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

3. Honors Physics, Pg 2 The Fundamental Forces of our Universe l Any object with mass will have an attraction to another object with mass Luckily it is VERY WEAK. çThis is called the Gravitational Force (due to the large mass of the earth)

4. Honors Physics, Pg 3 l Electromagnetic Force çElectric and magnetic forces çForces that give objects their strength, their ability to squeeze, stretch, or shatter çVery Large compared to the gravitational force The Fundamental Forces of our Universe 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)

5. Honors Physics, Pg 4 GUT Grand Unified Theory l 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 l Mathematical Models of the BIG BANG theory l Based on some observations between Electromagnetic and the WEAK force yielding the the combined Elecrtroweak Force

6. Honors Physics, Pg 5 Dynamics l Issac Newton (1643-1727) published Principia Mathematica in 1687. In this work, he proposed three “laws” of motion: See text: 5-1 and 5-2

7. Honors Physics, Pg 6 Newton’s First Law inertial reference frame l An object subject to no external forces is at rest or moves with a constant velocity if viewed from an inertial reference frame. çIf no forces act, there is no acceleration. l 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. l The first statement can be thought of as the definition of inertial reference frames. çAn IRF is a reference frame that is not accelerating (or rotating) with respect to the “fixed stars”. çIf one IRF exists, infinitely many exist since they are related by any arbitrary constant velocity vector! See text:pge 94

8. Honors Physics, Pg 7 Is Cincinnati a good IRF? l Is Cincinnati accelerating? l YES! çCincinnati is on the Earth. çThe Earth is rotating. l What is the centripetal acceleration of Cincinnati? çT = 1 day = 8.64 x 10 4 sec, çR ~ R E = 6.4 x 10 6 meters. l Plug this in: a U =.034 m/s 2 ( ~ 1/300 g) l Close enough to 0 that we will ignore it. l Cincinnati is a pretty good IRF.

9. Honors Physics, Pg 8 Newton’s Second Law... l What is a force? çA Force is a push or a pull. çA Force has magnitude & direction (vector). çAdding forces is like adding vectors.(next chapter) FF1FF1 FF2FF2 a FF1FF1 FF2FF2 a F F NET Fa F NET = ma See text: pge 93 and 4.2

10. Honors Physics, Pg 9 Newton’s Second Law F l For any object a= F NET /m a F çThe acceleration a of an object is proportional to the net force F NET acting on it and inversely proportional to the objects mass m FFa For any object, F NET =  F = ma. The constant of proportionality is called “mass”, denoted m. çThis is the definition of mass. çThe mass of an object is a constant property of that object, and is independent of external influences. l Force has units of [M]x[L/T 2 ] = kg m/s 2 = N (Newton)

11. Honors Physics, Pg 10 Newton’s Second Law... Fa l Components of F = ma : F X = ma X F Y = ma Y F Z = ma Z l Suppose we know m and F X, we can solve for a and apply the things we learned about kinematics over the last few weeks:

12. Honors Physics, Pg 11 Example: Pushing a Box on Ice. x l 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 ? F v = 0 m a x

13. Honors Physics, Pg 12 Example: Pushing a Box on Ice. x l 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 ? d F v m a x

14. Honors Physics, Pg 13 Example: Pushing a Box on Ice... l Start with F = ma. ça = F / m. çRecall that v 2 2 - v 1 2 = 2ad(lecture 1) çSo v 2 = 2Fd / m d F v m a x

15. Honors Physics, Pg 14 Example: Pushing a Box on Ice... l Plug in F = 50N, d = 10m, m = 100kg: çFind v = 3.2 m/s. d F v m a x

16. Honors Physics, Pg 15 Forces Units of force (mks): [F] = [m][a] = kg m s  2 = N (Newton) l We will consider two kinds of forces: çContact force: »This is the most familiar kind. n I push on the desk. n The ground pushes on the chair... çAction at a distance (a bit mysterious): »Gravity »Electromagnetic, strong & weak nuclear forces.

17. Honors Physics, Pg 16 Contact forces: l Objects in contact exert forces. F l Convention: F a,b means “the force acting on a due to b”. F l So F head,thumb means “the force on the head due to the thumb”. F F head,thumb

18. Honors Physics, Pg 17 Gravity... l Near the earth’s surface... Fa l But we have just learned that: F g = ma çThis must mean that g is the “acceleration due to gravity” that we already know! Fgg l So, the force on a mass m due to gravity near the earth’s surface is F g = mg where g is 9.8m/s 2 “down”. and

19. Honors Physics, Pg 18 Example gravity problem: l What is the force of gravity exerted by the earth on a typical physics student? çTypical student mass m = 55kg çg = 9.8 m/s 2. çF g = mg = (55 kg)x(9.8 m/s 2 ) çF g = 539 N l The force that gravity exerts on any object is called its Weight FFgFFg See text example Mass and Weight.

20. Honors Physics, Pg 19 Newton’s Third Law: FF l Forces occur in pairs: F A,B = - F B,A. çFor every “action” there is an equal and opposite “re- action”. l In the case of gravity: R 12 m1m1 m2m2 F F 12 F F 21

21. Honors Physics, Pg 20 Newton’s Third Law... FF l F A,B = - F B,A. is true for contact forces as well: F F m,w F F w,m F F m,f F F f,m

22. Honors Physics, Pg 21 Example of Bad Thinking FFFa l Since F m,b = -F b,m why isn’t F net = 0, and a = 0 ? a ?? F F m,b F F b,m ice

23. Honors Physics, Pg 22 Example of Good Thinking only the box l Consider only the box as the system! çFaF çF on box = ma box = F b,m çFree Body Diagram (next time). a box F F m,b F F b,m ice

24. Honors Physics, Pg 23 The Free Body Diagram Fa l Newtons 2nd says that for an object F = ma. for an object. l Key phrase here is for an object. Fa l So before we can apply F = ma to any given object we isolate the forces acting on this object:

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

26. Honors Physics, Pg 25 Example... l Draw a picture showing all of the forces F F F BF F F FB F F BE F F EB y x

27. Honors Physics, Pg 26 Example... l Draw a picture showing all of the forces. l Isolate the forces acting on the block. F F F BF Fg F FB = mg y x

28. Honors Physics, Pg 27 Example... l Draw a picture showing all of the forces. l Isolate the forces acting on the block. l Draw a free body diagram. F F F BF y x Fg F FB = mg

29. Honors Physics, Pg 28 Example... l Draw a picture showing all of the forces. l Isolate the forces acting on the block. l Draw a free body diagram. l Solve Newtons equations for each component. ç F X = ma X ç F BF - mg = ma Y F F F BF gmggmg y x See strategy: Solving Newton’s Law Problems,

30. Honors Physics, Pg 29 Example... l F X = ma X ç So a X = F X / m = (10 N)/(2 kg) = 5 m/s 2. l F BF - mg = ma Y ç But a Y = 0 ç So F BF = mg. Normal Force l The vertical component of the force of the floor on the object (F BF ) is often called the Normal Force (N). l Since a Y = 0, N = mg in this case. FXFX N mg y x

31. Honors Physics, Pg 30 Example Recap FXFX N = mg mg a X = F X / m y x

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

33. Honors Physics, Pg 32 Elevator... amaama gmggmg N l First draw a Free Body Diagram of the student: Fa l Recall that F Net = ma. y See text: 6-1 See example p 99: An Elevator

34. Honors Physics, Pg 33 Elevator... l Add up the vectors accordingly! F F Net = FNg l In this case F Net = N - mg. Ng (note that N and g are vectors) y l Considering the y (upward) component: N - mg = ma N = m (g + a) amaama gmggmg N += y See text: 6-1 See example p 99: An Elevator

35. Honors Physics, Pg 34 Elevator... mama mgmg N l Interesting limiting cases: l If a = 0, N = mg (ok). ç Like previous example. l If a = -g, N = 0 (free fall). ç The vomit comet! N = m (g + a) y See text: 6-1 See example : An Elevator

36. Honors Physics, Pg 35 Scales: l Springs can be calibrated to tell us the applied force. ç We can calibrate scales to read Newtons, or... çFishing scales usually read weight in kg or lbs. 0 2 4 6 8

37. Honors Physics, Pg 36 Tools: Pegs & Pulleys l Used to change the direction of forces. çAn ideal massless pulley or ideal smooth peg will change the direction of an applied force without altering the magnitude: FF1FF1 ideal peg or pulley FF2FF2 FF | F 1 | = | F 2 |

38. Honors Physics, Pg 37 Tools: Pegs & Pulleys l Used to change the direction of forces. çAn ideal massless pulley or ideal smooth peg will change the direction of an applied force without altering the magnitude: mg T m T = mg F W,S = mg

39. Honors Physics, Pg 38 Recap of Newton’s 3 laws of motion l 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. FFa Law 2: For any object, F NET =  F = ma FF Law 3: Forces occur in pairs: F A,B = - F B,A. For every “action” there is an equal and opposite “re-action”. l Textbook problems