1. Physics 215 -- Fall 2014 Lecture 15-21 Welcome back to Physics 215 Buoyancy Driven, damped oscillations Resonance Course evaluations

2. Physics 215 -- Fall 2014 Lecture 15-22 Current homework assignment HW11: –Knight Textbook Ch.13: 30, 32, 66 –Knight Textbook Ch.15: 32, 40, 56 –due Friday, Dec. 5 th in recitation

3. Physics 215 -- Fall 2014 Lecture 15-23 Final Exam: Thursday (Dec.11), 12:45PM Exam will be 2 hours long In Room 208 (here!) Cumulative! Material covered: –Textbook chapters 1-15 –Lectures -- all (slides online) –Workshop Activities -- all –Homework assignments -- all (solutions online) –Exams 1, 2 & 3 (solutions online) As with Exams 1, 2 & 3, Final is closed book, but you may bring calculator and one handwritten 8.5” x 11” sheet of notes -- this may be a different sheet from Exams 1, 2 & 3. Practice versions of Final Exam posted online

4. Physics 215 -- Fall 2014 Lecture 15-24 Archimedes’ principle The magnitude of the buoyant force is equal to the weight of the fluid displaced by the object. The buoyant force is the total upward force exerted on an object by the surrounding fluid.

5. Physics 215 -- Fall 2014 Lecture 15-25 How do boats float? If the density of an object is less than that of water, an object floats in water. If the density of an object is greater than that of water, an object sinks in water. …but boats can be made of metal, e.g., aluminum (  Al /  W ~ 2.7)…

6. Physics 215 -- Fall 2014 Lecture 15-26 A cubical block made of a certain type of plastic has a density of 0.75 g/cm 3. The density of water is 1.0 g/cm 3. If the block is allowed to float in water, what fraction of the volume of the block would be below the water level? 1.one quarter 2.one half 3.three quarters 4.some other fraction

7. Physics 215 -- Fall 2014 Lecture 15-27 Damped Harmonic Oscillator For example air drag for small speeds: F drag =  b v Damping constant Differential equation for x (t) Solution:

8. Physics 215 -- Fall 2014 Lecture 15-28 Forced Harmonic Oscillator Driving force Solution yields amplitude of response: Damping force Natural frequency Differential equation for x (t):

9. Physics 215 -- Fall 2014 Lecture 15-29 Resonance Small ( b ) damping Large ( b ) damping A dd

10. Physics 215 -- Fall 2014 Lecture 15-210 Reading assignment Prepare for Final Exam!