Physics 2210 Fall smartphysics Exam 3 Review smartphysics units /04/2015
|
|
- Elvin Gregory
- 5 years ago
- Views:
Transcription
1 Physics 22 Fall 25 smartphysics Exam 3 Review smartphysics units -3 /4/25
2 Review Problem The figure shown extends from x = to x = and is bounded on the left by the y-axis, on the bottom by the x-axis, and on top by the curve y = ae x b y = ae x b. It has h uniform density ρ and thickness t (in the z direction). Find the x- and y-coordinates of its center of mass. dd We first have to find the mass of this figure. It is finite even though its width is infinite. We divide the shape into vertical strips. The mass element here is then dd = ρ dd = ρρ dd = ρρρ dd x b Where dd is the width of the strip and h = ae M = dd = ρρρ dd = ρρρ e is the height of each strip. = ρρρ b e u du x b dd Where we have made the substitution u = x b, and du = b dd M = ρρρρ e u y a = ρρρρ = ρρρρ x The x-and y-coordinates of the center-of-mass of the figure, X CC, Y CC are given by: X CC = M x CCdd, Y CC = M y CCdd Where (x CC, y CC ) = x, h 2 is the center-of mass of each vertical strip.
3 Problem (continued) x b y = ae : x = to x = ; uniform density ρ and thickness t. Find the x- and y-coordinates of its center of mass. We first solve for X CC X CC = M x CCdd = ρρρρ x ρρρ dd = ρρρρ b ρρρ x e x dd Again let u = x x b b, but also v = e = e u, and we integrate by parts: X CC = u= ρρρρ ρρρ b b u eu dd Note that dv = d e u = e u dd, and so we have X CC = u= ρρρρ ρρρb2 u dv = b uu u= u= u= u = u = b ue u = eu dd u= = ρb X CC = b u = u = u= v du u= = b e u
4 Problem (continued) x b y = ae : x = to x = ; uniform density ρ and thickness t. Find the x- and y-coordinates of its center of mass. Next for Y CC Y CC = M y CCdd = ρρρρ h 2 ρρρ dd = a e 2x b dd 2b Again let w = 2x b dw = 2 b dd Y CC = a 2b b 2 ew dd = ρρρρ ρρ 2 a2 x b e x b e dd = a 4 ew = a 4 Y CC = a 4
5 Problem (continued) Alternate solution for Y CC : Divide figure into horizontal strips of height dd and width w = x(y). Invert relationship between x and y of curved border: x b y = ae x b e = y a x b = ln y a x = b ln y a And so the mass element is given by dd = ρρρ dd = ρρρ ln y dd a Y CC = M y CCdd = a ρρρρ ρρρ y ln y a dd = a a u ln u du = a a 4 dy y a w x = b ln y a x Y CC = a 4 Where we have made the substitution u = y a dd = aaa, We evaluate u ln u du by making the substitution v = u ln u u u ln u = v + u and dd = ln u dd, u= u ln u du = udd = uu u = u= u = vdu = u 2 ln u u 2 u= u ln u u dd u= u= u= u= = u ln u du + uuu = u ln u du + 2 u2 = u ln u du + 2 = u ln u du 2 2 u ln u du = 2 u= u ln u du = 4
6 Review Problem 2 (/4) A blue car of mass m =7kg was initially traveling east at v i =27.m/s. A red car of mass m 2 = kg was traveling north at v 2i =43.m/s. They collide at an intersection, and (kinetic) energy was lost. After the collision, the blue car is now traveling at φ = 5 north of east, and the red car at φ 2 = 2 north of east. (a) Find speeds v and v 2f after the collision. (b) How much energy was lost? y (north) Solution: (a) No external forces act horizontally on the system of two cars, so the horizontal components of their total momentum is conserved in the collision, even if energy is not. Before collision: P ii = m v i, P iy = m 2 v 2i After the collision we then have (using conservation of momentum): P fx = m v f cos φ + m 2 v 2f cos φ 2 P fy = m v f sin φ + m 2 v 2f sin φ 2 And so by conservation of momentum we have m v f cos φ + m 2 v 2f cos φ 2 = m v i () m v f sin φ + m 2 v 2f sin φ 2 = m 2 v 2i (2) m v i v 2i m 2 v f v 2f φ = 5 φ 2 = 2 x (east)
7 Review Problem 2 (2/4) blue car m =7kg east at v i =27.m/s. red car of mass m 2 = kg north at v 2i =43.m/s. Inelastic collision: after: blue car at φ = 5 north of east, and the red car at φ 2 = 2 north of east. (a) Find speeds v and v 2f after the collision. (b) How much energy was lost? (a) continued: m v f cos φ + m 2 v 2f cos φ 2 = m v i () m v f sin φ + m 2 v 2f sin φ 2 = m 2 v 2i (2) Taking sin φ 2 cos φ 2 2 : m v f cos φ sin φ 2 m v f sin φ cos φ 2 = m v i sin φ 2 m 2 v 2i cos φ 2 v f = m v i sin φ 2 m 2 v 2i cos φ 2 m (cos φ sin φ 2 sin φ cos φ 2 ) = m v i sin φ 2 m 2 v 2i cos φ 2 m sin( φ 2 φ ) = 7kg 27.m/s sin 2 kg 43.m/s cos 2 7kg sin( 3 ) v f = 33.8m/s
8 Review Problem 2 (3/4) blue car m =7kg east at v i =27.m/s. red car of mass m 2 = kg north at v 2i =43.m/s. Inelastic collision: after: blue car at φ = 5 north of east, and the red car at φ 2 = 2 north of east. (a) Find speeds v and v 2f after the collision. (b) How much energy was lost? (a) continued: m v f cos φ + m 2 v 2f cos φ 2 = m v i () m v f sin φ + m 2 v 2f sin φ 2 = m 2 v 2i (2) Taking sin φ cos φ 2 : m 2 v 2f cos φ 2 sin φ m 2 v 2f sin φ 2 cos φ = m v i sin φ m 2 v 2i cos φ v 2f = m v i sin φ m 2 v 2i cos φ m 2 (cos φ 2 sin φ sin φ 2 cos φ ) = m v i sin φ m 2 v 2i cos φ m 2 sin( φ φ 2 ) = 7kg 27.m/s sin 5 kg 43.m/s cos 5 kg sin 3 v 2f = 8.65m/s
9 Review Problem 2 (4/4) blue car m =7kg east at v i =27.m/s. red car of mass m 2 = kg north at v 2i =43.m/s. Inelastic collision: after: blue car at φ = 5 north of east, and the red car at φ 2 = 2 north of east. (a) Find speeds v f and v 2f after the collision. (b) How much energy was lost? (b) E LLLL = K = K i K f K i = 2 m v 2 i + 2 m 2v 2 2i = 7kg 27.m/s 2 + kg 43.m/s 2 =.64 6 J 2 K f = 2 m v 2 f + 2 m 2v 2 2i = 7kg 33.8m/s 2 + kg 8.65m/s 2 =. 6 J 2 E LLLL = K = K i K f =.64 6 J. 6 J E LLLL = J
10 Review Example 3 (/3) (hr9-65) A body of mass 2. kg makes a HEAD-ON elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its original speed. (a) What is the mass of the other body? (b) What is the speed of the two-body center of mass if the initial speed of the 2. kg body was 4. m/s? Solution: We denote the 2kg mass as body and the other as body 2 m = 2.kg, v f = 4 v i part a m 2 =?, v 2i = (a) Elastic Collision: So we first find V CC (in this case without assuming values) V CC = m v i + m 2 v 2i = m v i m + m 2 m + m 2 Transform velocity of body into the CM frame v i = v i V CC = v i m v i = m v i + m 2 v i m v i = m 2v i m + m 2 m + m 2 m + m 2 Elastic collision in D: v f = v i= m 2v i m + m 2
11 Review Example 3 (2/3) (hr9-65) A body of mass 2. kg makes a HEAD-ON elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its original speed. (a) What is the mass of the other body? (b) What is the speed of the two-body center of mass if the initial speed of the 2. kg body was 4. m/s? (a) continued Transform back into Lab frame v f = m 2v i m + m 2 v f = v f + V CC = m 2v i + m v i = m m 2 v m + m 2 m + m 2 m + m i 2 But we were given v f = 4 v i, m m 2 m + m 2 = 4 4m 4m 2 = m + m 2 3m = 5m 2 m 2 = 3 5 m = kg m 2 =.2kg
12 Review Example 3 (3/3) (hr9-65) A body of mass 2. kg makes a HEAD-ON elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its original speed. (a) What is the mass of the other body? (b) What is the speed of the two-body center of mass if the initial speed of the 2. kg body was 4. m/s? (b) Now given: v i =4. m/s We had from part (a) m 2 =.2 kg Again: the velocity of the center of mass is V CC = m v i m + m 2 2.kg 4. m s = 2.kg +.2kg V CC = 2.5m/s
13 Extra Review Example 4 (/3) Electrical interaction between two protons can be expressed as a potential energy: U = +k e 2 r, where e =.6 9 coulomb (C) is the charge of each proton (a.k.a. elementary charge ), k = N m 2 /C 2, and r is the distance between the two protons. A proton moving at v = m/s collides elastically head-on with a second proton moving at v 3 =.5 7 m/s. Protons have mass m = kg. The full process occurs strictly along the x-axis. Find (a) The final velocity of the second proton, and (b) The closest distance of approach of between the two protons. Solution: Since the interaction can be written as a potential energy it is conservative and so the collision is elastic. First we find the center of mass velocity: V CC = m v i + m 2 v 2i = mv + m( v 3) = + v m + m 2 2m 3 Transforming into the center-of-mass frame: we are concerned only with the second proton vv 2i = v 2i V CC = v 3 + v 3 = 2v 3 The collision is elastic, so the second proton reverses direction: vv 2f = v 2i = + 2v 3 Transforming back into the Lab Frame: vv 2f = vv 2f + V CC = + 2v v 3 = v = m/s
14 Extra Example 4 continued two protons U = +k e 2 r, e =.6 9 C, k = N m 2 /C 2, and r = distance between the two protons. Proton at v = m/s collides elastically head-on with proton 2 at v 3 =.5 7 m/s. Proton mass m = kg. Find (a) The final velocity of the second proton, and (b) The closest distance of approach of between the two protons. At closest approach in a D collision: x 2 x is a minimum, which means d dd x 2 x v 2 v = v 2 = v No net external force acts on the system, so V CC must be constant, so at closest approach we must have v 2 = v = V CC. And so at this moment then v 2 = v = + v 3. Electrical interaction is conservative (because it can be written as a potential energy): Total energy is conserved. The total energy is given by E = 2 m v m 2v kk2 r Before collision (assume the separation is infinite, so k e 2 r = ) At minimum separation: r = r mmm E = E = 2 m v m v 3 E = E 2 = 2 m + v m + v 3 2 = 5 9 mv kk2 r mmm = 9 mv 2
15 Extra Example 4 continued two protons U = +k e 2 r, e =.6 9 C, k = N m 2 /C 2, and r = distance between the two protons. Proton at v = m/s collides elastically head-on with proton 2 at v 3 =.5 7 m/s. Proton mass m = kg. Find (a) The final velocity of the second proton, and (b) The closest distance of approach of between the two protons. Setting E = E 2 by conservation of total energy: 9 mv 2 + kk2 = 5 r mmm 9 mv 2 kk 2 = 4 r mmm 9 mv 2 r mmm = 9kk2 4mv 2 r mmm = N m 2 /C C kg.5 7 m/s 2 r mmm =.38 5 m
Conservation of Momentum and Energy
ASU University Physics Labs - Mechanics Lab 5 p. 1 Conservation of Momentum and Energy As you work through the steps in the lab procedure, record your experimental values and the results on this worksheet.
More informationp p I p p p I p I p p
Net momentum conservation for collision on frictionless horizontal surface v1i v2i Before collision m1 F on m1 from m2 During collision for t v1f m2 F on m2 from m1 v2f +x direction After collision F F
More informationMomentum Revisited Momentum "Mass in Motion" p = mv. p > momentum (kgm/s) m > mass (kg) v > velocity (m/s) Change in Momentum.
Momentum Revisited Momentum "Mass in Motion" p = mv p > momentum (kgm/s) m > mass (kg) v > velocity (m/s) Change in Momentum p = p f p i p = mv f mv i p = m v 1 Unit 1 Section 4 Collisions/Explosions 2
More informationCollisions A + B C+D+
Collisions A + B C+D+ Conservation of Momentum Momentum in an isolated system in which a collision occurs is conserved An isolated system will not have external forces Specifically, the total momentum
More informationPhysics 2210 Fall smartphysics 10 Center-of-Mass 11 Conservation of Momentum 10/21/2015
Physics 2210 Fall 2015 smartphysics 10 Center-of-Mass 11 Conservation of Momentum 10/21/2015 Collective Motion and Center-of-Mass Take a group of particles, each with mass m i, position r i and velocity
More informationSystem of objects (particles)
Today Ch 6, Momentum and Collisions System of particles Elastic vs. inelastic collision Elastic collision in 1D Collision in 2D Center of mass Motion of system of particles (Motion of center of mass) 1
More informationConservation of Linear Momentum : If a force F is acting on particle of mass m, then according to Newton s second law of motion, we have F = dp /dt =
Conservation of Linear Momentum : If a force F is acting on particle of mass m, then according to Newton s second law of motion, we have F = dp /dt = d (mv) /dt where p =mv is linear momentum of particle
More informationGeneral Physics I Momentum
General Physics I Momentum Linear Momentum: Definition: For a single particle, the momentum p is defined as: p = mv (p is a vector since v is a vector). So p x = mv x etc. Units of linear momentum are
More informationPhysics 131: Lecture 15. Today s Agenda
Physics 131: Lecture 15 Today s Agenda Impulse and Momentum (or the chapter where physicists run out of letters) Non-constant t forces Impulse-momentum thm Conservation of Linear momentum External/Internal
More informationSection 1 Momentum and Impulse. Chapter 6. Preview. Objectives Linear Momentum. Houghton Mifflin Harcourt Publishing Company
Section 1 Momentum and Impulse Preview Objectives Linear Momentum Section 1 Momentum and Impulse Objectives Compare the momentum of different moving objects. Compare the momentum of the same object moving
More informationPhysics 2210 Fall smartphysics Conservation of Angular Momentum 11/20/2015
Physics 2210 Fall 2015 smartphysics 19-20 Conservation of Angular Momentum 11/20/2015 Poll 11-18-03 In the two cases shown above identical ladders are leaning against frictionless walls and are not sliding.
More informationConservation of Momentum. Chapter 9: Collisions, CM, RP. Conservation of Momentum. Conservation of Momentum. Conservation of Momentum
P H Y S I C S Chapter 9: Collisions, CM, RP Since impulse = change in momentum, If no impulse is exerted on an object, the momentum of the object will not change. If no external forces act on a system,
More informationChapter 9. Linear Momentum and Collisions
Chapter 9 Linear Momentum and Collisions Linear Momentum The linear momentum of a particle or an object that can be modeled as a particle of mass m moving with a velocity v is defined to be the product
More informationAn astronaut of mass 80 kg pushes away from a space Both!p x
Chapter 6 Momentum Collisions Definition: Momentum Important because it is CONSERVED proof: p = m v F = m v t = p t Ft = p Since F 12 =-F 21, p 1 + p 2 = 0 p i for isolated particles never changes Vector
More informationConservation of Momentum
Conservation of Momentum Newton: Quantity of Motion Forces applied for a period of time change an object s quantity of motion. F = ma F = m Δ v t F t = mδv = mv f mv i p mv Ft = Δp F = dp dt Conservation?
More informationCHAPTER 9 LINEAR MOMENTUM AND COLLISION
CHAPTER 9 LINEAR MOMENTUM AND COLLISION Couse Outline : Linear momentum and its conservation Impulse and Momentum Collisions in one dimension Collisions in two dimension The center of mass (CM) 9.1 Linear
More informationAnnouncements. The second midterm exam is March 8, 5-7 PM in White B51 (this room).
Announcements The second midterm exam is March 8, 5-7 PM in White B51 (this room). The makeup exam is March 5, 5-7 PM in Clark 317. All exam info, including this, is at the class webpage, http://community.wvu.edu/
More informationChapter 9. Linear Momentum and Collisions
Chapter 9 Linear Momentum and Collisions Momentum Analysis Models Force and acceleration are related by Newton s second law. When force and acceleration vary by time, the situation can be very complicated.
More informationMomentum and Its Relation to Force
Linear Momentum Momentum and Its Relation to Force Momentum is a vector symbolized by the symbol p, and is defined as: It is a vector and has units of: (kg m/s) or (Ns) The rate of change of momentum is
More informationPhys101 Lectures 14, 15, 16 Momentum and Collisions
Phys101 Lectures 14, 15, 16 Momentum and Collisions Key points: Momentum and impulse Condition for conservation of momentum and why How to solve collision problems Centre of mass Ref: 9-1,2,3,4,5,6,7,8,9.
More informationCompare the momentum of the same object moving with different velocities. Identify examples of change in the momentum of an object.
HOLT CH 6 notes Objectives :Compare the momentum of different moving objects. Compare the momentum of the same object moving with different velocities. Identify examples of change in the momentum of an
More informationAP Physics 2 Summer Assignment (2014)
Name: Date: AP Physics 2 Summer Assignment (2014) Instructions: 1. Read and study Chapter 16 Electric Charge and Electric Field. 2. Answer the questions below. Some questions may require you to use your
More informationPhysics 111: Mechanics Lecture 8
Physics 111: Mechanics Lecture 8 Bin Chen NJIT Physics Department Chapter 8 Momentum, Impulse, and Collisions q q q q q q 8.1 Momentum and Impulse 8.2 Conservation of Momentum 8.3 Momentum Conservation
More informationDylan Humenik Ben Daily Srikrishnan Varadarajan Double Cart Collisions
Double Cart Collisions Objective: -Apply knowledge of collisions in analysis of collision -Find momentum and kinetic energy of two different collisions (elastic and inelastic) Data: Mass (kg) Cart 1 (moving)
More information(k = force constant of the spring)
Lecture 10: Potential Energy, Momentum and Collisions 1 Chapter 7: Conservation of Mechanical Energy in Spring Problems The principle of conservation of Mechanical Energy can also be applied to systems
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 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 informationLast class, we learned Section 9-8, Momentum and Kinetic Energy in Collisions
Final Exam 8:30-11:00 am, May 8th, 2007, Tuesday 208 Kupfrian Hall (Different from the room for the previous exams) From Chapter 1 to Chapter 9 Bring your scientific calculators. Lecture notes at Last
More information1. A 1,160-kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a
Collisions Worksheet Honors: Name: Date: 1. A 1,160-kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a 9,900-kg truck moving in the same direction
More informationPhysics 11 Honours. x-dir px : m1 v1 = (m1 + m2 ) V cos y-dir py : m2 v2 = (m1 + m2 ) V sin A Collision at an Intersection Example 1:
Name: Physics 11 Honours Date: Unit 7 Momentum and Its Conservation 7.4 A perfectly inelastic collision in 2-D Consider a collision in 2-D (cars crashing at a slippery intersection...no friction). Because
More informationAll moving objects have what Newton called a quantity of motion.
MOMEMTUM MOMENTUM MOMEMTUM MOMENTUM All moving objects have what Newton called a quantity of motion. What is this quantity of motion? Today we call it momentum. Momentum is a characteristic of a moving
More informationConservation of Momentum: Marble Collisions Student Version
Conservation of Momentum: Marble Collisions Student Version In this lab you will roll a marble down a ramp, and at the bottom of the ramp the marble will collide with another marble. You will measure the
More informationEXAMPLE 2: CLASSICAL MECHANICS: Worked examples. b) Position and velocity as integrals. Michaelmas Term Lectures Prof M.
CLASSICAL MECHANICS: Worked examples Michaelmas Term 2006 4 Lectures Prof M. Brouard EXAMPLE 2: b) Position and velocity as integrals Calculate the position of a particle given its time dependent acceleration:
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 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 informationExercise 6: The conservation of energy and momentum
Physics 221 Name: Exercise 6: The conservation of energy and momentum Part 1: The projectile launcher s spring constant Objective: Through the use of the principle of conservation of energy (first law
More informationPart One Inelastic Collision:
Problem 3: Experiment 7: Collisions Analysis Part One Inelastic Collision: Analysis: Complete the analysis of your data table by following the two steps below, and answer Question below. You will analyze
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 informationEvaluations for all courses will be conducted online for Spring 2009.
Evaluations for all courses will be conducted online for Spring 2009. The course evaluation site will be active from 9:00 am Monday, April 20 until midnight of Wednesday, May 6th. The URL address to the
More informationMomentum & Energy Review Checklist
Momentum & Energy Review Checklist Impulse and Momentum 3.1.1 Use equations to calculate impulse; momentum; initial speed; final speed; force; or time. An object with a mass of 5 kilograms is moving at
More informationThink-Pair-Share. Linear Momentum (Ch 9) Linear Momentum, cont. Newton and Momentum
Linear Momentum (Ch 9) The linear momentum of a particle or an object that can be modeled as a particle of mass m moving with a velocity v is defined to be the product of the mass and velocity: p = m v
More information23. A force in the negative direction of an x-axis is applied for 27ms to a 0.40kg ball initially moving at 14m/s in the positive direction of the
23. A force in the negative direction of an x-axis is applied for 27ms to a 0.40kg ball initially moving at 14m/s in the positive direction of the axis. The force varies in magnitude, and the impulse has
More informationChapter 9. Linear Momentum
Chapter 9 Linear Momentum Linear Momentum Conservation of Linear Momentum Kinetic Energy of a System Collisions Collisions in Center of Mass Reference Frame MFMcGraw-PHY 45 Chap09Ha-Momentum-Revised-10//01
More informationPH 253 Exam I Solutions
PH 253 Exam I Solutions. An electron and a proton are each accelerated starting from rest through a potential difference of 0.0 million volts (0 7 V). Find the momentum (in MeV/c) and kinetic energy (in
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 informationChapter 7- Linear Momentum
Chapter 7- Linear Momentum Old assignments and midterm exams (solutions have been posted on the web) can be picked up in my office (LB-212) All marks, including assignments, have been posted on the web.
More informationConservation of Momentum
Conservation of Momentum Momentum is a vector quantity that is always conserved. If J = 0, p i = p f The total momentum of an isolated system is constant. Conservation of Energy Energy is a scalar quantity
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 informationPhysics 1A Fall 2013: Quiz 4 Version A 1. Department of Physics Physics 1A Fall Quarter 2013 Dr. Paddock. Version A
Physics 1A Fall 2013: Quiz 4 Version A 1 Department of Physics Physics 1A Fall Quarter 2013 Dr. Paddock Version A DO NOT TURN OVER THIS PAGE UNTIL INSTRUCTED TO DO SO PUT AWAY ALL BOOKS, NOTES, PHONES,
More informationMomentum Practice Problems
Momentum Practice Problems PSI AP Physics C Name Multiple Choice 1. A steel ball and a piece of clay have equal mass. They are dropped from the same height on a horizontal steel platform. The ball bounces
More informationLinear Momentum, Center of Mass, Conservation of Momentum, and Collision.
PHYS1110H, 2011 Fall. Shijie Zhong Linear Momentum, Center of Mass, Conservation of Momentum, and Collision. Linear momentum. For a particle of mass m moving at a velocity v, the linear momentum for the
More informationMomentum and Collisions. Chapter 6. Table of Contents. Section 1 Momentum and Impulse. Section 2 Conservation of Momentum
Table of Contents Momentum and Section 2 Conservation of Momentum Objectives Compare the momentum of different moving objects. Compare the momentum of the same object moving with different velocities.
More informationMomentum and Its Relation to Force
Linear Momentum Momentum and Its Relation to Force The linear momentum, or momentum, of an object is defined as the product of its mass and its velocity. Momentum, p, is a vector and its direction is the
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 informationA level Exam-style practice
A level Exam-style practice 1 a e 0 b Using conservation of momentum for the system : 6.5 40 10v 15 10v 15 3 v 10 v 1.5 m s 1 c Kinetic energy lost = initial kinetic energy final kinetic energy 1 1 6.5
More informationChapter 9. Linear momentum and collisions. PHY 1124 Fundaments of Physics for Engineers. Michael Wong PHY1124 Winter uottawa.
Chapter 9 Linear momentum and collisions Michael Wong PHY1124 Winter 2019 PHY 1124 Fundaments of Physics for Engineers uottawa.ca https://uottawa.brightspace.com/d2l/home Goals 2 Chapter 9 Momentum and
More informationCP1 REVISION LECTURE 1 INTRODUCTION TO CLASSICAL MECHANICS. Prof. N. Harnew University of Oxford TT 2017
CP1 REVISION LECTURE 1 INTRODUCTION TO CLASSICAL MECHANICS Prof. N. Harnew University of Oxford TT 2017 1 OUTLINE : CP1 REVISION LECTURE 1 : INTRODUCTION TO CLASSICAL MECHANICS 1. Force and work 1.1 Newton
More informationAP PHYSICS C Momentum Name: AP Review
AP PHYSICS C Momentum Name: AP Review Momentum How hard it is to stop a moving object. Related to both mass and velocity. For one particle p = mv For a system of multiple particles P = p i = m ivi Units:
More informationspacecraft mass = kg xenon ions speed = m s 1 Fig. 2.1 Calculate the mass of one xenon ion. molar mass of xenon = 0.
1 (a) A solar-powered ion propulsion engine creates and accelerates xenon ions. The ions are ejected at a constant rate from the rear of a spacecraft, as shown in Fig. 2.1. The ions have a fixed mean speed
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam #3 Name 1) A 2000. kg car, traveling to the right at 30. m/s, collides with a brick wall and comes to rest in 0.20 s. 1) The average force the car exerts on the wall is A) 60. kn. B) 12. kn. C) 300
More informationCircle correct course: PHYS 1P21 or PHYS 1P91 BROCK UNIVERSITY
Tutorial #: Circle correct course: PHYS 1P21 or PHYS 1P91 Name: Student #: BROCK UNIVERSITY Test 7: November 2015 Number of pages: 5 Course: PHYS 1P21/1P91 Number of students: 218 Examination date: 17
More information7-6 Inelastic Collisions
7-6 Inelastic Collisions With inelastic collisions, some of the initial kinetic energy is lost to thermal or potential energy. It may also be gained during explosions, as there is the addition of chemical
More informationLecture 41: Highlights
Lecture 41: Highlights The goal of this lecture is to remind you of some of the key points that we ve covered this semester Note that this is not the complete set of topics that may appear on the final
More informationOutline. Collisions in 1- and 2-D. Energies from Binary Star Expt. Energy Plot. Energies with Linear Fit. Energy Plot
Collisions in 1- and 2-D Momentum and Energy Conservation Physics 109, Class Period 9 Experiment Number 6 in the Physics 121 Lab Manual 16 October 2007 Outline Brief summary of Binary Star Experiment Description
More information(1) Center of mass of a symmetric object always lies on an axis of symmetry. (2) Center of mass of an object does NOT need to be on the object.
x com = 1 M N i=1 m ix i x com = 1 M xdm x com = 1 V xdv y com = 1 M N i=1 m iy i y com = 1 M ydm z com = 1 M N i=1 m iz i z com = 1 M zdm M = N i=1 m i ρ = dm dv = M V Here mass density replaces mass
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 informationChapter 9 Linear Momentum
Chapter 9 Linear Momentum 7 12/7 16/7 Units of Chapter 9 Momentum, Impulse and Collisions Momentum and Impulse Define momentum Force and rate of change of momentum; resultant force as rate of change of
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 informationα f k θ y N m mg Figure 1 Solution 1: (a) From Newton s 2 nd law: From (1), (2), and (3) Free-body diagram (b) 0 tan 0 then
Question [ Work ]: A constant force, F, is applied to a block of mass m on an inclined plane as shown in Figure. The block is moved with a constant velocity by a distance s. The coefficient of kinetic
More informationMomentum and Collisions
Momentum and Collisions Vocabulary linear momemtum second law of motion isolated system elastic collision inelastic collision completly inelastic center of mass center of gravity 9-1 Momentum and Its Relation
More informationPhysics 111: Week 8 10 Review
Physics 111: Week 8 10 Review Bin Chen NJIT Physics Department Announcements q Common Exam #3 on Nov 19 (Next Monday) from 4:15 pm to 5:45 pm in KUPF 107 q Must bring your NJIT ID q Cell phone and electronic
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 informationCollisions. Lecture 18. Chapter 11. Physics I. Department of Physics and Applied Physics
Lecture 18 Chater 11 Physics I Collisions Course website: htt://faculty.uml.edu/ndriy_danylov/teaching/physicsi Deartment of Physics and lied Physics IN THIS CHPTER, you will discuss collisions of two
More informationConceptual Physics Energy Sources Collisions
Conceptual Physics Energy ources Collisions Lana heridan De Anza College July 7, 2015 Last time energy and work kinetic energy potential energy conservation of energy energy transfer simple machines efficiency
More informationExtra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that.
Extra credit assignment #4 It can be handed in up until one class before Test 4 (check your course outline). It will NOT be accepted after that. NAME: 4. Units of power include which of the following?
More informationChapter 7. Impulse and Momentum
Chapter 7 Impulse and Momentum 7.1 The Impulse-Momentum Theorem There are many situations when the force on an object is not constant. 7.1 The Impulse-Momentum Theorem DEFINITION OF IMPULSE The impulse
More informationENGI 4430 Multiple Integration Cartesian Double Integrals Page 3-01
ENGI 4430 Multiple Integration Cartesian Double Integrals Page 3-01 3. Multiple Integration This chapter provides only a very brief introduction to the major topic of multiple integration. Uses of multiple
More informationTable of Contents. Pg. # Momentum & Impulse (Bozemanscience Videos) 1 1/11/16
Table of Contents g. # 1 1/11/16 Momentum & Impulse (Bozemanscience Videos) 2 1/13/16 Conservation of Momentum 3 1/19/16 Elastic and Inelastic Collisions 4 1/19/16 Lab 1 Momentum 5 1/26/16 Rotational Dynamics
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 informationCircle correct course: PHYS 1P21 or PHYS 1P91 BROCK UNIVERSITY. Course: PHYS 1P21/1P91 Number of students: 260 Examination date: 10 November 2014
Tutorial #: Circle correct course: PHYS P or PHYS P9 Name: Student #: BROCK UNIVERSITY Test 5: November 04 Number of pages: 5 + formula sheet Course: PHYS P/P9 Number of students: 0 Examination date: 0
More informationPHYSICS 113: Contemporary Physics Final Exam Solution Key (2016)
PHYSICS 113: Contemporary Physics Final Exam Solution Key (2016) 1. [25 points] (5 points each) Short Answers (a) The central reaction that governs the weak nuclear reactions of the sun reduces to: 4 p
More informationA Level. A Level Physics. MECHANICS: Momentum and Collisions (Answers) AQA, Edexcel, OCR. Name: Total Marks: /30
Visit http://www.mathsmadeeasy.co.uk/ for more fantastic resources. AQA, Edexcel, OCR A Level A Level Physics MECHANICS: Momentum and Collisions (Answers) Name: Total Marks: /30 Maths Made Easy Complete
More informationLinear Momentum 2D Collisions Extended or Composite Systems Center of Mass
Linear Momentum 2D Collisions Extended or Composite Systems Center of Mass Lana Sheridan De Anza College Nov 13, 2017 Last time inelastic collisions perfectly inelastic collisions the ballistic pendulum
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
PH105-004 Exam 1 A Name CWID MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) An object starts its motion with a constant velocity of 2.0 m/s toward
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 informationairplanes need Air Rocket Propulsion, 2 Rocket Propulsion Recap: conservation of Momentum
Announcements. HW6 due March 4.. Prof. Reitze office hour this week: Friday 3 5 pm 3. Midterm: grades posted in e-learning solutions and grade distribution posted on website if you want to look at your
More informationChapter 8 LINEAR MOMENTUM AND COLLISIONS
Chapter 8 LINEAR MOMENTUM AND COLLISIONS Linear Momentum Momentum and Newton s Second Law Impulse Conservation of Linear Momentum Inelastic Collisions Elastic Collisions Center of Mass Systems with Changing
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 informationMechanics and Special Relativity (MAPH10030) Assignment 4
MAPH0030) Assignment 4 Issue Date: Tuesday 3 April 00 Due Date: Wednesday April 00 Collection Date: Friday 3 April 00 In these questions, you may use the following conversion factor relating the electron-volt
More informationLinear Momentum Collisions and Energy Collisions in 2 Dimensions
Linear Momentum Collisions and Energy Collisions in 2 Dimensions Lana Sheridan De Anza College Mar 1, 2019 Last time collisions elastic collision example inelastic collisions Overview the ballistic pendulum
More informationName & Surname:... No:... Class: 11 /...
METU D. F. HIGH SCHOOL 2017-2018 ACADEMIC YEAR, 1 st SEMESTER GRADE 11 / PHYSICS REVIEW FOR GENERAL EXAM-3 UNIFORMLY ACCELERATED MOTION IN TWO DIMENSIONS, ENERGY, IMPULSE & MOMENTUM & TORQUE DECEMBER 2017
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 informationMomentum & Energy Review Checklist
Momentum & Energy Review Checklist Impulse and Momentum 3.1.1 Use equations to calculate impulse; momentum; initial speed; final speed; force; or time. An object with a mass of 5 kilograms is moving at
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 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 informationREVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions
REVISING MECHANICS (LIVE) 30 JUNE 2015 Exam Questions Question 1 (Adapted from DBE November 2014, Question 2) Two blocks of masses 20 kg and 5 kg respectively are connected by a light inextensible string,
More informationMomentum Conceptual Questions. 1. Which variable has more impact on an object s motion? Its mass or its velocity?
AP Physics I Momentum Conceptual Questions 1. Which variable has more impact on an object s motion? Its mass or its velocity? 2. Is momentum a vector or a scalar? Explain. 3. How does changing the duration
More informationImpulse/Momentum And Its Conservation
Impulse/Momentum And Its Conservation Which is easier to stop? Truck, car, bowling ball, or baseball all moving at 30 mph. Baseball -it is the least massive. Baseball at 30 mph or a baseball at 90 mph.
More informationPS113 Chapter 7. Impulse and Momentum
PS113 Chapter 7 Impulse and Momentum 1 The impulse-momentum theorem There are many situations in which the force acting on a object is not constant, but varies with time. The resulting motion can be simply
More informationSlide 1 / 47. Momentum by Goodman & Zavorotniy
Slide 1 / 47 Momentum 2009 by Goodman & Zavorotniy Slide 2 / 47 Conservation of Momentum s we pointed out with energy, the most powerful concepts in science are called "conservation principles". These
More information