In-Class Problems 22-23: Mechanical Energy Solution
|
|
- Ernest Carr
- 6 years ago
- Views:
Transcription
1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Deparent o Physics Physics 801 TEAL Fall Term 004 In-Class Problems -3: Mechanical Energy Solution Section Table and Group Number Names Hand in one solution per group We would like each group to apply the problem solving strategy with the our stages (see below) to answer the ollowing two problems I Understand get a conceptual grasp o the problem II Devise a Plan - set up a procedure to obtain the desired solution III Carry our your plan solve the problem! IV Look Back check your solution and method o solution 1
2 Problem : Escape Velocity and Mechanical Energy The asteroid Toro, discovered in 1964, has a radius o about R = 50 km and a mass o about m t = kg Let s assume that Toro is a perectly uniorm sphere What is the ape velocity or an object o mass m on the surace o Toro? Could a person reach this speed (on Earth) by running? Solution: The only potential energy in this problem is the gravitational potential energy We choose the zero point or the potential energy when the object and Toro are an ininite distance apart, U gravity (r 0 = ) 0 Then the potential energy when the object and Toro are an ininite distance r apart is given by Gm U gravity (r) = with U gravity (r 0 = ) 0 r The expression ape velocity reers to the minimum velocity necessary or the object to ape the gravitational interaction o the asteroid and move o to an ininite distance away I the object has a velocity less than the ape velocity, it will be unable to ape the gravitational orce and must return to Toro I it has a velocity greater than the ape velocity, it will have a non-zero kinetic energy at ininity So the condition or the ape velocity is that the object will have exactly zero kinetic energy at ininity We choose our initial state, at time t 0, when the object is at the surace o the planet with velocity equal to ape velocity We choose our inal state, at time t, to occur when the separation distance between the asteroid and the object is ininite Initial Energy: The initial kinetic energy is K 0 = 1 mv The initial potential energy is Gm U 0 = So the initial mechanical energy is R E 0 = K 0 +U 0 = 1 mv R t Gm m Final Energy: The inal kinetic energy is K = 0, since this is the condition that deines ape velocity The inal potential energy is zero, U = 0 since we chose the zero point or potential energy at ininity So the inal mechanical energy is E = K + U = 0 Non-conservative work: There is no non-conservative work
3 Change in Mechanical Energy: The change in mechanical energy 0 = W = E mech, nc is then 1 Gm 0 = mv R This equation can be solved or the ape velocity, v, ( N m kg )(0 10 kg) Gm v = t = = 73 m s 3 R (50 10 m) 1 Considering that Olympic sprinters typically reach velocities o 1 m s 1, this is an easy velocity to attain by running on Earth It may be harder on Toro to generate the acceleration necessary to reach this speed by pushing o the ground, since any slight upward orce will raise the center o mass and it will take substantially more time than on earth to come back down or another push o the ground Problem 3: Circular Motion and Conservation o Mechanical Energy An object o mass m is released rom rest at a height h above the surace o a table The object slides along the inside o the loop-the-loop track consisting o a ramp and a circular loop o radius R shown in the igure Assume that the track is rictionless When the object is at the top o the track it pushes against the track with a orce equal to three times it s weight What height was the object dropped rom? Solution: 3
4 We choose polar coordinates with origin at the center o the loop We choose the zero point or the potential energy U = 0 at the bottom o the loop Initial Energy: We choose or our initial state, the instant the mass is released The initial kinetic energy K 0 = 0 The initial potential energy is non-zero, U 0 = mgh So the initial mechanical energy is E 0 = K 0 +U = mgh 0 Final Energy: We choose or our inal state, the instant the mass is at the top o the loopthe-loop The inal kinetic energy K = 1 mv since the mass is in motionat rest The inal potential energy is non-zero, U = mg R So the inal mechanical energy is E = K +U = mgr + 1 mv Non-conservative Work: Since we are assuming the track is rictionless, there is no non- conservative work Change in Mechanical Energy: The change in mechanical energy is thereore zero, 0 = W nc = E mechanical = E E 0 Thus mechanical energy is conserved, E = E 0, or mgr + 1 mv = mgh Missing Condition: The normal orce o the track on the object is perpendicular to the direction o the motion o the object so this orce does zero work, r N d r = 0 4
5 Thereore the work-kinetic energy theorem does not account or the action o this orce When there are orces that do no work in some direction, set up the Second Law in that direction, r r F = ma We show the orce diagram when the mass is at the top o the loop Thereore Newton s Second Law in the radial direction, rˆ, is mg N = m v R Notice rom the inormation given in the example, the normal orce o the loop on the r r object is N = 3mg (This is the action-reaction pair) Thereore the Second Law becomes 4mg = m v R We can rewrite this condition in terms o the kinetic energy as Summary: Our two equations are thereore mgr = 1 mv mgr + 1 mv = mgh 1 mgr = mv The second equation (rom the Newton s Second Law) can be substituted into the conservation o mechanical energy equation to yield, So the initial height is 4mgR = mgh h= 4R 5
Module 14: Application of the Principle of Conservation of Energy
Module 14: Application of the Principle of Conservation of Energy In the preceding chapter we consider closed systems!e system = 0 in which the only interactions on the constituents of a system were due
More information14.9 Worked Examples. Example 14.2 Escape Velocity of Toro
14.9 Wored Examples Example 14. Escape Velocity of Toro The asteroid Toro, discovered in 1964, has a radius of about R = 5.0m and a mass of about m t =.0 10 15 g. Let s assume that Toro is a perfectly
More informationChapter 8 Conservation of Energy and Potential Energy
Chapter 8 Conservation o Energy and Potential Energy So ar we have analyzed the motion o point-like bodies under the action o orces using Newton s Laws o Motion. We shall now use the Principle o Conservation
More informationConservation of Mechanical Energy 8.01
Conservation o Mechanical Energy 8.01 Non-Conservative Forces Work done on the object by the orce depends on the path taken by the object Example: riction on an object moving on a level surace F riction
More informationFs (30.0 N)(50.0 m) The magnitude of the force that the shopper exerts is f 48.0 N cos 29.0 cos 29.0 b. The work done by the pushing force F is
Chapter 6: Problems 5, 6, 8, 38, 43, 49 & 53 5. ssm Suppose in Figure 6. that +1.1 1 3 J o work is done by the orce F (magnitude 3. N) in moving the suitcase a distance o 5. m. At what angle θ is the orce
More informationChapter 14 Potential Energy and Conservation of Energy
Chapter 4 Potential Energy and Conservation of Energy Chapter 4 Potential Energy and Conservation of Energy... 2 4. Conservation of Energy... 2 4.2 Conservative and Non-Conservative Forces... 3 4.3 Changes
More informationOne-Dimensional Motion Review IMPORTANT QUANTITIES Name Symbol Units Basic Equation Name Symbol Units Basic Equation Time t Seconds Velocity v m/s
One-Dimensional Motion Review IMPORTANT QUANTITIES Name Symbol Units Basic Equation Name Symbol Units Basic Equation Time t Seconds Velocity v m/s v x t Position x Meters Speed v m/s v t Length l Meters
More informationEnergy present in a variety of forms. Energy can be transformed form one form to another Energy is conserved (isolated system) ENERGY
ENERGY Energy present in a variety of forms Mechanical energy Chemical energy Nuclear energy Electromagnetic energy Energy can be transformed form one form to another Energy is conserved (isolated system)
More informationPractice Exam 2 Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department o Physis Physis 801T Fall Term 004 Problem 1: stati equilibrium Pratie Exam Solutions You are able to hold out your arm in an outstrethed horizontal position
More informationReview D: Potential Energy and the Conservation of Mechanical Energy
MSSCHUSETTS INSTITUTE OF TECHNOLOGY Department o Physics 8. Spring 4 Review D: Potential Energy and the Conservation o Mechanical Energy D.1 Conservative and Non-conservative Force... D.1.1 Introduction...
More informationPhysics 231 Lecture 9
Physics 31 Lecture 9 Mi Main points o today s lecture: Potential energy: ΔPE = PE PE = mg ( y ) 0 y 0 Conservation o energy E = KE + PE = KE 0 + PE 0 Reading Quiz 3. I you raise an object to a greater
More informationAP Physics QUIZ Gravitation
AP Physics QUIZ Gravitation Name: 1. If F1 is the magnitude of the force exerted by the Earth on a satellite in orbit about the Earth and F2 is the magnitude of the force exerted by the satellite on the
More informationPhysics 111. Lecture 18 (Walker: 8.3-4) Energy Conservation I March 11, Conservation of Mechanical Energy
Physics 111 Lecture 18 (Walker: 8.3-4) Energy Conservation I March 11, 2009 Lecture 18 1/24 Conservation o Mechanical Energy Deinition o mechanical energy: (8-6) I the only work done in going rom the initial
More informationPhysics 101 Lecture 12 Equilibrium and Angular Momentum
Physics 101 Lecture 1 Equilibrium and Angular Momentum Ali ÖVGÜN EMU Physics Department www.aovgun.com Static Equilibrium q Equilibrium and static equilibrium q Static equilibrium conditions n Net external
More informationNewton s Gravitational Law
1 Newton s Gravitational Law Gravity exists because bodies have masses. Newton s Gravitational Law states that the force of attraction between two point masses is directly proportional to the product of
More informationModule 27: Rigid Body Dynamics: Rotation and Translation about a Fixed Axis
Module 27: Rigid Body Dynamics: Rotation and Translation about a Fixed Axis 27.1 Introduction We shall analyze the motion o systems o particles and rigid bodies that are undergoing translational and rotational
More informationUniform Circular Motion
Circular Motion Uniform Circular Motion Uniform Circular Motion Traveling with a constant speed in a circular path Even though the speed is constant, the acceleration is non-zero The acceleration responsible
More informationThe content contained in all sections of chapter 6 of the textbook is included on the AP Physics B exam.
WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system is always
More informationChapter 13. Gravitation
Chapter 13 Gravitation 13.2 Newton s Law of Gravitation Here m 1 and m 2 are the masses of the particles, r is the distance between them, and G is the gravitational constant. G =6.67 x10 11 Nm 2 /kg 2
More informationTutorial 1 Calculating the Kinetic Energy of a Moving Object
5. Energy As you learned in Section 5.1, mechanical work is done by applying orces on objects and displacing them. How are people, machines, and Earth able to do mechanical work? The answer is energy:
More information7 - GRAVITATION Page 1 ( Answers at the end of all questions )
7 - GRAVITATION Page 1 1 ) The change in the value of g at a height h above the surface of the earth is the same as at a depth d below the surface of earth. When both d and h are much smaller than the
More informationPhysics 2414 Group Exercise 8. Conservation of Energy
Physics 244 Group Exercise 8 Name : OUID : Name 2: OUID 2: Name 3: OUID 3: Name 4: OUID 4: Section Number: Solutions Solutions Conservation of Energy A mass m moves from point i to point f under the action
More informationStudy of work done by a variable force. Overview of energy. Study of work done by a constant force. Understanding of energy conservation.
Chap. 7: Work and Energy Overview of energy. Study of work done by a constant force as defined in physics. Relation between work and kinetic energy. Study of work done by a variable force. Study of potential
More informationLecture 10 Mechanical Energy Conservation; Power
Potential energy Basic energy Lecture 10 Mechanical Energy Conservation; Power ACT: Zero net work The system of pulleys shown below is used to lift a bag of mass M at constant speed a distance h from the
More informationPhysics 2211 A & B Quiz #4 Solutions Fall 2016
Physics 22 A & B Quiz #4 Solutions Fall 206 I. (6 points) A pendulum bob of mass M is hanging at rest from an ideal string of length L. A bullet of mass m traveling horizontally at speed v 0 strikes it
More informationVersion 001 circular and gravitation holland (2383) 1
Version 00 circular and gravitation holland (383) This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. AP B 993 MC
More informationMidterm 3 Thursday April 13th
Welcome back to Physics 215 Today s agenda: rolling friction & review Newtonian gravity Planetary orbits Gravitational Potential Energy Physics 215 Spring 2017 Lecture 13-1 1 Midterm 3 Thursday April 13th
More informationSteve Smith Tuition: Physics Notes
Steve Smith Tuition: Physics Notes E = mc 2 F = GMm sin θ m = mλ d hν = φ + 1 2 mv2 Static Fields IV: Gravity Examples Contents 1 Gravitational Field Equations 3 1.1 adial Gravitational Field Equations.................................
More informationPhysics 2211 ABC Quiz #3 Solutions Spring 2017
Physics 2211 ABC Quiz #3 Solutions Spring 2017 I. (16 points) A block of mass m b is suspended vertically on a ideal cord that then passes through a frictionless hole and is attached to a sphere of mass
More informationPSI AP Physics I Work and Energy
PSI AP Physics I Work and Energy Multiple-Choice questions 1. A driver in a 2000 kg Porsche wishes to pass a slow moving school bus on a 4 lane road. What is the average power in watts required to accelerate
More informationUniversal Gravitation
Universal Gravitation Newton s Law of Universal Gravitation Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely
More informationWork Up an Incline. Work = Force x Distance. Push up: 1500J. What is the PE at the top? mg = 500N. An incline is a simple machine!
Quick Question Work Up an Incline The block o ice weighs 500 Newtons. How much work does it take to push it up the incline compared to liting it straight up? Ignore riction. Work Up an Incline Work = Force
More informationLAST NAME FIRST NAME DATE. Rotational Kinetic Energy. K = ½ I ω 2
LAST NAME FIRST NAME DATE Work, Energy and Power CJ - Assignment 3 6.5 The Conservation of Mechanical Energy Problems 3, 34, 38, 40 page 190 Work Kinetic Energy Rotational Kinetic Energy W = F d cosθ KE
More informationPotential Energy, Conservation of Energy, and Energy Diagrams. Announcements. Review: Conservative Forces. (path independent) 8.
Potential Energy, Conservation of Energy, and Energy Diagrams 8.01 W06D Today s Reading ssignment: Chapter 14 Potential Energy and Conservation of Energy, Sections 14.1-14.7 nnouncements Problem Set 5
More informationPhysics 101 Lecture 10 Rotation
Physics 101 Lecture 10 Rotation Assist. Pro. Dr. Ali ÖVGÜN EMU Physics Department www.aovgun.com Rotational Motion Angular Position and Radians Angular Velocity Angular Acceleration Rigid Object under
More informationCopyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Chapter 13. Newton s Theory of Gravity The beautiful rings of Saturn consist of countless centimeter-sized ice crystals, all orbiting the planet under the influence of gravity. Chapter Goal: To use Newton
More informationChapter 4 FORCES AND NEWTON S LAWS OF MOTION PREVIEW QUICK REFERENCE. Important Terms
Chapter 4 FORCES AND NEWTON S LAWS OF MOTION PREVIEW Dynaics is the study o the causes o otion, in particular, orces. A orce is a push or a pull. We arrange our knowledge o orces into three laws orulated
More informationChapter 12 Gravity. Copyright 2010 Pearson Education, Inc.
Chapter 12 Gravity Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws of Orbital Motion Gravitational Potential Energy Energy Conservation
More informationChapter 6. Work and Kinetic Energy. Richard Feynman Nobel Prize in physics (1965)
Chapter 6 ork and Kinetic Energy 1 Deinitions ebster s dictionary: Energy the capacity to do work ork the transer o energy Richard Feynman Nobel Prize in physics (1965) The Feynman Lectures on Physics....in
More informationPhysics 231 Lecture 12
Physics 31 Lecture 1 Work energy theorem W Potential energy o gravity: ΔPE total = = PE KE PE KE 0 mg Conservation o energy ( y ) 0 y 0 E = KE + PE = KE 0 + PE 0 Potential energy o a spring = PE = 1 kx
More informationP = dw dt. P = F net. = W Δt. Conservative Force: P ave. Net work done by a conservative force on an object moving around every closed path is zero
Power Forces Conservative Force: P ave = W Δt P = dw dt P = F net v Net work done by a conservative force on an object moving around every closed path is zero Non-conservative Force: Net work done by a
More informationChapter 8 - Gravity Tuesday, March 24 th
Chapter 8 - Gravity Tuesday, March 24 th Newton s law of gravitation Gravitational potential energy Escape velocity Kepler s laws Demonstration, iclicker and example problems We are jumping backwards to
More informationPHYSICS. Chapter 13 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 13 Lecture RANDALL D. KNIGHT Chapter 13 Newton s Theory of Gravity IN THIS CHAPTER, you will learn to understand the motion of satellites
More informationChapter 6 Work and Energy
Chapter 6 Work and Energy Midterm exams will be available next Thursday. Assignment 6 Textbook (Giancoli, 6 th edition), Chapter 6: Due on Thursday, November 5 1. On page 162 of Giancoli, problem 4. 2.
More informationChapter 4. Forces and Newton s Laws of Motion. continued
Chapter 4 Forces and Newton s Laws of Motion continued Quiz 3 4.7 The Gravitational Force Newton s Law of Universal Gravitation Every particle in the universe exerts an attractive force on every other
More informationPotential and Kinetic Energy: Roller Coasters Student Advanced Version
Potential and Kinetic Energy: Roller Coasters Student Advanced Version Key Concepts: Energy is the ability of a system or object to perform work. It exists in various forms. Potential energy is the energy
More informationWelcome back to Physics 215
Welcome back to Physics 215 Today s agenda: More rolling without slipping Newtonian gravity Planetary orbits Gravitational Potential Energy Physics 215 Spring 2018 Lecture 13-1 1 Rolling without slipping
More informationPHYSICS 12 NAME: Electrostatics Review
NAME: Electrostatics Review 1. The diagram below shows two positive charges of magnitude Q and 2Q. Which vector best represents the direction of the electric field at point P, which is equidistant from
More informationThe Electric Potential Energy
Lecture 6 Chapter 25 The Electric Potential Energy Course website: http://aculty.uml.edu/andriy_danylov/teaching/physicsii Today we are going to discuss: Chapter 25: Section 25.1 Electric Potential Energy
More informationChapter 07: Kinetic Energy and Work
Chapter 07: Kinetic Energy and Work Like other undamental concepts, energy is harder to deine in words than in equations. It is closely linked to the concept o orce. Conservation o Energy is one o Nature
More informationAP1 WEP. Answer: E. The final velocities of the balls are given by v = 2gh.
1. Bowling Ball A is dropped from a point halfway up a cliff. A second identical bowling ball, B, is dropped simultaneously from the top of the cliff. Comparing the bowling balls at the instant they reach
More informationChapter 5 Review : Circular Motion; Gravitation
Chapter 5 Review : Circular Motion; Gravitation Conceptual Questions 1) Is it possible for an object moving with a constant speed to accelerate? Explain. A) No, if the speed is constant then the acceleration
More informationPhysics 2211 M Quiz #2 Solutions Summer 2017
Physics 2211 M Quiz #2 Solutions Summer 2017 I. (16 points) A block with mass m = 10.0 kg is on a plane inclined θ = 30.0 to the horizontal, as shown. A balloon is attached to the block to exert a constant
More informationAP1 WEP. Answer: E. The final velocities of the balls are given by v = 2gh.
1. Bowling Ball A is dropped from a point halfway up a cliff. A second identical bowling ball, B, is dropped simultaneously from the top of the cliff. Comparing the bowling balls at the instant they reach
More informationConservation of mechanical energy *
OpenStax-CNX module: m15102 1 Conservation of mechanical energy * Sunil Kumar Singh This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 2.0 Abstract When only
More informationChapter 6. Work and Energy
Chapter 6 Work and Energy The Ideal Spring HOOKE S LAW: RESTORING FORCE OF AN IDEAL SPRING The restoring orce on an ideal spring is F x = k x SI unit or k: N/m The Ideal Spring Example: A Tire Pressure
More informationCircular Motion Dynamics Concept Questions
Circular Motion Dynamics Concept Questions Problem 1: A puck of mass m is moving in a circle at constant speed on a frictionless table as shown above. The puck is connected by a string to a suspended bob,
More informationPhysics Lecture 02: FRI 16 JAN
Physics 2113 Jonathan Dowling Isaac Newton (1642 1727) Physics 2113 Lecture 02: FRI 16 JAN CH13: Gravitation II Version: 1/9/15 Michael Faraday (1791 1867) 13.5: Gravitation Inside Earth: Shell Game II
More informationThere are two types of forces: conservative (gravity, spring force) nonconservative (friction)
Chapter 8: Conservation o Energy There are two types o orces: conservative (gravity, spring orce) nonconservative (riction) Conservative Forces Conservative Force the work done by the orce on an object
More informationWork and Energy Definition of work Examples. Definition of Mechanical Energy. Conservation of Mechanical Energy, Pg 1
Work and Energy Definition of work Examples Work and Energy Today s Agenda Definition of Mechanical Energy Conservation of Mechanical Energy Conservative forces Conservation of Mechanical Energy, Pg 1
More informationGravitational & Electric Fields
Gravitational & Electric Fields Jessica Wade (jess.wade@kcl.ac.uk) www.makingphysicsfun.com Department of Physics & Centre for Plastic Electronics, Imperial College London Faculty of Natural & Mathematical
More informationPractice Problem Solutions
Chapter 14 Fields and Forces Practice Problem Solutions Student Textbook page 638 1. Conceptualize the Problem - Force, charge and distance are related by Coulomb s law. The electrostatic force, F, between
More informationChapter 9. Gravitation
Chapter 9 Gravitation 9.1 The Gravitational Force For two particles that have masses m 1 and m 2 and are separated by a distance r, the force has a magnitude given by the same magnitude of force acts on
More informationRotational Equilibrium and Rotational Dynamics
8 Rotational Equilibrium and Rotational Dynamics Description: Reasoning with rotational inertia. Question CLICKER QUESTIONS Question E.0 The rotational inertia o the dumbbell (see igure) about axis A is
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 informationSAPTARSHI CLASSES PVT. LTD.
SAPTARSHI CLASSES PVT. LTD. NEET/JEE Date : 13/05/2017 TEST ID: 120517 Time : 02:00:00 Hrs. PHYSICS, Chem Marks : 360 Phy : Circular Motion, Gravitation, Che : Halogen Derivatives Of Alkanes Single Correct
More informationAP Physics Multiple Choice Practice Gravitation
AP Physics Multiple Choice Practice Gravitation 1. Each of five satellites makes a circular orbit about an object that is much more massive than any of the satellites. The mass and orbital radius of each
More informationFOCUS ON CONCEPTS Section 7.1 The Impulse Momentum Theorem
WEEK-6 Recitation PHYS 3 FOCUS ON CONCEPTS Section 7. The Impulse Momentum Theorem Mar, 08. Two identical cars are traeling at the same speed. One is heading due east and the other due north, as the drawing
More informationDesign a Rollercoaster
Design a Rollercoaster This activity has focussed on understanding circular motion, applying these principles to the design of a simple rollercoaster. I hope you have enjoyed this activity. Here is my
More informationPhysics 110 Homework Solutions Week #5
Physics 110 Homework Solutions Week #5 Wednesday, October 7, 009 Chapter 5 5.1 C 5. A 5.8 B 5.34. A crate on a ramp a) x F N 15 F 30 o mg Along the x-axis we that F net = ma = Fcos15 mgsin30 = 500 cos15
More informationChapter 8: Newton s Laws Applied to Circular Motion
Chapter 8: Newton s Laws Applied to Circular Motion Centrifugal Force is Fictitious? F actual = Centripetal Force F fictitious = Centrifugal Force Center FLEEing Centrifugal Force is Fictitious? Center
More informationWork and Energy continued
Chapter 6 Work and Energy continued 6.2 The Work-Energy Theorem and Kinetic Energy Chapters 1 5 Motion equations were been developed, that relate the concepts of velocity, speed, displacement, time, and
More informationSolution of HW4. and m 2
Solution of HW4 9. REASONING AND SOLUION he magnitude of the gravitational force between any two of the particles is given by Newton's law of universal gravitation: F = Gm 1 m / r where m 1 and m are the
More informationChapter 5 Part 2. Newton s Law of Universal Gravitation, Satellites, and Weightlessness
Chapter 5 Part 2 Newton s Law of Universal Gravitation, Satellites, and Weightlessness Newton s ideas about gravity Newton knew that a force exerted on an object causes an acceleration. Most forces occurred
More informationPHYSICS 570 Master's of Science Teaching. Electricity Lecture 8 Work, Potential Energy and Kinetic Energy
1 PHYSICS 570 Master's o Science Teaching Electricity Lecture 8 Work, Potential Energy and Kinetic Energy Instructor Richard Sonneneld mpsonneneld@gmail.com 575 835 6434 1 Course Goals Math 2 You will
More informationAP Physics C. Work and Energy. Free-Response Problems. (Without Calculus)
AP Physics C Work and Energy Free-Response Problems (Without Calculus) 1. A block with a mass m =10 kg is released from rest and slides a distance d = 5 m down a frictionless plane inclined at an angle
More informationPHYSICS 12 NAME: Gravitation
NAME: Gravitation 1. The gravitational force of attraction between the Sun and an asteroid travelling in an orbit of radius 4.14x10 11 m is 4.62 x 10 17 N. What is the mass of the asteroid? 2. A certain
More informationIn this lecture we will discuss three topics: conservation of energy, friction, and uniform circular motion.
1 PHYS:100 LECTURE 9 MECHANICS (8) In this lecture we will discuss three topics: conservation of energy, friction, and uniform circular motion. 9 1. Conservation of Energy. Energy is one of the most fundamental
More informationIn vertical circular motion the gravitational force must also be considered.
Vertical Circular Motion In vertical circular motion the gravitational force must also be considered. An example of vertical circular motion is the vertical loop-the-loop motorcycle stunt. Normally, the
More information1 A car moves around a circular path of a constant radius at a constant speed. Which of the following statements is true?
Slide 1 / 30 1 car moves around a circular path of a constant radius at a constant speed. Which of the following statements is true? The car s velocity is constant The car s acceleration is constant The
More informationPotential and Kinetic Energy: The Roller Coaster Lab Teacher Version
Potential and Kinetic Energy: The Roller Coaster Lab Teacher Version This lab illustrates the type of energy conversions that are experienced on a roller coaster, and as a method of enhancing the students
More informationA 30 o 30 o M. Homework #4. Ph 231 Introductory Physics, Sp-03 Page 1 of 4
Hoework #4. Ph 231 Introductory Physics, Sp-03 Page 1 o 4 4-1A. A particle o ass 2 kg is initially at rest at the origin x = 0. I the only orce acting on the particle is a constant 4 in the x-direction,
More informationQuestions Chapter 13 Gravitation
Questions Chapter 13 Gravitation 13-1 Newton's Law of Gravitation 13-2 Gravitation and Principle of Superposition 13-3 Gravitation Near Earth's Surface 13-4 Gravitation Inside Earth 13-5 Gravitational
More informationAP Physics. Chapters 7 & 8 Review
AP Physics Chapters 7 & 8 Review 1.A particle moves along the x axis and is acted upon by a single conservative force given by F x = ( 20 4.0x)N where x is in meters. The potential energy associated with
More informationNewton s Laws of Motion
Chapter 4 Newton s Second Law: in vector form Newton s Laws of Motion σ റF = m റa in component form σ F x = ma x σ F y = ma y in equilibrium and static situations a x = 0; a y = 0 Strategy for Solving
More informationSPH 4U: Unit 3 - Electric and Magnetic Fields
Name: Class: _ Date: _ SPH 4U: Unit 3 - Electric and Magnetic Fields Modified True/False (1 point each) Indicate whether the statement is true or false. If false, change the identified word or phrase to
More informationPhysics 218: Exam 2. Sections 501 to 506, 522, 524, and 526. March 8th, You have the full class period to complete the exam.
Physics 18: Exam Sections 501 to 506, 5, 54, and 56. March 8th, 013. ules of the exam: 1. You have the full class period to complete the exam.. Formulae are provided on the last page. You may NOT use any
More informationToday. Events. Energy. Gravity. Homework Due Next time. Practice Exam posted
Today Energy Gravity Events Homework Due Next time Practice Exam posted Autumn is here! Autumnal equinox occurred at 11:09pm last night night and day very nearly equal today days getting shorter Moon is
More informationFirst-Year Engineering Program. Physics RC Reading Module
Physics RC Reading Module Frictional Force: A Contact Force Friction is caused by the microscopic interactions between the two surfaces. Direction is parallel to the contact surfaces and proportional to
More informationChapter 12 Gravity. Copyright 2010 Pearson Education, Inc.
Chapter 12 Gravity Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws of Orbital Motion Gravitational Potential Energy Energy Conservation
More informationPhysics 111 Lecture 6 Work-Energy -Power Dr.Ali ÖVGÜN
Physics 111 Lecture 6 Work-Energy -Power Dr.Ali ÖVGÜN EMU Physics Department www.aovgun.com Why Energy? q Why do we need a concept o energy? q The energy approach to describing motion is particularly useul
More informationIn the last lecture the concept of kinetic energy was introduced. Kinetic energy (KE) is the energy that an object has by virtue of its motion
1 PHYS:100 LETUE 9 MEHANIS (8) I. onservation of Energy In the last lecture the concept of kinetic energy was introduced. Kinetic energy (KE) is the energy that an object has by virtue of its motion KINETI
More informationLecture 16. Gravitation
Lecture 16 Gravitation Today s Topics: The Gravitational Force Satellites in Circular Orbits Apparent Weightlessness lliptical Orbits and angular momentum Kepler s Laws of Orbital Motion Gravitational
More informationPotential and Kinetic Energy: Roller Coasters Teacher Version
Potential and Kinetic Energy: Roller Coasters Teacher Version This lab illustrates the type of energy conversions that are experienced on a roller coaster, and as a method of enhancing the students understanding
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 informationPHYSICS 12 NAME: Electrostatics Review
NAME: Electrostatics Review 1. The diagram below shows two positive charges of magnitude Q and 2Q. Which vector best represents the direction of the electric field at point P, which is equidistant from
More informationNm kg. The magnitude of a gravitational field is known as the gravitational field strength, g. This is defined as the GM
Copyright FIST EDUCATION 011 0430 860 810 Nick Zhang Lecture 7 Gravity and satellites Newton's Law of Universal Gravitation Gravitation is a force of attraction that acts between any two masses. The gravitation
More informationWelcome back to Physics 211. Physics 211 Spring 2014 Lecture Gravity
Welcome back to Physics 211 Today s agenda: Newtonian gravity Planetary orbits Gravitational Potential Energy Physics 211 Spring 2014 Lecture 14-1 1 Gravity Before 1687, large amount of data collected
More informationCircular Motion Test Review
Circular Motion Test Review Name: Date: 1) Is it possible for an object moving with a constant speed to accelerate? Explain. A) No, if the speed is constant then the acceleration is equal to zero. B) No,
More informationConservation of Energy Challenge Problems Problem 1
Conservation of Energy Challenge Problems Problem 1 An object of mass m is released from rest at a height h above the surface of a table. The object slides along the inside of the loop-the-loop track consisting
More information