Information. Complete Ch 6 on Force and Motion Begin Ch 7 on Work and Energy

Transcription

1 Information Lecture today Complete Ch 6 on Force and Motion Begin Ch 7 on Work and Energy Exam in one week will emphasize material up through chapter 6. Chapter 7 material (work, energy, ) will not be on the first midterm. Mention again at end of lecture slide 1

2 reiew Fluid Drag Forces Noniscous flow no drag force Viscous but laminar hiscosity Viscous and turbulent Fd K h Fd 1 C ra slide

3 reiew Terminal Speed Between 0 term : d m dt mg K η D m (1 e ) In either case, D - 1 or Object will attain a terminal speed Text does the turbulent flow case Laminar flow case: K η D mg when with solution for start at rest term Kη t [culture] term mg Kη slide 3

4 reiew Centripetal Force Must always be a force to hold an object in circular motion This force supplies the centripetal acceleration! Hey! What happened to centifugal force? T m R slide 4

5 reiew Centrifugal Force is a FICTION! (Fake Force) Real life experiences that make clear objects without force trael in a straight line at the elocity with which they started! We use fake forces to explain real sense because we are not recognizing acceleration! slide 5

6 reiew Fma better than using fake forces Accelerometer Problem We found tanqa/g from F x ma But if postulated fictional force in direction of a, this would explain the angle, but would not be correct Same rationale holds for centrifugal forces slide 6

7 What speed will m trael at, so as to maintain circular motion of radius, r? For gien M and r, specific works! Prob (unassigned) T T Mg T m r T so M rg m Mg slide 7

8 Conical Pendulum Ball rotating stably in fixed circle Rotate the ball, tension in string supplies centripetal force Notice that circle is always below the hand F F T T cosθ sinθ tanθ rg mg m r Note r Lsinθ Lg sinθ tanθ slide 8

9 An Abnormal Normal Force Go to the amusement park! slide 9

10 The ROTOR Rotates fast giing rider speed tangential speed at the outer wall Floor falls Rider stays up Needed: friction at the wall Sample Problem 6-8 Gien: R and m s What must be? slide 10

11 Race cars on a track Note required force on car (tires) from friction forces on people! all turns are arcs of circles R slide 11

12 Sample Problem 6-9 Problem: driing in car on a circular, leel track. What is the static coefficient of friction required? (so it won t skid!) N f s mg m R f max s m critical s m critical s Rg mg slide 1

13 Make life easier - Bank the track! R higher Eleate outer ring of track relatie to inner ring Look at it from the front (next slide) lower slide 13

14 No friction...what speed ( c ) is required to keep car from sliding! Lets work it out! c FN cosθ mg FN sinθ m R tanθ Rg c c Car on banked track circle center to right Rg tanθ What happens if is Bigger than c? Smaller than c? slide 14

15 Work and Energy Highly useful concept (Newton missed it) work & energy scalars, rather than ectors Work is performed wheneer force is applied to an object with some component along or opposite the direction of displacement Work doneforce distance moed in the direction of the force Energy of seeral general types: kinetic: energy inoled in motion (often recoerable) potential: energy aailable by irtue of aailability to do work; recoerable in future as kinetic dissipated energy: lost, conerted to heat Work creates energy energy conert between kinetic (motion) and potential (eg graity) slide 15

16 Quantities and Units Quantity Displacement (x) Time Velocity Unit Meters (m) Seconds (s) Meters/second (m/s) Acceleration m/s/s (m/s ) Mass Kilogram (kg) Force Newton (N) kg-m/s Work (Energy) Joule (j) N-m slide 16

17 Quantitatie Definition of Work W Dr Work done W displacement Fi in same direction W F r Man does work on system of bed and penquin Note that normal and graitational do NO work in this case. Only the force component moing the system in the same direction as the displacement does work slide 17

18 K 1 Bead on a Wire with constant Force (and acceleration) no friction Fx a W Fd Fx d Work is + or -, depending on whether force has component in the same direction as displacement or opposite to the displacement Positie work increases Kinetic Energy x W m + 0 Fd x m 1 1 W m m W K K x 0 m ( Kinetic energy - new concept) 0 slide 18

19 Work-Energy Theorem Take F in x-direction and F dependent on x: Each increment in x produces W F x Add up all the work to get total work: W W m m W K K Workchange in Kin. Energy General Theorem is alid so long as no energy dissipated slide 19

20 Consistent with what you know get it easier! Simpler way to get many of the answers got before (with gra force) Note for any height y, then Work done (by gra) Chg K mgy m m gy slide 0

21 Conclusions Begun to discuss important topic of work and energy Next time, we use it for seeral cases HW solutions posted today Sample exam and solution for MT1 will be posted today General exam guide posted at the Exam Specifics web page What to expect on exam day is described there please read We will go oer it quickly in the next lecture slide 1