Physics 114C - Mechanics Lecture 16 (Walker: Ch ) Work & Energy February 3, 2012 John G. Cramer Professor Emeritus, Department of Physics B451 PAB

Announcements Because the last two problems of HW#4 are covered in today’s lecture, I moved the due date for HW#4 to 11:59 PM on Friday, February 3 (tonight). HW#5 is still due at 11:59 PM on Thursday, February 9. HW#6 is due at 11:59 PM on Thursday, February 16. Register your clicker. We will have Exam 2 on Friday, February 10. It will cover Chapters 5-8 and will be similar to Exam 1 in its structure. There will again be assigned seating. If you have not already done so and would like to request a left-handed seat, right- handed aisle seat, or front row seat, your request to me ASAP. February 3, 20122/28Physics 114A - Lecture 16

Physics 114A - Introduction to Mechanics - Winter-2012 Lecture: Professor John G. Cramer Textbook: Physics, Vol. 1 (UW Edition), James S. Walker WeekDateL#Lecture TopicPagesSlidesReadingHW DueLab 4 23-Jan-12E1 EXAM 1 - Chapters D Dynamics 24-Jan-1210Newton's Laws to Jan-1211Common Forces to Jan-1212Free Body Diagrams-24- HW Jan-1213Friction Newton's Laws Tension 31-Jan-1214Strings & Springs to Feb-1215Circular Motion Feb-1216Work & Energy to 7-2HW4 6 6-Feb-1217Work & Power to 7-4 Work-energy 7-Feb-1218Potential Energy to Feb-1219Energy Conservation I to 8-5HW5 10-Feb-12E2EXAM 2 - Chapters 5-8 Lecture Schedule (Part 2) We are here. February 3, 20123/28Physics 114A - Lecture 16

Circular Orbits (1) Thought Experiment: On an airless planet, cannon balls are shot from a cannon mounted on a tower ar increasing muzzle velocities, and go farther and farther as the velocity is increased. What limits their range? February 3, 20124/28Physics 114A - Lecture 16

Circular Orbits (2) February 3, 20125/28Physics 114A - Lecture 16

A satellite moves at constant speed in a circular orbit about the center of the Earth and near the surface of the Earth. If the magnitude of its acceleration is g = 9.81 m/s 2 and the Earth’s radius is 6,370 km, find: (a) its speed v ; and (b) the time T required for one complete revolution. Example: A Satellite’s Motion February 3, 20126/28Physics 114A - Lecture 16 Note: if you dug a tunnel directly through the center of the Earth and dropped in a subway car, its round-trip transit time would also be 84.3 minutes.

Work Done by a Constant Force The definition of work, when the force is parallel to the displacement: (7-1) SI work unit: newton-meter (N·m) = joule, J February 3, 20127/28Physics 114A - Lecture 16

Typical Work February 3, 20128/28Physics 114A - Lecture 16

Work for Force at an Angle If the force is at an angle to the displacement: (7-3) Only the horizontal component of the force does any work (horizontal displacement). February 3, 20129/28Physics 114A - Lecture 16

Work Summary Energy is transferred from person to spring as the person stretches the spring. This is “work”. Work = 0 SI Units for work: 1 joule = 1 J = 1 N·m 1 electron-volt = 1 eV = x J February 3, /28Physics 114A - Lecture 16

Work Done by a Constant Force The work can also be written as the dot product of the force F and the displacement d : February 3, /28Physics 114A - Lecture 16

Negative and Positive Work The work done may be positive, zero, or negative, depending on the angle between the force and the displacement: February 3, /28Physics 114A - Lecture 16

Perpendicular Force and Work A car is traveling on a curved highway. The force due to friction f s points toward the center of the circular path. How much work does the frictional force do on the car? Zero! General Result: A force that is everywhere perpendicular to the motion does no work. February 3, /24Physics 114A - Lecture 16

Work on a System with Many Forces February 3, /24Physics 114A - Lecture 16

Work Done by a Constant Force If there is more than one force acting on an object, we can find the work done by each force, and also the work done by the net force: (7-5) February 3, /24Physics 114A - Lecture 16

Example: Pulling a Suitcase A rope inclined upward at 45 o pulls a suitcase through the airport. The tension on the rope is 20 N. How much work does the tension do, if the suitcase is pulled 100 m? Note that the same work could have been done by a tension of just 14.1 N by pulling in the horizontal direction. February 3, /28Physics 114A - Lecture 16

Gravitational Work In lifting an object of weight mg by a height h, the person doing the lifting does an amount of work W = mgh. If the object is subsequently allowed to fall a distance h, gravity does work W = mgh on the object. February 3, /24Physics 114A - Lecture 16

Example: Loading with a Crane A 3,000 kg truck is to be loaded onto a ship by a crane that exerts an upward force of 31 kN on the truck. This force, which is large enough to overcome the gravitational force and keep the truck moving upward, is applied over a distance of 2.0 m. (a) Find the work done on the truck by the crane. (b) Find the work done on the truck by gravity. (c) Find the net work done on the truck. February 3, /28Physics 114A - Lecture 16

Positive & Negative Gravitational Work When positive work is done on an object, its speed increases; when negative work is done, its speed decreases. February 3, /28Physics 114A - Lecture 16

Kinetic Energy & The Work-Energy Theorem After algebraic manipulations of the equations of motion, we find: Therefore, we define the kinetic energy: (7-6) February 3, /28Physics 114A - Lecture 16

Kinetic Energy & The Work-Energy Theorem Work-Energy Theorem: The total work done on an object is equal to its change in kinetic energy. (7-7) February 3, /28Physics 114A - Lecture 16

Clicker Question 1 b) v a) 0.50 ve) 2.00 vd) vc) v Car 1 has twice the mass of Car 2, but they both have the same kinetic energy. If the speed of Car 1 is v, approximately what is the speed of Car 2? February 3, /28Physics 114A - Lecture 16

Problem Solving Strategy Picture: The way you choose the +y direction or the +x direction can help you to easily solve a problem that involves work and kinetic energy. Solve: 1. Draw the particle first at its initial position and second at its final position. For convenience, the object can be represented as a dot or box. Label the initial and final positions of the object. 2. Put one or more coordinate axes on the drawing. 3. Draw arrows for the initial and final velocities, and label them appropriately. 4. On the initial-position drawing of the particle, place a labeled vector for each force acting on it. 5. Calculate the total work done on the particle by the forces and equate this total to the change in the particle’s kinetic energy. Check: Make sure you pay attention to negative signs during your calculations. For example, values for work done can be positive or negative, depending on the direction of the displacement relative to the direction of the force. Kinetic energy values, however, are always positive. February 3, /28Physics 114A - Lecture 16

Example: A Dogsled Race During your winter break, you enter a “dogsled” race across a frozen lake, in which the sleds are pulled by students instead of dogs. To get started, you pull the sled (mass 80 kg) with a force of 180 N at 40° above the horizontal. The sled moves  x = 5.0 m, starting from rest. Assume that there is no friction. (a) Find the work you do. (b) Find the final speed of your sled. February 3, /28Physics 114A - Lecture 16

Example: Work and Kinetic Energy in a Rocket Launch A 150,000 kg rocket is launched straight up. The rocket engine generates a thrust of 4.0 x 10 6 N. What is the rocket’s speed at a height of 500 m? (Ignore air resistance and mass loss due to burned fuel.) February 3, /28Physics 114A - Lecture 16

Example: Pushing a Puck A 500 g ice hockey puck slides across frictionless ice with an initial speed of 2.0 m/s. A compressed air gun is used to exert a continuous force of 1.0 N on the puck to slow it down as it moves 0.50 m. The air gun is aimed at the front edge of the puck, with the compressed air flow 30 o below the horizontal. What is the puck’s final speed? February 3, /28Physics 114A - Lecture 16

Example: Work on an Electron In a television picture tube, electrons are accelerated by an electron gun. The force that accelerates the electron is an electric force due to the electric field in the gun. An electron is accelerated from rest by an electron gun to an energy of 2.5 keV (2,500 eV) over a distance of 2.5 cm. (1 eV = 1.60 x J) Find the force on the electron, assuming that it is constant and in the direction of the electron’s motion. February 3, /28Physics 114A - Lecture 16

Before Monday, read Walker Chapter Homework Assignments #4 should be submitted using the Tycho system by 11:59 PM on Friday, February 3 (Tonight!) Register your clicker, using the “Clicker” link on the Physics 114A Syllabus page. End of Lecture 16 February 3, /28Physics 114A - Lecture 16