Physics 151: Lecture 7 Today’s Agenda

1. Physics 151: Lecture 7Today’s Agenda • Announcements: • Homework #2 : due Fri. (Sept. 15) by 5.00 PM • Homework #3 : due Fri. (Sept. 22) by 5.00 PM • Physics learning Center (P207-C) Mon.-Fri 9 am - 5pm • Review sessions: • Today’s topics • Newton’s Laws 1 and 2 (Chapter 5.1-4)

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.

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 ?

4. Isaac Newton (1643 - 1727) published Principia Mathematica in 1687.

5. See text: Chapter 5 Dynamics • 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. Law 2: For any object, FNET = F = ma Law 3: Forces occur in pairs: FA ,B = - FB ,A (For every action there is an equal and opposite reaction.)

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

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

8. See text: 5-2 Newton’s First Law An object subject to no external forces moves with a constant velocity if viewed from aninertial reference frame. • If no forces act, there is no acceleration. • The above 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!

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

10. See text: 5-2 Question / Newton’s First Law 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.

11. See text: 5-4 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. • Units • The units of force are kg m/s2 = Newtons (N) • The English unit of force is Pounds (lbs)

12. Lecture 7,ACT 1Newton’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). F= 2N Cart AirTrack 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

13. Cart Cart Dx1 Dx2 Lecture 7, ACT 1 t2 =2s, v2 t1 =1s, v1 to , vo = 0 F= 2N Cart AirTrack A) 8 x as long B) 4 x as long C) Same D) 2 as long E) can’t determine B) 4 x as long

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

15. otherwise v1=v01, cart keeps moving ! Cart Cart Dx1 Dx2 Lecture 7, ACT 1aWhat is the distances traveled after Fapp removed ? Ftot = 0 ? Fapp = 0 t1 , v1 = 0 to , vo1 Fapp= 2N Cart Cart at rest AirTrack Fapp = 0 Ftot = 0 ? to , vo2 t2 , v2 = 0 Fapp= 2N Cart Cart AirTrack at rest B) 4 x as long

16. Lecture 7, ACT 2Newton’s Second Law 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: F 60o vo A) the body will stop moving. B) the body will move in the direction of the force. the body’s velocity will increase in magnitude but not change direction. the body will gradually change direction more and more toward that of the force while speeding up. the body will first stop moving and then move in the direction of the force.

17. See text: 5-6 Newton’s Third Law: If object 1 exerts a force on object 2 (F1,2 ) then object 2 exerts an equal and opposite force on object 1 (F2,1) F1,2 = -F2,1 For every “action” there is an equal and opposite “reaction” 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.

18. See text: 5-6 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?

19. FB,E = - mB g FE,B = mB g An Example Consider the forces on an object undergoing projectile motion

20.  Lecture 7, ACT 3aNewton’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.

21.  Lecture 7, ACT 3bNewton’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.

22. See text: 5-6 Newton's Third Law... • FA ,B = - FB ,A an example, Fm,w Fw,m Ff,m Fm,f

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

24. Fm,b Example of Good Thinking • Consider only the box as the system! • Free Body Diagram Fb,m ice

25. abox Fg FN Example of Good Thinking • Consider only the box as the system! • Free Body Diagram abox = Fb,m/mbox Fb,m

26. FB,T FT,B 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).

27. FB,E = -mg FE,B = mg 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. FB,T FT,B

28. An Example Consider the following two cases

29. mg FB,T= N mg An Example The Free Body Diagrams Ball Falls For Static Situation N = mg

30. FB,E = -mg FB,T= N FT,B= -N FB,E = -mg FE,B = mg FE,B = mg An Example The action/reaction pair forces

31. Recap for today: • Definition of force and mass (Ch. 5.1 and 5.3) • Newton’s Laws • Reading assignment for Monday • Newton’s Laws 2 and 3 • Homework #2 : due Fri. (Sept. 15) by 5.00 PM • Homework #3 : due Fri. (Sept. 22) by 5.00 PM