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Physics 114C - MechanicsLecture 17 (Walker: Ch. 7.1-2)Work & EnergyApril 30, 2009John G. CramerProfessor of PhysicsB451 [email protected]

AnnouncementsHW#4 is due at 11:59 PM on Thursday, April 30 (Tonight!). Homework up to 24 hours late will receive 70% credit.We will have Exam 2 on Friday, May 8. 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, E-mail your request to me ASAP.As of today, all 94/94 clickers are registered! Well done! Clicker numbers and cumulative scores as of last Friday (26 max) are posted on Tycho under Lecture Score 1 and 2.My office hours are 12:30-1:20 PM on Tuesdays and 2:30-3:20 PM on Thursdays, both in the 114 area of the Physics Study Center on the Mezzanine floor of PAB A (this building).Physics 114B now has a UW GoPost discussion board at: https://catalysttools.washington.edu/gopost/board/jcramer/11164/

*Physics 114B - Lecture 17

Lecture Schedule (Part 2)

Physics 114B - Introduction to MechanicsLecture: Professor John G. Cramer Textbook: Physics, Vol. 1 (UW Edition), James S. WalkerWeekDateL#Lecture TopicPagesSlidesReadingHW DueLab420-Apr-0911Newton's Laws14295-1 to 5-41-D Dynamics21-Apr-0912Common Forces11265-5 to 5-723-Apr-0913Free Body Diagrams-24-HW324-Apr-0914Friction9276-1527-Apr-0915Strings & Springs12296-2 to 6-4Newton's Laws Tension28-Apr-0916Circular Motion5306-530-Apr-0917Work & Energy11237-1 to 7-2HW41-May-0918Work & Power7257-3 to 7-464-May-0919Potential Energy10268-1 to 8-2Work-energy5-May-0920Energy Conservation I16188-3 to 8-57-May-09R2Review & Extension-44-HW58-May-09E2EXAM 2 - Chapters 5-8


Example: A Satellites Motion 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/s2 and the Earths radius is 6,370 km, find:(a) its speed v; and(b) the time T required for one complete revolution.


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?


Circular Orbits (2)


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 (Nm) = joule, J


Typical Work


Work for Force at an AngleIf the force is at an angle to the displacement:(7-3) Only the horizontal component of the force does any work (horizontal displacement).


Work Summary Energy is transferred from person to spring as the person stretches the spring. This is work.Work = 0SI Units for work:1 joule = 1 J = 1 Nm1 electron-volt = 1 eV = 1.602 x 10-19 J


Work Done by a Constant Force The work can also be written as the dot product of the force F and the displacement d:


Negative and Positive Work The work done may be positive, zero, or negative, depending on the angle between the force and the displacement:


Perpendicular Force and Work A car is traveling on a curved highway. The force due to friction fs 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.


Work on a System withMany Forces


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)


Example: Pulling a Suitcase A rope inclined upward at 45o 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.


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.


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.


Positive & Negative Gravitational Work When positive work is done on an object, its speed increases; when negative work is done, its speed decreases.


Kinetic Energy & The Work-Energy Theorem After algebraic manipulations of the equations of motion, we find: Therefore, we define the kinetic energy:(7-6)


Kinetic Energy & The Work-Energy TheoremWork-Energy Theorem: The total work done on an object is equal to its change in kinetic energy.(7-7)


Clicker Question 1b) 0.707 va) 0.50 ve) 2.00 vd) 1.414 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?


Problem Solving StrategyPicture: 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 particles 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.


Example: A Dogsled Race During your winter break, you enter a dogsled race across a frozen lake, in which the sleds are pulled by people 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 Dx = 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.


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 106 N. What is the rockets speed at a height of 500 m? (Ignore air resistance and mass loss due to burned fuel.)


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 30o below the horizontal.What is the pucks final speed?


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 10-19 J) Find the force on the electron, assuming that it is constant and in the direction of the electrons motion.


Before Friday, read Walker Chapter 7.3-4 Homework Assignments #4 should be submitted using the Tycho system by 11:59 PM on Thursday, April 30 (Tonight!) (24 hours late 70% credit) Register your clicker, using the Clicker link on the Physics 114B Syllabus page.End of Lecture 17


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