1. Review Introduction Section 0 Lecture 1 Slide 1 Lecture 17 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 18 Review for Test 2

2. Review Introduction Section 0 Lecture 1 Slide 2 Lecture 17 Slide 2 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet *Homework Handout

3. Review Introduction Section 0 Lecture 1 Slide 3 Lecture 17 Slide 3 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 8 Circular Motion Gravitational Forces Conservation of Energy Conservation of Momentum Conservation of Angular Momentum Introduction and Review

4. Review Introduction Section 0 Lecture 1 Slide 4 Lecture 17 Slide 4 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Notes on Test 1.Covers Chapters 5-8 (Chapter 8 only qualitatively) 2.~8 short answer problems or questions (5 point each) 3.3 Numerical problems based heavily on the material from the homework and Lab/Demo sessions (20 points each). One problem each from Chapters 5, 6 and 7. 4.You will have a formula sheet just like the one in the handout. 5.Test is Thursday February 19 1:30-2:45 in ESLC 46.

5. Review Introduction Section 0 Lecture 1 Slide 5 Lecture 17 Slide 5 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 What Do We Need To Measure? What is the minimum about things we need to know? Where things are—a length, L When things are there—a time, T How thing interact with gravity—a mass, M How things interact with E&M—a charge, Q How thing inter act with weak nuclear force How things interact with strong nuclear force

6. Review Introduction Section 0 Lecture 1 Slide 6 Lecture 17 Slide 6 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Describing Motion and Interactions Position—where you are in space (L or meter) Velocity—how fast position is changing with time (LT -1 or m/s) Acceleration—how fast velocity is changing with time (LT -2 or m/s 2 ) Force— what is required to change to motion of a body (MLT -2 or kg-m/s 2 or N) Energy—the potential for an object to do work. (ML 2 T -2 or kg m 2 /s 2 or N-m or J) Work is equal to the force applied times the distance moved. W = F d Kinetic Energy is the energy associated with an object’s motion. KE=½ mv 2 Potenital Energy is the energy associated with an objects position. Gravitational potential energy PE gravity =mgh Spring potential energy PE apring = -kx In this chapter we will develop the concept of…MOMENTUM…and and its associated law of Conservation of Momentum and apply this to collisions.

7. Review Introduction Section 0 Lecture 1 Slide 7 Lecture 17 Slide 7 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws in Review 1 st Law —a special case of the 2 nd Law for statics, with a=0 or F net =0 An objects velocity remains unchanged, unless a force acts on the object. 2 nd Law (and 1 st Law)—How motion of a object is effected by a force. –The acceleration of an object is directly proportional to the magnitude of the imposed force and inversely proportional to the mass of the object. The acceleration is the same direction as that of the imposed force. 3 rd Law —Forces come from interactions with other objects. For every action (force), there is an equal but opposite reaction (force).

8. Review Introduction Section 0 Lecture 1 Slide 8 Lecture 17 Slide 8 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Central Forces and Gravity

9. Review Introduction Section 0 Lecture 1 Slide 9 Lecture 17 Slide 9 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The Math Approach We are going to explore a different kind of central force that is no longer constant, but is proportional to 1/r 2.  k/r 2 We will take a pragmatic approach (hindsight is 20-20!) We simply replace the force of the “string” with the force of gravity

10. Review Introduction Section 0 Lecture 1 Slide 10 Lecture 17 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Law of Universal Gravitation Newton recognized the similarity between the motion of a projectile on Earth and the orbit of the moon. If a projectile is fired with enough velocity, it could fall towards Earth but never reach the surface. The projectile would be in orbit. Newton’s law of universal gravitation says the gravitational force between two objects is proportional to the mass of each object, and inversely proportional to the square of the distance between the two objects. G is the Universal gravitational constant G.

11. Review Introduction Section 0 Lecture 1 Slide 11 Lecture 17 Slide 11 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Energy

12. Review Introduction Section 0 Lecture 1 Slide 12 Lecture 17 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The mechanical advantage of a simple machine is the ratio of the output force to the input force. –For the pulley example, the mechanical advantage is 2. Work is equal to the force applied times the distance moved. –Work = Force x Distance: W = F d –Work output = Work input units: 1 joule (J) = 1 Nm= 1 kg m 2 / s 2 [ML 2 T -2 ] Mechanical Advantage and Simple Machines

13. Review Introduction Section 0 Lecture 1 Slide 13 Lecture 17 Slide 13 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Energy: The potential to do work. Conservation of Energy: The total energy of a closed system remains constant. –Energy can be converted from one form to another. –Not all forms of energy can be fully recovered. Conservation of Energy Time  Energy 

14. Review Introduction Section 0 Lecture 1 Slide 14 Lecture 17 Slide 14 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The horizontal position x of the mass on the spring is plotted against time as the mass moves back and forth. The period T is the time taken for one complete cycle. The frequency f is the number of cycles per unit time. F=1/T The amplitude is the maximum distance from equilibrium. X(t) = A sin (2π f t)

15. Review Introduction Section 0 Lecture 1 Slide 15 Lecture 17 Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Impulse-Momentum Principles

16. Review Introduction Section 0 Lecture 1 Slide 16 Lecture 17 Slide 16 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Momentum and Impulse Multiply both sides of Newton’s second law by the time interval over which the force acts: The left side of the equation is impulse, the (average) force acting on an object multiplied by the time interval over which the force acts. How a force changes the motion of an object depends on both the size of the force and how long the force acts. The right side of the equation is the change in the momentum of the object. The momentum of the object is the mass of the object times its velocity.

17. Review Introduction Section 0 Lecture 1 Slide 17 Lecture 17 Slide 17 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Impulse-Momentum Principle The impulse acting on an object produces a change in momentum of the object that is equal in both magnitude and direction to the impulse. In analogy, work = change in energy = ΔE

18. Review Introduction Section 0 Lecture 1 Slide 18 Lecture 17 Slide 18 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Rotational Motion and Forces

19. Review Introduction Section 0 Lecture 1 Slide 19 Lecture 17 Slide 19 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Formulas We Know and Love