2. Physics 151: Lecture 7, Pg 1 Physics 151: Lecture 7 Today’s Agenda l Announcements: çHomework #2 : due Fri. (Sept. 15) by 5.00 PM çHomework #3 : due Fri. (Sept. 22) by 5.00 PM çPhysics learning Center (P207-C) Mon.-Fri 9 am - 5pm çReview sessions: l Today’s topics çNewton’s Laws 1 and 2 (Chapter 5.1-4)

3. Physics 151: Lecture 7, Pg 2 KYNEMATICS (previous chapters): description of motion: r(t), v(t), a(t) DYNAMICS (next chapter): what makes the objects move the way they do, learn about forces and how to calculate just what acceleration is.

4. Physics 151: Lecture 7, Pg 3 EXAMPLE from EVERYDAY LIFE : A passenger sitting in the rear of a bus claims that he was injured when the driver slammed on the brakes, causing a suitcase to come flying toward the passenger from the front of the bus. Do you agree with this statement ?

5. Physics 151: Lecture 7, Pg 4 Isaac Newton (1643 - 1727) published Principia Mathematica in 1687.

6. Physics 151: Lecture 7, Pg 5 Dynamics l Isaac Newton (1643 - 1727) published Principia Mathematica in 1687. In this work, he proposed three “laws” of motion: 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 reaction.) See text: Chapter 5

7. Physics 151: Lecture 7, Pg 6 Force l We have an idea of what a force is from everyday life. l Physicist must be precise. çA force is that which causes a body to accelerate. (See Newton’s Second Law) Examples Contact Non-Contact l On a microscopic level, all forces are non-contact See text: 5-1 Question: What force causes an automobile to move ?

8. Physics 151: Lecture 7, Pg 7 Mass l We have an idea of what mass is from everyday life. l Physicist must be precise. çmass (for this class) is a quantity that specifies how much inertia an object has. (See Newton’s First Law) l Mass is an inherent property of an object. l Mass and weight are different quantities. weight is a force. See text: 5-3 Animation

9. Physics 151: Lecture 7, Pg 8 Newton’s First Law inertial reference frame An object subject to no external forces moves with a constant velocity if viewed from an inertial reference frame. çIf no forces act, there is no acceleration. l The above 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: 5-2

10. Physics 151: Lecture 7, Pg 9 Is Storrs a good IRF? çT = 1 day = 8.64 x 10 4 sec, çR ~ R E = 6.4 x 10 6 meters. l Plug this in: a S =.034 m/s 2 ( ~ 1/300 g) l Close enough to 0 that we will ignore it. l Storrs is a pretty good IRF. l Is Storrs accelerating? l YES! çStorrs is on the Earth. çThe Earth is rotating. l What is the centripetal acceleration of Storrs?

11. Physics 151: Lecture 7, Pg 10 Question / Newton’s First Law See text: 5-2 What is wrong with this statement, "Because the car is at rest, there are no forces acting on it” ? Mistake one: The car might be momentarily at rest, in the process of (suddenly) reversing forward into the backward motion. In this case, the forces on it add to a (large) backward resultant. Mistake two: There are no cars in interstellar space. If the car is remaining at rest, there are some large forces on it, including its weight and some force or forces of support. Mistake three: The statement reverses cause and effect.

12. Physics 151: Lecture 7, Pg 11 Newton’s Second Law The acceleration of an object is directly proportional to the net force acting upon it. The constant of proportionality is the mass. See text: 5-4 l Units ç The units of force are kg m/s 2 = Newtons (N) ç The English unit of force is Pounds (lbs)

13. Physics 151: Lecture 7, Pg 12 Lecture 7, ACT 1 Newton’s Second Law I push with a force of 2 Newtons on a cart that is initially at rest on an air table with no air. I push for a second. Because there is no air, the cart stops after I finish pushing. It has traveled a certain distance (before removing the force). For a second shot, I push just as hard but keep pushing for 2 seconds. The distance the cart moves the second time versus the first is (before removing the force) : A) 8 x as long B) 4 x as long C) Same D) 2 as long E) can’t determine Air Track Cart F= 2N

14. Physics 151: Lecture 7, Pg 13 Lecture 7, ACT 1 B) 4 x as long Air Track Cart F= 2N t 1 =1s, v 1 t 2 =2s, v 2 t o, v o = 0 Cart x1x1 x2x2 A) 8 x as long B) 4 x as long C) Same D) 2 as long E) can’t determine

15. Physics 151: Lecture 7, Pg 14 Lecture 7, ACT 1a Air Track Cart F app at rest What is the distances traveled after F app removed in the two cases: (i) after applying F app for 1 s vs. (ii) after aplying F app for 2 s ? What is the distances traveled after F app removed in the two cases: (i) after applying F app for 1 s vs. (ii) after aplying F app for 2 s ? A) 8 x as long B) 4 x as long C) Same D) 2 as long E) can’t determine

16. Physics 151: Lecture 7, Pg 15 Lecture 7, ACT 1a What is the distances traveled after F app removed ? Air Track Cart t o, v o1 t o, v o2 Cart Air Track Cart t 1, v 1 = 0 t 2, v 2 = 0 Cart F app = 2N x1x1 x2x2 F app = 0 F app = 2N F app = 0 F tot = 0 ? at rest otherwise v 1 =v 01, cart keeps moving ! B) 4 x as long

17. Physics 151: Lecture 7, Pg 16 Lecture 7, ACT 2 Newton’s Second Law A) the body will stop moving. B) the body will move in the direction of the force. C) the body’s velocity will increase in magnitude but not change direction. D) the body will gradually change direction more and more toward that of the force while speeding up. E) the body will first stop moving and then move in the direction of the force. F A constant force is applied to a body that is already moving. The force is directed at an angle of 60 degrees to the direction of the body’s velocity. What is most likely to happen is that: vovo 60 o

18. Physics 151: Lecture 7, Pg 17 Newton’s Third Law: If object 1 exerts a force on object 2 (F 1,2 ) then object 2 exerts an equal and opposite force on object 1 (F 2,1 ) F 1,2 = -F 2,1 See text: 5-6 This is among the most abused and misunderstood concepts in physics, along with Einstein’s ideas of relative motion (inertial reference frames) and Heisenberg’s uncertainty principle. For every “action” there is an equal and opposite “reaction”

19. Physics 151: Lecture 7, Pg 18 Newton's Third Law... "When the locomotive in Figure on the right broke through the wall of the train station, the force exerted by the locomotive on the wall was greater than the force the wall could exert on the locomotive.” Is this statement true or in need of correction? See text: 5-6

20. Physics 151: Lecture 7, Pg 19 An Example F B,E = - m B g F E,B = m B g Consider the forces on an object undergoing projectile motion

21. Physics 151: Lecture 7, Pg 20 Lecture 7, ACT 3a Newton’s Third Law A fly gets smushed onto the windshield of a speeding bus.  The force exerted by the bus on the fly is, A) greater than B) the same as C) less than that exerted by the fly on the bus.

22. Physics 151: Lecture 7, Pg 21 Lecture 7, ACT 3b Newton’s Third Law A fly gets smushed onto the windshield of a speeding bus.  The acceleration due to this collision of the bus is, A) greater than B) the same as C) less than that of the fly.

23. Physics 151: Lecture 7, Pg 22 Newton's Third Law... FF l F A,B = - F B,A an example, F F m,w F F w,m F F m,f F F f,m See text: 5-6

24. Physics 151: Lecture 7, Pg 23 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

25. Physics 151: Lecture 7, Pg 24 Example of Good Thinking only the box l Consider only the box as the system! çFree Body Diagram F F m,b F F b,m ice

26. Physics 151: Lecture 7, Pg 25 Example of Good Thinking only the box l Consider only the box as the system! çFree Body Diagram a box F F b,m FgFg FNFN a box = F b,m /m box

27. Physics 151: Lecture 7, Pg 26 Normal Forces Certain forces act to keep an object in place. These have what ever force needed to balance all others (until a breaking point). F T,B F B,T

28. Physics 151: Lecture 7, Pg 27 Force Pairs Newton’s 3rd law concerns force pairs. Two members of a force pair cannot act on the same object. Don’t confuse gravity (the force of the earth on an object) and normal forces. It’s an extra part of the problem. F T,B F B,T F B,E = -mg F E,B = mg

29. Physics 151: Lecture 7, Pg 28 An Example Consider the following two cases

30. Physics 151: Lecture 7, Pg 29 An Example The Free Body Diagrams mgmgmgmg F B,T = N Ball Falls For Static Situation N = mg

31. Physics 151: Lecture 7, Pg 30 An Example The action/reaction pair forces F B,E = -mg F B,T = N F E,B = mg F B,E = -mg F E,B = mg F T,B = -N

32. Physics 151: Lecture 7, Pg 31 Recap for today: l Definition of force and mass (Ch. 5.1 and 5.3) l Newton’s Laws l Reading assignment for Monday çNewton’s Laws 2 and 3 l Homework #2 : due Fri. (Sept. 15) by 5.00 PM l Homework #3 : due Fri. (Sept. 22) by 5.00 PM