1. 9/10/2013PHY 113 C Fall 2013 -- Lecture 51 PHY 113 A General Physics I 11 AM-12:15 PM MWF Olin 101 Plan for Lecture 5: Chapter 5 – NEWTON’S GENIUS 1.Concept of force 2.Relationship between force and acceleration 3.Net force Note: today we are going to neglect friction.

2. 9/10/2013 PHY 113 C Fall 2013 -- Lecture 52

3. 9/10/2013PHY 113 C Fall 2013 -- Lecture 53 Webassign question from Assignment #4 East North 3 1 2 4

4. 9/10/2013PHY 113 C Fall 2013 -- Lecture 54 Webassign question from Assignment #4 Given: h,H,x,  Determine: v i vivi x=

5. 9/10/2013PHY 113 C Fall 2013 -- Lecture 55 Problem solving steps 1.Visualize problem – labeling variables 2.Determine which basic physical principle(s) apply 3.Write down the appropriate equations using the variables defined in step 1. 4.Check whether you have the correct amount of information to solve the problem (same number of knowns and unknowns). 5.Solve the equations. 6.Check whether your answer makes sense (units, order of magnitude, etc.). Two-dimensional motion with constant acceleration

6. 9/10/2013PHY 113 C Fall 2013 -- Lecture 56 Isaac Newton, English physicist and mathematician (1642—1727) http://www.newton.ac.uk/newton.html 1.In the absence of a net force, an object remains at constant velocity or at rest. 2.In the presence of a net force F, the motion of an object of mass m is described by the form F=ma. 3.F 12 =– F 21.

7. 9/10/2013PHY 113 C Fall 2013 -- Lecture 57 Detail: “Inertial” frame of reference Strictly speaking, Newton’s laws work only in a reference frame (coordinate system) that is stationary or moving at constant velocity. In a non-inertial (accelerating) reference frame, there are some extra contributions. iclicker question: Are we (here in Winston-Salem) A.In an inertial frame of reference (exactly) B.In a non-inertial frame of reference Newton’s laws are only approximately true in Winston- Salem, but the corrections are very small.

8. 9/10/2013PHY 113 C Fall 2013 -- Lecture 58

9. 9/10/2013PHY 113 C Fall 2013 -- Lecture 59 Example force – weight 1 lb = 4.45 N 1 N = 0.225 lb Newton

10. 9/10/2013PHY 113 C Fall 2013 -- Lecture 510 Gravitational mass versus inertial mass – The concept of mass (“inertial” mass m) is distinct from the concept of weight mg. In fact the gravitation “constant” g varies slightly throughout the globe. The weight of mass m on the surface of the earth is different from its weight measured on the surface of the moon or on the surface of Mars. (Stay tuned to Chapter 13 – “Universal Gravitation”.) iclicker question Will we always need to take gravity into account? A.Yes B.No

11. 9/10/2013PHY 113 C Fall 2013 -- Lecture 511 Isaac Newton, English physicist and mathematician (1642—1727) http://www.newton.ac.uk/newton.html 1.In the absence of a net force, an object remains at constant velocity or at rest. 2.In the presence of a net force F, the motion of an object of mass m is described by the form F=ma. 3.F 12 =– F 21.

12. 9/10/2013PHY 113 C Fall 2013 -- Lecture 512 Examples F gravity =-mg j F tension = T j F=F net =F tension +F gravity =(T-mg) j =0

13. 9/10/2013PHY 113 C Fall 2013 -- Lecture 513 Examples F gravity =-mg j F tension = T j F=F net =F tension +F gravity =(T-mg) j =0 F gravity =-mg j F=F net =F gravity =(-mg) j = ma a=-gj

14. vivi x= 9/10/2013PHY 113 C Fall 2013 -- Lecture 514 Two-dimensional motion with constant acceleration

15. 9/10/2013PHY 113 C Fall 2013 -- Lecture 515 iclicker question: An object having a mass of 2 kg is moving at constant velocity of 3 m/s in the upward direction near the surface of the Earth. What is the net force acting on the object? A.0 N. B.6 N in the upward direction. C.25.6 N in the upward direction. D.19.6 N in the downward direction.

16. 9/10/2013PHY 113 C Fall 2013 -- Lecture 516 Example: (assume surface is frictionless) Suppose T measured a observed & measured T = m a

17. 9/10/2013PHY 113 C Fall 2013 -- Lecture 517 Example of two dimensional motion on a frictionless horizontal surface m

18. 9/10/2013PHY 113 C Fall 2013 -- Lecture 518 Example of two dimensional motion on a frictionless horizontal surface -- continued m

19. 9/10/2013PHY 113 C Fall 2013 -- Lecture 519 Example – support forces  F support acts in direction  to surface (in direction of surface “normal”)

20. 9/10/2013PHY 113 C Fall 2013 -- Lecture 520 Another example of support force:

21. 9/10/2013PHY 113 C Fall 2013 -- Lecture 521 iclicker question: Why do we care about forces in equilibrium? A.Normal people don’t care. B.Physicist care because they are weird. C.It might be important if the materials responsible for the support forces are near their breaking point.

22. 9/10/2013PHY 113 C Fall 2013 -- Lecture 522 Example of forces in equilibrium

23. 9/10/2013PHY 113 C Fall 2013 -- Lecture 523 Example of forces in equilibrium -- continued

24. 9/10/2013PHY 113 C Fall 2013 -- Lecture 524 Example of forces in equilibrium -- continued

25. 9/10/2013PHY 113 C Fall 2013 -- Lecture 525 Newton’s second law F = m a Types of forces: Fundamental Approximate Empirical Gravitational F=-mg j Friction Electrical Support Magnetic Elastic Elementary particles

26. 9/10/2013PHY 113 C Fall 2013 -- Lecture 526 Examples (one dimension): (constant)

27. 9/10/2013PHY 113 C Fall 2013 -- Lecture 527 Newton’s third law F 12 = - F 21 12 FPFP T T T=m 1 a a=F P /(m 1 +m 2 ) F P -T=m 2 a T=F P (m 1 /(m 1 +m 2 ))

28. 9/10/2013PHY 113 C Fall 2013 -- Lecture 528 T-m 1 g=m 1 a T-m 2 g=-m 2 a => after some algebra:

29. 9/10/2013PHY 113 C Fall 2013 -- Lecture 529 F gravity =-mg j F scale F scale + F gravity = 0; F scale = mg Question: What if you step on the scale in the elevator? F scale + F gravity = m a; F scale = mg +m a

30. 9/10/2013PHY 113 C Fall 2013 -- Lecture 530

31. 9/10/2013PHY 113 C Fall 2013 -- Lecture 531 Exercise For this exercise, you should ride the elevator from the first floor of Olin Physical Laboratory up to the second or third floor. While in the elevator, stand on the scale and record the scale readings to answer the following questions. 1. What is the scale reading when the elevator is stationary? 2. What is the scale reading when the elevator just starts moving upward? 3. What is the scale reading when the elevator is coming to a stop just before your destination floor? x <x >x

32. 9/10/2013PHY 113 C Fall 2013 -- Lecture 532 mg F floor = mg mg F floor = mg-T T T Mg Mg=12 lb mg=14.5 lb T=? iclicker exercise A.mg B.Mg C.Not enough info

33. 9/10/2013PHY 113 C Fall 2013 -- Lecture 533 Example: 2-dimensional forces A car of mass m is on an icy (frictionless) driveway, inclined at an angle t as shown. Determine its acceleration. Conveniently tilted coordinate system:

34. 9/10/2013PHY 113 C Fall 2013 -- Lecture 534 vivi v f =0 Another example: Note: we are using a tilted coordinate frame i