Lecture 07: Work and Kinetic Energy Physics 2210 Fall Semester 2014
Announcements Schedule next few weeks: 9/08 Unit 3 9/10 Unit 4 9/15 Unit 5 (guest lecturer) 9/17 Unit 6 (guest lecturer) 9/22 Unit 7, Exam Review work practice exam in discussion 9/24 Exam 1, Units 1-6 9/25 Unit 7 HW due
Unit 7: Prelecture Feedback Review dot product Derive relation between work and K.E. Review all checkpoint problems Work through examples Why is work relevant? Mechanics Lecture 6, Slide 3
The Dot (also scalar, inner ) Product of Two Vectors Mechanics Lecture 7, Slide 4
Work-Kinetic Energy Theorem The net work done on a body is equal to the change in kinetic energy of the body Formal definition of work ( Force times distance generalized) Formal definition of kinetic energy Mechanics Lecture 7, Slide 5
Flashcard Question A lighter car and a heavier van, each initially at rest, are pushed with the same constant force F. After both vehicles travel a distance d, which of the following statements is true? (Ignore friction) F d car van F d A) They will have the same velocity B) They will have the same kinetic energy C) They will have the same momentum Mechanics Lecture 7, Slide 6
Flashcard Question A lighter car and a heavier van, each initially at rest, are pushed with the same constant force F. After both vehicles travel a distance d, which of the following statements is true? (Ignore friction) F d car van F d A) They will have the same velocity B) They will have the same kinetic energy C) They will have the same momentum Mechanics Lecture 7, Slide 7
Example: I lift an object of mass m, starting at rest, and place it at rest on a table of height h. 1) What is the work done by gravity? 2) What is the work done by me? 3) What is the change in kinetic energy? 4) Do the answers above depend on the path taken by the object?
Work-Kinetic Energy Theorem If there are several forces acting then W is the work done by the net (total) force: W = K NET = W W + + 1 2... You can just add up the work done by each force W = W NET TOT Mechanics Lecture 7, Slide 9
Example: I drop an object of mass m, from a height h, starting at rest. What is its speed v when it hits the floor... a) As calculated by 1D kinematics? b) As calculated by the Work-KE theorem?
CheckPoint Three objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string. H Free Fall Frictionless incline String In which case does the object have the biggest net work done on it by all forces during its motion? A) Free Fall B) Incline C) String D) All the same Mechanics Lecture 7, Slide 11
CheckPoint Three objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string. H Free Fall Frictionless incline String In which case does the object have the biggest net work done on it by all forces during its motion? A) Free Fall B) Incline C) String D) All the same Mechanics Lecture 7, Slide 12
Flashcard Question Three objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string. What is the relationship between their velocities when they reach the bottom? H Free Fall Frictionless incline String A) v f > v i > v s B) v f > v s > v i C) v f = v s = v i Mechanics Lecture 7, Slide 13
Flashcard Question Three objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string. What is the relationship between their velocities when they reach the bottom? H Free Fall Frictionless incline String A) v f > v i > v s B) v f > v s > v i C) v f = v s = v i Mechanics Lecture 7, Slide 14
CheckPoint A car drives up a hill with constant speed. Which statement best describes the total work W TOT done on the car by all forces as it moves up the hill? A) W TOT > 0 B) W TOT = 0 C) W TOT < 0 v Mechanics Lecture 7, Slide 15
CheckPoint A car drives up a hill with constant speed. Which statement best describes the total work W TOT done on the car by all forces as it moves up the hill? A) W TOT > 0 B) W TOT = 0 C) W TOT < 0 v Mechanics Lecture 7, Slide 16
CheckPoint A box sits on the horizontal bed of a moving truck. Static friction between the box and the truck keeps the box from sliding around as the truck drives. a µ S The work done on the box by the static frictional force as the truck moves a distance D is: A) Positive B) Negative C) Zero Mechanics Lecture 7, Slide 17
CheckPoint A box sits on the horizontal bed of a moving truck. Static friction between the box and the truck keeps the box from sliding around as the truck drives. a µ S The work done on the box by the static frictional force as the truck moves a distance D is: A) Positive B) Negative C) Zero Mechanics Lecture 7, Slide 18
Work done by a Spring Physics 211 Lecture 7, Slide 19
I am confused about the positive work and negative work and also the positive and negative forces for the spring problems. Use the formula to get the magnitude of the work Use a picture to get the sign (look at directions) In this example the spring does negative work since F and x are in opposite direction. The axes don t matter. Physics 211 Lecture 7, Slide 20
Example: Simple Gravitational Orbit A space telescope of mass 10,000 kg is in a stable orbit above the Earth at an altitude h = 3,630 km. The radius and mass of the Earth are R E = 6,370 km and M E = 6.0x10 24 kg, respectively. Newton's gravitational constant is G=6.672x10-11 Nm 2 /kg 2. (a) what is the acceleration of the space telescope? (b) if the telescope's mass were to increase, what would need to happen to its speed in order to maintain the same orbit?
Example I move an object from the surface of the Earth to a height of one Earth radius above the Earth, and to a position on the far side of the Earth from the launch position. The object is at rest with respect to the Earth before and after the move. What is the work that I must do on the object? If the object were instead moved to infinity (or at least very, very far away), what work must I do?
Coverage: Units 1-6 1D Kinematics 2D Kinematics Relative and Circular Motion Newton's Laws Free Body Diagrams Friction Exam Details Problem types: Multiple choice & workout. Study recommendations: Review homework See practice exam on course webpage Solve problems, problems, problems... Allowed materials Calculator (not on cell phone) Straightedge Blue or black pen required for regrade Equation sheet will be provided
1D Kinematics Precise physicist definitions of words you use every day. Differential and integral representations. Graphical representation.
2D Kinematics Generalize 1D kinematics to 2 or 3D Vectors, vector addition and subtraction. Projectile motion: Horizontal constant v Vertical constant a Horizontal and vertical independent
Relative and Circular Motion Kinematics may be described in different coordinate systems. These systems may be in relative motion. Circular motion at constant linear speed is accelerated motion. Acceleration is towards center of circle.
Newton's Laws 2nd Law: define force in terms of mass and acceleration. 1st Law: Special case of 2 nd. Inertia 3rd Law: forces come in pairs, but act in opposite directions.
Free-Body Diagrams Tool for generating equations that relate knowns to unknowns. Useful for many types of forces Support forces Spring forces Gravity (near Earth and far from Earth). Friction
Friction Contact force between two objects. Parallel to adjoining surface. Two types: Kinetic (moving) Static (at rest)