE AND MOMENTUM AND CONSERVATION OF LINEAR MOMENTUM FOR SYSTEMS OF PARTICLES Today s Objectives: Students will be able to: 1. Apply the principle of linear impulse and momentum
More informationConservation of Momentum. Last modified: 08/05/2018
Conservation of Momentum Last modified: 08/05/2018 Links Momentum & Impulse Momentum Impulse Conservation of Momentum Example 1: 2 Blocks Initial Momentum is Not Enough Example 2: Blocks Sticking Together
More informationt-tw~4 F = ( 100 )( 20 ) = N (100 kg) (20 mls) - Fave(0.110 s) = 0 /).t = s = -Fm(0.110s) = (18182 N) (0.110 s) PROBLEM 13.
;6 t-tw~4 PROBLEM 13.144 An estimate of the expected load on over-the-shoulder seat belts is made before designing prototype belts that will be evaluated in automobile crash tests. Assuming that an automobile
More informationOCR Maths M2. Topic Questions from Papers. Collisions
OCR Maths M2 Topic Questions from Papers Collisions 41 Three smooth spheres A, B and C, ofequalradiusandofmassesm kg, 2m kg and 3m kg respectively, lie in a straight line and are free to move on a smooth
More informationAnnouncements. There will still be a WebAssign due this Friday, the last before the midterm.
Announcements THERE WILL BE NO CLASS THIS FRIDAY, MARCH 5 (We are 1 full lecture ahead of the syllabus, so we will still have review/problem solving on March 7 and 9). There will still be a WebAssign due
More information(t)dt I. p i. (impulse) F ext. Δ p = p f. Review: Linear Momentum and Momentum Conservation q Linear Momentum. Physics 201, Lecture 15
Physics 0, Lecture 5 Today s Topics q ore on Linear omentum nd Collisions Elastic and Perfect Inelastic Collision (D) Two Dimensional Elastic Collisions Exercise: illiards oard Explosion q ulti-particle
More informationTHE WORK OF A FORCE, THE PRINCIPLE OF WORK AND ENERGY & SYSTEMS OF PARTICLES
THE WORK OF A FORCE, THE PRINCIPLE OF WORK AND ENERGY & SYSTEMS OF PARTICLES Today s Objectives: Students will be able to: 1. Calculate the work of a force. 2. Apply the principle of work and energy to
More information(A) 0 (B) mv (C) 2mv (D) 2mv sin θ (E) 2mv cos θ
Physics 1 Lesson 8 Forces and Momentum Homework Outcomes 1. Define linear momentum. 2. Determine the total linear momentum of a system. 3. Apply the Law of Conservation of Momentum to solve problems. 4.
More informationChapter 3 Kinetics of Particle: Work & Energy
Chapter 3 Kinetics of Particle: Work & Energy Dr. Khairul Salleh Basaruddin Applied Mechanics Division School of Mechatronic Engineering Universiti Malaysia Perlis (UniMAP) khsalleh@unimap.edu.my THE WORK
More informationCollisions. Conservation of Momentum Elastic and inelastic collisions. Serway For practice: Chapter 9, problems 10, 11, 23, 70, 75
Collisions Conservation of Momentum Elastic and inelastic collisions Serway 9.3-9.4 For practice: Chapter 9, problems 10, 11, 23, 70, 75 Momentum: p = mv Impulse (a vector) is defined as F t (for a constant
More informationEQUATIONS OF MOTION: RECTANGULAR COORDINATES
EQUATIONS OF MOTION: RECTANGULAR COORDINATES Today s Objectives: Students will be able to: 1. Apply Newton s second law to determine forces and accelerations for particles in rectilinear motion. In-Class
More informationName: Class: Date: so sliding friction is better so sliding friction is better d. µ k
Name: Class: Date: Exam 2--PHYS 101-F08 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. You put your book on the seat next to you. When the bus stops,
More informationAnnouncements. Principle of Work and Energy - Sections Engr222 Spring 2004 Chapter Test Wednesday
Announcements Test Wednesday Closed book 3 page sheet sheet (on web) Calculator Chap 12.6-10, 13.1-6 Principle of Work and Energy - Sections 14.1-3 Today s Objectives: Students will be able to: a) Calculate
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 23: Ch.16, Sec.7
1 / 26 CEE 271: Applied Mechanics II, Dynamics Lecture 23: Ch.16, Sec.7 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Tuesday, Nov. 8, 2012 2 / 26 RELATIVE MOTION
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 1: Ch.12, Sec.1-3h
1 / 30 CEE 271: Applied Mechanics II, Dynamics Lecture 1: Ch.12, Sec.1-3h Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Tuesday, August 21, 2012 2 / 30 INTRODUCTION
More informationPHY131 Summer 2011 Class 9 Notes 6/14/11
PHY131H1F Summer Class 9 Today: Hooke s Law Elastic Potential Energy Energy in Collisions Work Calories Conservation of Energy Power Dissipative Forces and Thermal Energy Ch.10 Reading Quiz 1 of 3: Two
More informationMomentum in 2 Dimensions. Unit 1B
Momentum in 2 Dimensions Unit 1B You were introduced to momentum and momentum calculations, including 1D collisions, in Physics 2204. In this part of unit 1 we will study: 2D collisions Explosions where
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
PH 105 Exam 2 VERSION A Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Is it possible for a system to have negative potential energy? A)
More information1 Motion of a single particle - Linear momentum, work and energy principle
1 Motion of a single particle - Linear momentum, work and energy principle 1.1 In-class problem A block of mass m slides down a frictionless incline (see Fig.). The block is released at height h above
More informationRecap: Energy Accounting
Recap: Energy Accounting Energy accounting enables complex systems to be studied. Total Energy = KE + PE = conserved Even the simple pendulum is not easy to study using Newton s laws of motion, as the
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 informationLECTURE 13- PROBLEMS. Chapter 1-9,13 Professor Noronha-Hostler Professor Montalvo
LECTURE 13- PROBLEMS Chapter 1-9,13 Professor Noronha-Hostler Professor Montalvo FARADAY LECTURES! Physics Lecture Hall Friday Dec. 7 Demos: 6pm Show: 7-8:30pm Saturday Dec. 8 Demos: 2pm Show: 3-4:30pm
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
PH 105 Exam 2 VERSION B Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A boy throws a rock with an initial velocity of 2.15 m/s at 30.0 above
More informationConserv. of Momentum (Applications)
Conserv. of Momentum (Applications) Announcements: Next midterm a week from Thursday (3/15). Chapters 6 9 will be covered LA information session at 6pm today, UMC 235. Will do some longer examples today.
More informationLecture 17 - Gyroscopes
Lecture 17 - Gyroscopes A Puzzle... We have seen throughout class that the center of mass is a very powerful tool for evaluating systems. However, don t let yourself get carried away with how useful it
More informationPotential Energy & Conservation of Energy
PHYS 101 Previous Exam Problems CHAPTER 8 Potential Energy & Conservation of Energy Potential energy Conservation of energy conservative forces Conservation of energy friction Conservation of energy external
More informationAddis Ababa University Addis Ababa Institute of Technology School Of Mechanical and Industrial Engineering Extension Division Assignment 2
Addis Ababa University Addis Ababa Institute of Technology School Of Mechanical and Industrial Engineering Extension Division Assignment 2 1. The 50-kg crate is projected along the floor with an initial
More informationChapter 9 Linear Momentum and Collisions
Chapter 9 Linear Momentum and Collisions The Center of Mass The center of mass of a system of particles is the point that moves as though (1) all of the system s mass were concentrated there and (2) all
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 informationMain Ideas in Class Today
Main Ideas in Class Today You should be able to: Distinguish between Elastic and Inelastic Collisions Solve Collisions in 1 & 2 Dimensions Practice: 6.31, 6.33, 6.39, 6.41, 6.43, 6.45, 6.47, 6.49, 6.51,
More information1. A tennis ball of mass m moving horizontally with speed u strikes a vertical tennis racket. The ball bounces back with a horizontal speed v.
1. A tennis ball of mass m moving horizontally with speed u strikes a vertical tennis racket. The ball bounces back with a horizontal speed v. The magnitude of the change in momentum of the ball is A.
More informationPhysics 10 Lecture 6A. "And in knowing that you know nothing, that makes you the smartest of all. --Socrates
Physics 10 Lecture 6A "And in knowing that you know nothing, that makes you the smartest of all. --Socrates Momentum Which is harder to stop a small ball moving at 1 m/s or a car moving at 1 m/s? Obviously
More informationWork and energy. 15 m. c. Find the work done by the normal force exerted by the incline on the crate.
Work and energy 1. A 10.0-kg crate is pulled 15.0 m up along a frictionless incline as shown in the figure below. The crate starts at rest and has a final speed of 6.00 m/s. motor 15 m 5 a. Draw the free-body
More informationVISUAL PHYSICS ONLINE DYNAMICS CONSERVATION OF ENERGY AND MOMENTUM COLLISIONS / EXPLOSIONS
VISUAL PHYSICS ONLINE DYNAMICS CONSERVATION OF ENERGY AND MOMENTUM COLLISIONS / EXPLOSIONS Exercise View images of conservation of momentum What story do the images tell? Select 5 good images. State why
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS LSN 8-7: ROTATIONAL KINETIC ENERGY Questions From Reading Activity? Big Idea(s): The interactions of an object with other objects can be described by
More informationKing Fahd University of Petroleum and Minerals Physics Department Physics 101 Recitation Term 131 Fall 013 Quiz # 4 Section 10 A 1.50-kg block slides down a frictionless 30.0 incline, starting from rest.
More informationDYNAMICS VECTOR MECHANICS FOR ENGINEERS: Plane Motion of Rigid Bodies: Energy and Momentum Methods. Tenth Edition CHAPTER
Tenth E CHAPTER 7 VECTOR MECHANICS FOR ENGINEERS: DYNAMICS Ferdinand P. Beer E. Russell Johnston, Jr. Phillip J. Cornwell Lecture Notes: Brian P. Self California State Polytechnic University Plane Motion
More informationChapter Work, Energy and Power. Q1. The co-efficient of restitution e for a perfectly elastic collision is [1988] (a) 1 (b) 0 (c) (d) 1 Ans: (a)
Chapter Work, Energy and Power Q1. The co-efficient of restitution e for a perfectly elastic collision is [1988] (a) 1 (b) 0 (c) (d) 1 Q2. A bullet of mass 10g leaves a rifle at an initial velocity of
More informationVersion PREVIEW Semester 1 Review Slade (22222) 1
Version PREVIEW Semester 1 Review Slade () 1 This print-out should have 48 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Holt SF 0Rev 10A
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
PH105-007 Exam 2 VERSION A Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A 1.0-kg block and a 2.0-kg block are pressed together on a horizontal
More informationImpulse (J) J = FΔ t Momentum Δp = mδv Impulse and Momentum j = (F)( p = ( )(v) F)(Δ ) = ( )(Δv)
Impulse (J) We create an unbalancing force to overcome the inertia of the object. the integral of force over time The unbalancing force is made up of the force we need to unbalance the object and the time
More informationChap. 8: Collisions and Momentum Conservation
Chap. 8: Collisions and Momentum Conservation 1. System in Collision and Explosion C.M. 2. Analysis of Motion of System (C.M.) Kinematics and Dynamics Conservation between Before and After a) b) Energy
More informationA Level Maths Notes: M2 Equations for Projectiles
A Level Maths Notes: M2 Equations for Projectiles A projectile is a body that falls freely under gravity ie the only force acting on it is gravity. In fact this is never strictly true, since there is always
More informationExam 3 Practice Solutions
Exam 3 Practice Solutions Multiple Choice 1. A thin hoop, a solid disk, and a solid sphere, each with the same mass and radius, are at rest at the top of an inclined plane. If all three are released at
More informationWelcome back to Physics 211
Welcome back to Physics 211 Today s agenda: Impulse and momentum 09-2 1 Current assignments Reading: Chapter 10 in textbook Prelecture due next Tuesday HW#8 due this Friday at 5 pm. 09-2 2 9-2.1 A crash
More information