Honors Physics Today’s Agenda

1. Honors Physics Today’s Agenda • Newton’s 3 laws. • How and why do objects move? • Dynamics. • Textbook problems Chapter 4 59-80 • You should also try answering 41-58

2. The Fundamental Forces of our Universe • Any object with mass will have an attraction to another object with mass Luckily it is VERY WEAK. • This is called the Gravitational Force (due to the large mass of the earth)

3. The Fundamental Forces of our Universe • Electromagnetic Force • Electric and magnetic forces • Forces that give objects their strength, their ability to squeeze, stretch, or shatter • Very Large compared to the gravitational force • Strong Nuclear Force • Holds the particles in the nucleus together • Strongest force (100 times stronger than electromagnetic) • Weak Nuclear Force • Radioactive decay of some nuclei (enough said)

4. GUTGrand Unified Theory • At one time in the history of our universe (BIG BANG) all of the forces could not be differentiated due to the nature, temperature, and pressure of the universe. Therefore there was only one force which ruled the universe • Mathematical Models of the BIG BANG theory • Based on some observations between Electromagnetic and the WEAK force yielding the the combined Elecrtroweak Force

5. See text: 5-1 and 5-2 Dynamics • Issac Newton (1643-1727) published Principia Mathematicain 1687. In this work, he proposed three “laws” of motion:

6. See text:pge 94 Newton’s First Law • An object subject to no external forces is at rest or moves with a constant velocity if viewed from aninertial reference frame. • If no forces act, there is no acceleration. • For Normal Folks- An object at rest remains at rest and an object in motion remains in motion unless acted upon by an external force. • The first statement can be thought of as the definition of inertial reference frames. • An IRF is a reference frame that is not accelerating (or rotating) with respect to the “fixed stars”. • If one IRF exists, infinitely many exist since they are related by any arbitrary constant velocity vector!

7. Is Cincinnati a good IRF? • Is Cincinnati accelerating? • YES! • Cincinnati is on the Earth. • The Earth is rotating. • What is the centripetal acceleration of Cincinnati? • T = 1 day = 8.64 x 104 sec, • R ~ RE = 6.4 x 106 meters . • Plug this in: aU = .034 m/s2 ( ~ 1/300 g) • Close enough to 0 that we will ignore it. • Cincinnati is a pretty good IRF.

8. See text: pge 93 and 4.2 Newton’s Second Law... • What is a force? • A Force is a push or a pull. • A Force has magnitude & direction (vector). • Adding forces is like adding vectors.(next chapter) a a FNET = ma F1 F1 FNET F2 F2

9. Newton’s Second Law • For any object a= FNET /m • The acceleration a of an object is proportional to the net force FNET acting on it and inversely proportional to the objects mass m • For any object, FNET = S F = ma. The constant of proportionality is called “mass”, denoted m. • This is the definition of mass. • The mass of an object is a constant property of thatobject, and is independent of external influences. • Force has units of [M]x[L/T2] = kg m/s2= N (Newton)

10. Newton’s Second Law... • Components of F = ma : FX = maX FY = maY FZ = maZ • Suppose we know m and FX , we can solve for aand apply the things we learned about kinematics over the last few weeks:

11. v = 0 F m a Example: Pushing a Box on Ice. • A skater is pushing a heavy box (mass m = 100 kg) across a sheet of ice (horizontal & frictionless). He applies a force of 50N in the x direction. If the box starts at rest, what is it’s speed v after being pushed a distance d=10m ? x

12. v F m a x d Example: Pushing a Box on Ice. • A skater is pushing a heavy box (mass m = 100 kg) across a sheet of ice (horizontal & frictionless). He applies a force of 50N in the x direction. If the box starts at rest, what is it’s speed v after being pushed a distance d=10m ?

13. v F m a x d Example: Pushing a Box on Ice... • Start with F = ma. • a= F / m. • Recall that v22 - v12 = 2ad (lecture 1) • So v2 = 2Fd / m

14. v F m a x d Example: Pushing a Box on Ice... • Plug in F = 50N, d = 10m, m = 100kg: • Find v = 3.2 m/s.

15. Forces • Units of force (mks): [F] = [m][a] = kg m s-2 = N (Newton) • We will consider two kinds of forces: • Contact force: • This is the most familiar kind. • I push on the desk. • The ground pushes on the chair... • Action at a distance (a bit mysterious): • Gravity • Electromagnetic, strong & weak nuclear forces.

16. Fhead,thumb Contact forces: • Objects in contact exert forces. • Convention: Fa,bmeans “the force acting on adue to b”. • So Fhead,thumb means “the force on the head due to the thumb”.

17. Gravity... • Near the earth’s surface... • But we have just learned that: Fg= ma • This must mean that g is the “acceleration due to gravity” that we already know! • So, the force on a mass m due to gravity near the earth’s surface is Fg= mg where g is 9.8m/s2 “down”. and

18. Example gravity problem: • What is the force of gravity exerted by the earth on a typical physics student? • Typical student mass m = 55kg • g = 9.8 m/s2. • Fg = mg = (55 kg)x(9.8 m/s2 ) • Fg = 539 N • The force that gravity exerts on any object is called its Weight Fg See text example Mass and Weight.

19. Newton’s Third Law: • Forces occur in pairs: FA ,B = - FB ,A. • For every “action” there is an equal and opposite “re-action”. • In the case of gravity: m1 m2 F12 F21 R12

20. Fm,w Fw,m Ff,m Fm,f Newton’s Third Law... • FA ,B = - FB ,A. is true for contact forces as well:

21. Example of Bad Thinking • Since Fm,b = -Fb,m why isn’t Fnet = 0, and a = 0 ? Fm,b Fb,m a ?? ice

22. Example of Good Thinking • Consider only the box as the system! • Fon box= mabox =Fb,m • Free Body Diagram (next time). Fm,b Fb,m abox ice

23. The Free Body Diagram • Newtons 2nd says that for an object F = ma. • Key phrase here isfor an object. • So before we can apply F = ma to any given object we isolate the forces acting on this object:

24. Example • Example dynamics problem: A box of mass m = 2kg slides on a horizontal frictionless floor. A force Fx = 10N pushes on it in the x direction. What is the acceleration of the box? y F = Fx i a= ? x m

25. Example... • Draw a picture showing all of the forces y FBF F x FBE FFB FEB

26. Example... • Draw a picture showing all of the forces. • Isolate the forces acting on the block. y FBF F x FFB = mg

27. Example... • Draw a picture showing all of the forces. • Isolate the forces acting on the block. • Draw a free body diagram. y FBF x F FFB = mg

28. Example... • Draw a picture showing all of the forces. • Isolate the forces acting on the block. • Draw a free body diagram. • Solve Newtons equations for each component. • FX = maX • FBF - mg = maY y x FBF F mg See strategy: Solving Newton’s Law Problems,

29. Example... • FX = maX • So aX = FX / m = (10 N)/(2 kg) = 5 m/s2. • FBF - mg = maY • But aY = 0 • So FBF = mg. • The vertical component of the forceof the floor on the object (FBF ) isoften called the Normal Force (N). • Since aY = 0, N = mg in this case. N y FX x mg

30. Example Recap N = mg y FX aX= FX / m x mg

31. Problem: Elevator • A student of mass m stands in an elevator accelerating upward with acceleration a. What is her apparent weight? • Apparent weight = the magnitude of the normal force of the floor on her feet. • This is the weight a scale would read if she were standing on one! See example pge. 99: An Elevator

32. See text: 6-1 Elevator... • First draw a Free Body Diagram of the student: • Recall that FNet= ma. y ma mg N See example p 99: An Elevator

33. See text: 6-1 Elevator... • Add up the vectors accordingly! FNet= • In this case FNet = N - mg. (note that N and g are vectors) • Considering the y (upward) component: N - mg = ma N = m (g + a) y mg N + = ma See example p 99: An Elevator

34. See text: 6-1 Elevator... • N = m (g + a) • Interesting limiting cases: • If a = 0, N = mg (ok). • Like previous example. • If a = -g, N = 0 (free fall). • The vomit comet! y ma mg N See example : An Elevator

35. Scales: • Springs can be calibrated to tell us the applied force. • We can calibrate scales to read Newtons, or... • Fishing scales usually read weight in kg or lbs. 0 2 4 6 8

36. ideal peg or pulley Tools: Pegs & Pulleys • Used to change the direction of forces. • An ideal massless pulley or ideal smooth peg will change the direction of an applied force without altering the magnitude: F1 | F1 | = | F2 | F2

37. T m mg Tools: Pegs & Pulleys • Used to change the direction of forces. • An ideal massless pulley or ideal smooth peg will change the direction of an applied force without altering the magnitude: FW,S = mg T = mg

38. Recap of Newton’s 3 laws of motion • Newtons 3 laws: • Law 1: An object subject to no external forces is at rest or moves with a constant velocity if viewed from an inertial reference frame. • Law 2: For any object, FNET = S F = ma • Law 3: Forces occur in pairs: FA ,B = - FB ,A. For every “action” there is an equal and opposite “re-action”. • Textbook problems