Chapter 8: Potential Energy and Conservation of Energy. Work and kinetic energy are energies of motion.


 Howard Ramsey
 2 years ago
 Views:
Transcription
1 Chapter 8: Potential Energy and Conservation of Energy Work and kinetic energy are energies of motion. Consider a vertical spring oscillating with mass m attached to one end. At the extreme ends of travel the kinetic energy is zero, but something caused it to accelerate back to the equilibrium point. We need to introduce an energy that depends on location or position. This energy is called potential energy.
2 Chapter 8: Potential Energy and Conservation of Energy Work done by gravitation for a ball thrown upward that then falls back down W ab + W ba = mgd + mg d = 0 The gravitational force is said to be a conservative force. b A force is a conservative force if the net work it does on a particle moving around every closed path is zero. a
3 W ab,1 + W ba,2 = 0 W ab,2 + W ba,2 = 0 therefore: W ab,1 = W ab,2 Conservative forces i.e. The work done by a conservative force on a particle moving between two points does not depend on the path taken by the particle. So,... choose the easiest path!!
4 Conservative & Nonconservative forces Conservative Forces: (path independent) gravitational spring electrostatic Nonconservative forces: (dependent on path) friction air resistance electrical resistance These forces will convert mechanical energy into heat and/or deformation.
5 Gravitation Potential Energy Potential energy is associated with the configuration of a system in which a conservative force acts: U = W For a general conservative force F = F(x) Gravitational potential energy: assume U i = 0 at y i = 0 (reference point) U(y) = mgy (gravitational potential energy) only depends on vertical position
6 Nature only considers changes in Potential energy important. Thus, we will always measure U. So,... We need to set a reference point! The potential at that point could be defined to be zero (i.e., U ref. point = 0) in which case we drop the for convenience. BUT, it is always understood to be there!
7 Potential energy and reference point (y = 0 at ground) A 0.5 kg physics book falls from a table 1.0 m to the ground. What is U and U if we take reference point y = 0 (assume U = 0 at y = 0) at the ground? y U = U f U i = (mgh) Physics y = h 0 The book lost potential energy. Actually, it was converted into kinetic energy h y = 0
8 Potential energy and reference point ( y= 0 at table) A 0.5 kg physics book falls from a table 1.0 m to the ground. What is U and U if we take reference point y = 0 (assume U = 0 at y = 0) at the table? y U = U f U i = mg( h) Physics y = 0 0 h The book lost the same potential energy. (independent of y axis assignment) y = h
9 Sample problem 81: A block of cheese, m = 2 kg, slides along frictionless track from a to b, the cheese traveled a total distance of 2 m along the track, and a net vertical distance of 0.8 m. How much is W g? W net = b a F g d r But,... We don t know the angle between F and dr Easier (or another) way?
10 Sample problem 81: A block of cheese, m = 2 kg, slides along frictionless track from a to b, the cheese traveled a total distance of 2 m along the track, and a net vertical distance of 0.8 m. How much is W g? Split the problem into two parts (two paths) since gravity is conservative c }=d 0 mg(b c) = mgd
11 Elastic Potential Energy Spring force is also a conservative force F = kx U f U i = ½ kx f 2 ½ kx i 2 Choose the free end of the relaxed spring as the reference point: that is: U i = 0 at x i = 0 U = ½ kx 2 Elastic potential energy
12 Conservation of Mechanical Energy Mechanical energy E mec = K + U For an isolated system (no external forces), if there are only conservative forces causing energy transfer within the system. We know: K = W (workkinetic energy theorem) Also: U = W (definition of potential energy) Therefore: K + U = 0 (K f K i ) + (U f U i ) = 0 therefore K 1 + U 1 = K 2 + U 2 (States 1 and 2 of system) E mec,1 = E mec,2 the mechanical energy is conserved
13 Conservation of mechanical energy For an object moved by a spring in the presence of a gravitational force. This is an isolated system with only conservative forces ( F = mg, F = kx ) acting inside the system E mec,1 = E mec,2 K 1 + U 1 = K 2 + U 2 ½ mv mgy 1 + ½ kx 1 2 = ½ mv mgy 2 + ½ kx 2 2
14 The bowling ball pendulum demonstration Mechanical energy is conserved if there are only conservative forces acting on the system.
15 Pendulum (1D) vertically Find the maximum speed of the mass. Isolated system with only gravity (conservative force) acting on it. θ L y=0 Let 1 be at maximum height (y = y max ), Let 2 be at minimum height (y = 0), and 3 be somewhere between max and min. 3 y 1 mg 2 y = L(1 cosθ)
16 Pendulum (1D) vertically Where is the speed a max? L Isolated system with only gravity (conservative force) acting on it. 0 K 1 + U 1 = K 2 + U 2 = E total ½ mv mgy 1 = ½ mv mgy K max must be when U min (= 0) Lcosθ 3 y=0 y 2 L 1 mg In general, y = L(1 cosθ) Answer: 2
17 Pendulum (1D) vertically Find the maximum speed of the mass. Let 1 be at maximum height (y = y max ) and 2 be at minimum height (y = 0) E mech,1 = E mech,2 = E total y = L(1 cosθ) θ L K 1 + U 1 = K 2 + U 2 = E total 0 0 mgy max = ½ mv 2 max = E total y y=0 mg
18 Pendulum (1D) vertically Now find the speed of the mass as a function of angle. Let 1 be at maximum height (y = y max ) and 2 be at some height (y) E mech,1 = E mech,2 = E total y = L(1 cosθ) θ L K 1 + U 1 = K 2 + U 2 = E total mgy max = ½ mv 2 + mgy = E total y y=0 mg
19 Pendulum (1D) vertically Find the speed of the mass as a function of angle. Let 1 be at maximum height (y = y max ) and 2 be at some height (y) y θ L y=0 mg U K 0 θ max 0 +θ max 0 θ max θ
20 Pendulum (1D) vertically Find the speed of the mass as a function of angle. Let 1 be at maximum height (y = y max ) and 2 be at some height (y) y θ L y=0 mg E Sum of U + K is constant, =E K 0 θ max 0 +θ max 0 θ max θ U
21 Potential Energy Curve We know U(x) = W = F(x) x Therefore F(x) = du(x)/dx
22 Work done by external force When no friction acts within the system, the net work done by the external force equals to the change in mechanical energy W = E mec = K + U Friction is a nonconservative force When a kinetic friction force acts within the system, then the thermal energy of the system changes: E th = f k d Therefore W = E mec + E th
23 Work done by external force When there are nonconservative forces (like friction) acting on the system, the net work done by them equals to the change in mechanic energy W net = E mec = K + U W friction = f k d
24 Conservation of Energy The total energy E of a system can change only by amounts of energy that are transferred to or from the system W = E = E mec + E th + E int If there is no change in internal energy, but friction acts within the system: W = E mec + E th If there are only conservative forces acting within the system: W = E mec If we take only the single object as the system W = K
25 Law of Conservation of Energy For an isolated system (W = 0), the total energy E of the system cannot change E mec + E th + E int = 0 For an isolated system with only conservative forces, E th and E int are both zero. Therefore: E mec = 0
26 Chapter 8: Potential Energy and The Conservation of Total Energy Work and kinetic energy are energies of motion. Potential energy is an energy that depends on location. 1Dimension 3Dimensions
27 Force Potential Energy Relationship F(x) = du(x)/dx Thus, the force in the xdirection is the negative derivative of the potential energy! The same holds true for y and zdirections.
28 Potential Energy Curve Thus, what causes a force is the variation of the potential energy function, i.e., the force is the negative 3D derivative of the potential energy!
29 Potential Energy Curve We know: Therefore: U(x) = W = F(x) x F(x) = du(x)/dx Now integrate along the displacement: = Rearrange terms:
30 Conservation of Mechanical Energy Holds only for an isolated system (no external forces) and if only conservative forces are causing energy transfer between kinetic and potential energies within the system. Mechanical energy: E mec = K + U We know: K = W (workkinetic energy theorem) U = W (definition of potential energy) Therefore: K + U = 0 (K f K i ) + (U f U i ) = 0 Rearranging terms: K f + U f = K i + U i = K 2 + U 2 = E mec (a constant)
31 A x=0 A Horizontal spring with mass oscillating with maximum amplitude x max = A. At which displacement(s) would the kinetic energy equal the potential energy? 5) none of the above
32 U f U i = ½ kx f 2 ½ kx i 2 U i = 0 at x i = 0; U max = ½ kx max 2 Since K = U Horizontal spring with mass oscillating with maximum amplitude x max = A. At which displacement(s) would the kinetic energy equal the potential energy? A x=0 A 5) none of the above
33 Conservation of mechanical energy For an isolated system with only conservative forces (e.g., F = mg and F = kx) acting on the system: E mec,1 = E mec,2 = E total => K 1 + U 1 = K 2 + U 2 = E total ½ mv mgx 1 + ½ kx 1 2 = ½ mv mgx 2 + ½ kx 2 2 = E total Initial mechanical energy Final mechanical energy
34 Horizontal Spring x=0 Isolated system with only conservative forces acting on it. (e.g., ) E mech,1 = E mech,2 = E total K 1 + U 1 = K 2 + U 2 = E total ½ mv ½ kx 1 2 = ½ mv ½ kx 2 2 = E total
35 Work done by Spring Force Spring force is a conservative force Work done by the spring force: If x f > x i (further away from equilibrium position); W s < 0 My hand did positive work, while the spring did negative work so the total work on the object = 0
36 Work done by Spring Force Spring force is a conservative force Work done by the spring force: If x f < x i (closer to equilibrium position); W s > 0 My hand did negative work, while the spring did positive work so the total work on the object = 0
37 Work done by Spring Force  Summary Spring force is a conservative force Work done by the spring force: If x f > x i (further away from equilibrium position); W s < 0 If x f < x i (closer to equilibrium position); W s > 0 Let x i = 0, x f = x then W s = ½ k x 2
38 Elastic Potential Energy Spring force is a conservative force Choose the free end of the relaxed spring as the reference point: U i = 0 at x i = 0 The work went into potential energy, since the speeds are zero before and after.
39 Vertical Spring with mass m Consider that mass m was held so the spring was relaxed (y 1 =0) and then slowly + let down to the equilibrium position. y 1 =0 Find this equilibrium position. y= y Equilibrium position (F g + F s = 0): 0 F g = mg F s = ky 0 (now the spring is not relaxed!) => y 0 = mg/k (substitute for y o ) y 2 = A ky mg K e = 0, U g,e = mgy 0 = mg( mg/k) = (mg) 2 /k, U s,e = ½ ky 0 2 = ½ k ( mg/k) 2 = ½ (mg) 2 /k
40 Vertical Spring with mass m Now consider that the mass m was dropped from y 1 =0 + Find maximum amplitude A. y 1 =0 Initial position (y 1 = 0): ky y= y K 1 = 0, U g,1 = 0, U s,1 = ½ ky 2 = 0 0 => E mech,1 = 0 Choose = 0 Since y 1 = 0 mg y Final position (y 2 = A) : 2 = A K 2 = 0, U g,2 = mgy 2 = mg( A) = mga, U s,2 = ½ ky 2 2 = ½ ka 2 E mech,1 =E mech,2 = 0 = U g,2 +U s,2 = mga + ½ ka 2 => A = 2mg/k (= 2y 0 )
41 Vertical Spring with mass m Now consider that the mass m was dropped from y 1 =0 Where does the max speed occur? Maximum speed occurs when the potential energy is a minimum. For an Arbitrary position: y 2 = A E mech = 0 = K + U g +U s =½ mv 2 + mgy + ½ ky 2 + y 1 =0 y= y 0 ky mg du/dy = d(mgy + ½ ky 2 )/dy = 0 => mg + ky = 0 => y = mg/k which is y o (from 2 slides ago) => maximum speed is at equilibrium point (as expected)
42 Vertical Spring with mass m Now consider that the mass m was dropped from y 1 =0 What is the max speed? Maximum speed position: 0 = K max + U g + U s = ½ mv 2 + mg( mg/k) + ½ k( mg/k) 2 + y 1 =0 y= y 0 y 2 = A ky mg = ½ mv 2 (mg) 2 /k + ½ k(mg/k) 2 = ½ mv 2 ½ (mg) 2 /k => v 2 = mg 2 /k
43 Vertical Spring with mass m Now consider that the mass m was dropped from y 1 =0 Find the mechanical energy of the mass at the equilibrium point. Kinetic energy at y = y 0 : K y0 = ½ (mg) 2 /k + y 1 =0 y= y 0 y 2 = A Potential energy at y = y 0 : (U g +U s ) y = y0 = mg( y 0 ) + ½ k( y 0 ) 2 = mgy 0 + ½k(y 0 ) 2 = mg(mg/k) + ½k(mg/k) 2 = ½(mg) 2 /k Mechanical energy at y = y 0 : E mech = K y0 + (U g +U s ) y = y0 = ½ (mg) 2 /k ½(mg) 2 /k = 0 ky mg
44 Vertical Spring with mass m When we slowly let the mass relax to y 0, the mechanical energy is: E mech = K y0 + (U g +U s ) y = y0 0 => E mech = ½(mg) 2 /k (mg) 2 /k ½ (mg) 2 /k But when we let the mass drop, the mechanical energy at y = y 0 is E mech = 0 + y 1 =0 y= y 0 y 2 = A ky mg Where did the missing energy (½(mg) 2 /k) go? Answer: Our hand provided a nonconservative force on m!
45 Work done by external force When no friction acts within the system, the net work done by an external force from outside the system equals the change in mechanical energy of the system W net = E mec = K + U Friction is a nonconservative force that opposes motion Work done by friction is: W friction = f k d When a kinetic friction force acts within the system, then the thermal energy of the system changes: E th = f k d Therefore W = E mec + E th
46 Conservation of Total Energy The total energy E of a system can change only by an amount of energy that is transferred to or from the system. W = E = E mec + E th + E int Here, E int are energy changes due to other nonconservative internal forces. If there is no internal energy change, but friction acts within the system: W = E mec + E th If there are only conservative forces acting within the system: W = E mec
47 Isolated Systems For an isolated system (no work done on the system, W = 0), the total energy E of the system cannot change E mec + E th + E int = 0 For an isolated system with only conservative forces, E th and E int are both zero. Therefore: E mec = 0
48 Law of Conservation of Total Energy in an Isolated System Rearrange terms.
49 Law of Conservation of Energy Count up the initial energy in all of its forms. Count up the final energy in all of its forms. These two must be equal (if nothing is added form outside the system).
50 Sample Problem 86 A wooden crate of m = 14kg is pushed along a horizontal floor with a constant force of F = 40N for a total distance of d = 0.5m, during which the crate s speed decreased from v o = 0.60 m/s to v = 0.20m/s. A) Find the work done by F. W = Fd cosθ = (40N)(0.50m)cos0 o = 20J B) Find the increase in thermal energy. (Consider the work done on the block/spring system) W = E mec + E thermal = 20J = ½mv 2 ½mv o 2 + E thermal => E thermal = W E mec =20J (½mv 2 ½mv o2 ) = 22.2J
51 Sample Problem 87 In the figure, a 2.0kg package slides along a floor with speed v 1 = 4.0m/s. It then runs into and compresses a spring, until the package momentarily stops. Its path to the initially relaxed spring is frictionless, but as it compresses the spring, a kinetic friction force from the floor, of magnitude 15 N, acts on it. The spring constant is 10,000 N/m. By what distance d is the spring compressed when the package stops?
52 The net change in energy in the system must equal zero. Initial mechanical energy, (The spring is relaxed) Final mechanical energy, (The mass is stopped)
53 The change in mechanical energy must equal the energy converted to thermal energy. Thus, a quadratic equation in d with: m = 2.0 kg, v 1 = 4.0 m/s, f k = 15 N, and k = 10,000 N/m
WORK DONE BY A CONSTANT FORCE
WORK DONE BY A CONSTANT FORCE The definition of work, W, when a constant force (F) is in the direction of displacement (d) is W = Fd SI unit is the Newtonmeter (Nm) = Joule, J If you exert a force of
More informationCh 8 Potential energy and Conservation of Energy. Question: 2, 3, 8, 9 Problems: 3, 9, 15, 21, 24, 25, 31, 32, 35, 41, 43, 47, 49, 53, 55, 63
Ch 8 Potential energ and Conservation of Energ Question: 2, 3, 8, 9 Problems: 3, 9, 15, 21, 24, 25, 31, 32, 35, 41, 43, 47, 49, 53, 55, 63 Potential energ Kinetic energ energ due to motion Potential energ
More information8. Potential Energy and Conservation of Energy Potential Energy: When an object has potential to have work done on it, it is said to have potential
8. Potential Energy and Conservation of Energy Potential Energy: When an object has potential to have work done on it, it is said to have potential energy, e.g. a ball in your hand has more potential energy
More informationChapter 6 Work and Energy
Chapter 6 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
More informationKE = ½mv 2 PE = mgh W = Fdcosθ THINK ENERGY! (KE F + PE F ) = (KE 0 + PE 0 ) + W NC. Tues Oct 6 Assign 7 Fri Preclass Thursday
Tues Oct 6 Assign 7 Fri Preclass Thursday Conservation of Energy Work, KE, PE, Mech Energy Power To conserve total energy means that the total energy is constant or stays the same. With Work, we now have
More information7. Kinetic Energy and Work
Kinetic Energy: 7. Kinetic Energy and Work The kinetic energy of a moving object: k = 1 2 mv 2 Kinetic energy is proportional to the square of the velocity. If the velocity of an object doubles, the kinetic
More informationChapter 8: Conservation of Energy
Chapter 8: Conservation of Energy This chapter actually completes the argument established in the previous chapter and outlines the standing concepts of energy and conservative rules of total energy. I
More informationMechanics 1: Conservation of Energy and Momentum
Mechanics : Conservation of Energy and Momentum If a certain quantity associated with a system does not change in time. We say that it is conserved, and the system possesses a conservation law. Conservation
More informationCurso20122013 Física Básica Experimental I Cuestiones Tema IV. Trabajo y energía.
1. A body of mass m slides a distance d along a horizontal surface. How much work is done by gravity? A) mgd B) zero C) mgd D) One cannot tell from the given information. E) None of these is correct. 2.
More informationcharge is detonated, causing the smaller glider with mass M, to move off to the right at 5 m/s. What is the
This test covers momentum, impulse, conservation of momentum, elastic collisions, inelastic collisions, perfectly inelastic collisions, 2D collisions, and centerofmass, with some problems requiring
More informationPhysics Notes Class 11 CHAPTER 6 WORK, ENERGY AND POWER
1 P a g e Work Physics Notes Class 11 CHAPTER 6 WORK, ENERGY AND POWER When a force acts on an object and the object actually moves in the direction of force, then the work is said to be done by the force.
More informationWeight The weight of an object is defined as the gravitational force acting on the object. Unit: Newton (N)
Gravitational Field A gravitational field as a region in which an object experiences a force due to gravitational attraction Gravitational Field Strength The gravitational field strength at a point in
More informationPotential Energy and Equilibrium in 1D
Potential Energy and Equilibrium in 1D Figures 627, 628 and 629 of TiplerMosca. du = F x dx A particle is in equilibrium if the net force acting on it is zero: F x = du dx = 0. In stable equilibrium
More informationReview D: Potential Energy and the Conservation of Mechanical Energy
MSSCHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.01 Fall 2005 Review D: Potential Energy and the Conservation of Mechanical Energy D.1 Conservative and Nonconservative Force... 2 D.1.1 Introduction...
More informationwww.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x
Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity
More informationAP Physics C. Oscillations/SHM Review Packet
AP Physics C Oscillations/SHM Review Packet 1. A 0.5 kg mass on a spring has a displacement as a function of time given by the equation x(t) = 0.8Cos(πt). Find the following: a. The time for one complete
More informationPHYSICS 149: Lecture 15
PHYSICS 149: Lecture 15 Chapter 6: Conservation of Energy 6.3 Kinetic Energy 6.4 Gravitational Potential Energy Lecture 15 Purdue University, Physics 149 1 ILQ 1 Mimas orbits Saturn at a distance D. Enceladus
More informationGravitational Potential Energy
Gravitational Potential Energy Consider a ball falling from a height of y 0 =h to the floor at height y=0. A net force of gravity has been acting on the ball as it drops. So the total work done on the
More informationWork, Power, Energy Multiple Choice. PSI Physics. Multiple Choice Questions
Work, Power, Energy Multiple Choice PSI Physics Name Multiple Choice Questions 1. A block of mass m is pulled over a distance d by an applied force F which is directed in parallel to the displacement.
More informationWork, Kinetic Energy and Potential Energy
Chapter 6 Work, Kinetic Energy and Potential Energy 6.1 The Important Stuff 6.1.1 Kinetic Energy For an object with mass m and speed v, the kinetic energy is defined as K = 1 2 mv2 (6.1) Kinetic energy
More informationCHAPTER 6 WORK AND ENERGY
CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS. REASONING AND SOLUTION The work done by F in moving the box through a displacement s is W = ( F cos 0 ) s= Fs. The work done by F is W = ( F cos θ). s From
More informationC B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N
Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a
More informationWork. Work = Force x parallel distance (parallel component of displacement) F v
Work Work = orce x parallel distance (parallel component of displacement) W k = d parallel d parallel Units: N m= J = " joules" = ( kg m2/ s2) = average force computed over the distance r r When is not
More informationConservative vs. Nonconservative forces Gravitational Potential Energy. Work done by nonconservative forces and changes in mechanical energy
Next topic Conservative vs. Nonconservative forces Gravitational Potential Energy Mechanical Energy Conservation of Mechanical energy Work done by nonconservative forces and changes in mechanical energy
More informationAP Physics  Chapter 8 Practice Test
AP Physics  Chapter 8 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A single conservative force F x = (6.0x 12) N (x is in m) acts on
More informationProblem Set 5 Work and Kinetic Energy Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department o Physics Physics 8.1 Fall 1 Problem Set 5 Work and Kinetic Energy Solutions Problem 1: Work Done by Forces a) Two people push in opposite directions on
More informationConservation of Energy Workshop. Academic Resource Center
Conservation of Energy Workshop Academic Resource Center Presentation Outline Understanding Concepts Kinetic Energy Gravitational Potential Energy Elastic Potential Energy Example Conceptual Situations
More informationChapter 4. Forces and Newton s Laws of Motion. continued
Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting
More informationSprings. Spring can be used to apply forces. Springs can store energy. These can be done by either compression, stretching, or torsion.
WorkEnergy Part 2 Springs Spring can be used to apply forces Springs can store energy These can be done by either compression, stretching, or torsion. Springs Ideal, or linear springs follow a rule called:
More informationphysics 111N work & energy
physics 111N work & energy conservation of energy entirely gravitational potential energy kinetic energy turning into gravitational potential energy gravitational potential energy turning into kinetic
More informationChapter 7 WORK, ENERGY, AND Power Work Done by a Constant Force Kinetic Energy and the WorkEnergy Theorem Work Done by a Variable Force Power
Chapter 7 WORK, ENERGY, AND Power Work Done by a Constant Force Kinetic Energy and the WorkEnergy Theorem Work Done by a Variable Force Power Examples of work. (a) The work done by the force F on this
More informationWork, Energy and Power
Work, Energy and Power In this section of the Transport unit, we will look at the energy changes that take place when a force acts upon an object. Energy can t be created or destroyed, it can only be changed
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 informationPhysics 2101, First Exam, Fall 2007
Physics 2101, First Exam, Fall 2007 September 4, 2007 Please turn OFF your cell phone and MP3 player! Write down your name and section number in the scantron form. Make sure to mark your answers in the
More information1 of 10 11/23/2009 6:37 PM
hapter 14 Homework Due: 9:00am on Thursday November 19 2009 Note: To understand how points are awarded read your instructor's Grading Policy. [Return to Standard Assignment View] Good Vibes: Introduction
More informationCh 7 Kinetic Energy and Work. Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43
Ch 7 Kinetic Energy and Work Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43 Technical definition of energy a scalar quantity that is associated with that state of one or more objects The state
More informationWork and Kinetic Energy
Chapter 6 Work and Kinetic Energy PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 6 To understand and calculate
More informationKE =? v o. Page 1 of 12
Page 1 of 12 CTEnergy1. A mass m is at the end of light (massless) rod of length R, the other end of which has a frictionless pivot so the rod can swing in a vertical plane. The rod is initially horizontal
More informationWork and Energy continued
Chapter 6 Work and Energy continued Requested Seat reassignments (Sec. 1) Gram J14 Weber C22 Hardecki B5 Pilallis B18 Murray B19 White B20 Ogden C1 Phan C2 Vites C3 Mccrate C4 Demonstrations Swinging mass,
More informationLab 5: Conservation of Energy
Lab 5: Conservation of Energy Equipment SWS, 1meter stick, 2meter stick, heavy duty bench clamp, 90cm rod, 40cm rod, 2 double clamps, brass spring, 100g mass, 500g mass with 5cm cardboard square
More informationObjective: Work Done by a Variable Force Work Done by a Spring. Homework: Assignment (125) Do PROBS # (64, 65) Ch. 6, + Do AP 1986 # 2 (handout)
Double Date: Objective: Work Done by a Variable Force Work Done by a Spring Homework: Assignment (125) Do PROBS # (64, 65) Ch. 6, + Do AP 1986 # 2 (handout) AP Physics B Mr. Mirro Work Done by a Variable
More informationSimple Harmonic Motion
Simple Harmonic Motion Restating Hooke s law The equation of motion Phase, frequency, amplitude Simple Pendulum Damped and Forced oscillations Resonance Harmonic Motion A lot of motion in the real world
More informationv v ax v a x a v a v = = = Since F = ma, it follows that a = F/m. The mass of the arrow is unchanged, and ( )
Week 3 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationEnergy transformations
Energy transformations Objectives Describe examples of energy transformations. Demonstrate and apply the law of conservation of energy to a system involving a vertical spring and mass. Design and implement
More informationGeneral Physical Science
General Physical Science Chapter 4 Work and Energy Work The work done by a constant force F acting upon an object is the product of the magnitude of the force (or component of the force) and the parallel
More informationPhysics 201 Homework 5
Physics 201 Homework 5 Feb 6, 2013 1. The (nonconservative) force propelling a 1500kilogram car up a mountain 1.21 10 6 joules road does 4.70 10 6 joules of work on the car. The car starts from rest
More informationA1. An object of mass m is projected vertically from the surface of a planet of radius R p and mass M p with an initial speed v i.
OBAFMI AWOLOWO UNIVRSITY, ILIF, IF, NIGRIA. FACULTY OF SCINC DPARTMNT OF PHYSICS B.Sc. (Physics) Degree xamination PHY GNRAL PHYSICS I TUTORIAL QUSTIONS IN GRAVITATION, FLUIDS AND OSCILLATIONS SCTION
More informationCenter of Mass/Momentum
Center of Mass/Momentum 1. 2. An Lshaped piece, represented by the shaded area on the figure, is cut from a metal plate of uniform thickness. The point that corresponds to the center of mass of the Lshaped
More informationSpring Simple Harmonic Oscillator. Spring constant. Potential Energy stored in a Spring. Understanding oscillations. Understanding oscillations
Spring Simple Harmonic Oscillator Simple Harmonic Oscillations and Resonance We have an object attached to a spring. The object is on a horizontal frictionless surface. We move the object so the spring
More informationTHE NOT SO SIMPLE PENDULUM
INTRODUCTION: THE NOT SO SIMPLE PENDULUM This laboratory experiment is used to study a wide range of topics in mechanics like velocity, acceleration, forces and their components, the gravitational force,
More informationFRICTION, WORK, AND THE INCLINED PLANE
FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle
More informationWork, Energy & Power. AP Physics B
ork, Energy & Power AP Physics B There are many dierent TYPES o Energy. Energy is expressed in JOULES (J) 4.19 J = 1 calorie Energy can be expressed more speciically by using the term ORK() ork = The Scalar
More informationVELOCITY, ACCELERATION, FORCE
VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how
More informationPhysics 1120: Simple Harmonic Motion Solutions
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Physics 1120: Simple Harmonic Motion Solutions 1. A 1.75 kg particle moves as function of time as follows: x = 4cos(1.33t+π/5) where distance is measured
More informationPractice Test SHM with Answers
Practice Test SHM with Answers MPC 1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one
More informationClicker Question. A tractor driving at a constant speed pulls a sled loaded with firewood. There is friction between the sled and the road.
A tractor driving at a constant speed pulls a sled loaded with firewood. There is friction between the sled and the road. A. positive. B. negative. C. zero. Clicker Question The total work done on the
More informationChapter 6. Work and Energy
Chapter 6 Work and Energy The concept of forces acting on a mass (one object) is intimately related to the concept of ENERGY production or storage. A mass accelerated to a nonzero speed carries energy
More informationProblem Set #8 Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01L: Physics I November 7, 2015 Prof. Alan Guth Problem Set #8 Solutions Due by 11:00 am on Friday, November 6 in the bins at the intersection
More informationPHY121 #8 Midterm I 3.06.2013
PHY11 #8 Midterm I 3.06.013 AP Physics Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension
More informationB) 286 m C) 325 m D) 367 m Answer: B
Practice Midterm 1 1) When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) the acceleration is equal to g. B) the force of
More informationPhysics 41 HW Set 1 Chapter 15
Physics 4 HW Set Chapter 5 Serway 8 th OC:, 4, 7 CQ: 4, 8 P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59, 67, 74 OC CQ P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59,
More informationF mg (10.1 kg)(9.80 m/s ) m
Week 9 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationPHYS 101 Lecture 10  Work and kinetic energy 101
PHYS 101 Lecture 10  Work and kinetic energy 101 Lecture 10  Work and Kinetic Energy What s important: impulse, work, kinetic energy, potential energy Demonstrations: block on plane balloon with propellor
More informationChapter 6. Work and Energy
Chapter 6 Work and Energy ENERGY IS THE ABILITY TO DO WORK = TO APPLY A FORCE OVER A DISTANCE= Example: push over a distance, pull over a distance. Mechanical energy comes into 2 forms: Kinetic energy
More informationA B = AB sin(θ) = A B = AB (2) For two vectors A and B the cross product A B is a vector. The magnitude of the cross product
1 Dot Product and Cross Products For two vectors, the dot product is a number A B = AB cos(θ) = A B = AB (1) For two vectors A and B the cross product A B is a vector. The magnitude of the cross product
More information9. The kinetic energy of the moving object is (1) 5 J (3) 15 J (2) 10 J (4) 50 J
1. If the kinetic energy of an object is 16 joules when its speed is 4.0 meters per second, then the mass of the objects is (1) 0.5 kg (3) 8.0 kg (2) 2.0 kg (4) 19.6 kg Base your answers to questions 9
More informationMidterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m
Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of
More informationPHYSICS 111 HOMEWORK#6 SOLUTION. February 22, 2013
PHYSICS 111 HOMEWORK#6 SOLUTION February 22, 2013 0.1 A block of mass m = 3.20 kg is pushed a distance d = 4.60 m along a frictionless, horizontal table by a constant applied force of magnitude F = 16.0
More informationAP1 Oscillations. 1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false?
1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The
More informationPhysics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationB) 40.8 m C) 19.6 m D) None of the other choices is correct. Answer: B
Practice Test 1 1) Abby throws a ball straight up and times it. She sees that the ball goes by the top of a flagpole after 0.60 s and reaches the level of the top of the pole after a total elapsed time
More informationPhysics General Physics I
Physics 1114  General Physics I Midterm Solutions 1. Your cat drops from a shelf 1.22 m above the floor and lands on all four feet. His legs bring him to a stop in a distance of 12 cm. Ignoring air resistance,
More informationPhysics 122 Exam #2 Spring 2015
Physics 122 Exam #2 Spring 2015 You are subject to the Bryn Mawr College honor code while taking this exam. This is a closed book exam. You may use a simple calculator and a pencil during this exam, as
More informationLesson 39: Kinetic Energy & Potential Energy
Lesson 39: Kinetic Energy & Potential Energy Total Mechanical Energy We sometimes call the total energy of an object (potential and kinetic) the total mechanical energy of an object. Mechanical energy
More informationPhysics 201 Fall 2009 Exam 2 October 27, 2009
Physics 201 Fall 2009 Exam 2 October 27, 2009 Section #: TA: 1. A mass m is traveling at an initial speed v 0 = 25.0 m/s. It is brought to rest in a distance of 62.5 m by a force of 15.0 N. The mass is
More informationPhysics 125 Practice Exam #3 Chapters 67 Professor Siegel
Physics 125 Practice Exam #3 Chapters 67 Professor Siegel Name: Lab Day: 1. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the
More informationWork, Energy, Conservation of Energy
This test covers Work, echanical energy, kinetic energy, potential energy (gravitational and elastic), Hooke s Law, Conservation of Energy, heat energy, conservative and nonconservative forces, with soe
More informationConservative forces and the potential energy function. Nonconservative forces and the workenergy theorem
Nonconservative forces and the workenergy theorem Consider an object falling with airresistance. There are two forces to consider; the gravitational force (conservative) and the drag force (nonconservative).
More informationPOTENTIAL ENERGY AND CONSERVATION OF ENERGY
Chapter 8: POTENTIAL ENERGY AND CONSERVATION OF ENERGY 1 A good eample of kinetic energy is provided by: A a wound clock spring B the raised weights of a grandfather's clock C a tornado D a gallon of gasoline
More information10.1 Quantitative. Answer: A Var: 50+
Chapter 10 Energy and Work 10.1 Quantitative 1) A child does 350 J of work while pulling a box from the ground up to his tree house with a rope. The tree house is 4.8 m above the ground. What is the mass
More informationHooke s Law. Spring. Simple Harmonic Motion. Energy. 12/9/09 Physics 201, UWMadison 1
Hooke s Law Spring Simple Harmonic Motion Energy 12/9/09 Physics 201, UWMadison 1 relaxed position F X = kx > 0 F X = 0 x apple 0 x=0 x > 0 x=0 F X =  kx < 0 x 12/9/09 Physics 201, UWMadison 2 We know
More informationExercises on Work, Energy, and Momentum. A B = 20(10)cos98 A B 28
Exercises on Work, Energy, and Momentum Exercise 1.1 Consider the following two vectors: A : magnitude 20, direction 37 North of East B : magnitude 10, direction 45 North of West Find the scalar product
More informationWork Energy & Power. September 2000 Number 05. 1. Work If a force acts on a body and causes it to move, then the force is doing work.
PhysicsFactsheet September 2000 Number 05 Work Energy & Power 1. Work If a force acts on a body and causes it to move, then the force is doing work. W = Fs W = work done (J) F = force applied (N) s = distance
More informationUnit 3 Practice Test: Dynamics
Unit 3 Practice Test: Dynamics Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. What is the common formula for work? a. W = F x c. W = Fd
More informationVectors; 2D Motion. Part I. Multiple Choice. 1. v
This test covers vectors using both polar coordinates and ij notation, radial and tangential acceleration, and twodimensional motion including projectiles. Part I. Multiple Choice 1. v h x In a lab experiment,
More informationA Review of Vector Addition
Motion and Forces in Two Dimensions Sec. 7.1 Forces in Two Dimensions 1. A Review of Vector Addition. Forces on an Inclined Plane 3. How to find an Equilibrant Vector 4. Projectile Motion Objectives Determine
More informationQUESTIONS : CHAPTER5: LAWS OF MOTION
QUESTIONS : CHAPTER5: LAWS OF MOTION 1. What is Aristotle s fallacy? 2. State Aristotlean law of motion 3. Why uniformly moving body comes to rest? 4. What is uniform motion? 5. Who discovered Aristotlean
More informationLesson 40: Conservation of Energy
Lesson 40: Conservation of Energy A large number of questions you will do involve the total mechanical energy. As pointed out earlier, the mechanical energy is just the total of all types of energy. In
More informationChapter 11 Work. Chapter Goal: To develop a deeper understanding of energy and its conservation Pearson Education, Inc.
Chapter 11 Work Chapter Goal: To develop a deeper understanding of energy and its conservation. Motivation * * There are also ways to gain or lose energy that are thermal, but we will not study these in
More informationUnit 3 Work and Energy Suggested Time: 25 Hours
Unit 3 Work and Energy Suggested Time: 25 Hours PHYSICS 2204 CURRICULUM GUIDE 55 DYNAMICS Work and Energy Introduction When two or more objects are considered at once, a system is involved. To make sense
More informationSample Questions for the AP Physics 1 Exam
Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiplechoice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each
More information2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration.
2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration. Dynamics looks at the cause of acceleration: an unbalanced force. Isaac Newton was
More informationMechanics 2. Revision Notes
Mechanics 2 Revision Notes November 2012 Contents 1 Kinematics 3 Constant acceleration in a vertical plane... 3 Variable acceleration... 5 Using vectors... 6 2 Centres of mass 8 Centre of mass of n particles...
More informationChapter 9. particle is increased.
Chapter 9 9. Figure 936 shows a three particle system. What are (a) the x coordinate and (b) the y coordinate of the center of mass of the three particle system. (c) What happens to the center of mass
More informationAt the skate park on the ramp
At the skate park on the ramp 1 On the ramp When a cart rolls down a ramp, it begins at rest, but starts moving downward upon release covers more distance each second When a cart rolls up a ramp, it rises
More informationLab 8: Ballistic Pendulum
Lab 8: Ballistic Pendulum Equipment: Ballistic pendulum apparatus, 2 meter ruler, 30 cm ruler, blank paper, carbon paper, masking tape, scale. Caution In this experiment a steel ball is projected horizontally
More informationLecture L222D Rigid Body Dynamics: Work and Energy
J. Peraire, S. Widnall 6.07 Dynamics Fall 008 Version.0 Lecture L  D Rigid Body Dynamics: Work and Energy In this lecture, we will revisit the principle of work and energy introduced in lecture L3 for
More informationIMPORTANT NOTE ABOUT WEBASSIGN:
Week 8 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationA) F = k x B) F = k C) F = x k D) F = x + k E) None of these.
CT161 Which of the following is necessary to make an object oscillate? i. a stable equilibrium ii. little or no friction iii. a disturbance A: i only B: ii only C: iii only D: i and iii E: All three Answer:
More information