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1. Motion & Force: Dynamics

2. A Forceis “A push or a pull” on an object. Usually, for a force, we use the symbol F. F is a VECTOR! Force Obviously, vector addition is needed to add forces!

3. “Pushing” Forces “Pulling” Forces 1. “Contact” Forces: Classes of Forces

4. Classes of Forces • Contact Forces involve physical contactbetween two objects • Examples (in the pictures): spring forces, pulling force, pushing force

5. “Pushing” Forces “Pulling” Forces 1. “Contact” Forces: Classes of Forces 2. “Field” Forces: Physics II: Electricity & Magnetism Physics I: Gravity

6. Classes of Forces • Contact Forces involve physical contactbetween two objects • Examples (in the pictures): spring forces, pulling force, pushing force • Field Forcesact through empty space. • No physical contact is required. • Examples (in the pictures): gravitation, electrostatic, magnetic

7. The 4 Fundamental Forces of Nature • Gravitational Forces • Between masses • Electromagnetic Forces • Between electric charges • Nuclear Weak Forces • Certain radioactive decay processes • Nuclear Strong Forces • Between subatomic particles Note: These are all field forces!

8. The 4 Fundamental Forces of NatureSourcesof the forces: In the order of decreasing strength This table shows details of the 4 Fundamental Forces of Nature, & their relative strength for 2 protons in a nucleus.

9. Sir Isaac Newton 1642 – 1727 • Formulated the basic laws of mechanics. • Discovered the Law of Universal Gravitation. • Invented a form of Calculus • Made many observations dealing with light & optics.

10. Sir Isaac Newton 1642 – 1727 Also • Research on Alchemy! • Biblical Research! Was NOT a nice man! Bad Treatment of Scientific Colleagues! • Never Married • Entered Politics Late in Life

11. Newton’s Laws of Motion • The ancient (& 100% wrong! ) view (of Aristotle): A force is needed to keep an object in motion. The “natural” state of an object is at rest. In the 21st Century, its still a common Misconception!! • The Correct View:(Galileo & Newton): It’s just as natural for an object to be in motion at constant speed in a straight line as to be at rest.

12. Newton’s Laws of Motion • The Correct View: (Galileo & Newton): It’s just as natural for an object to be in motion at constant speed in a straight line as to be at rest. • At first, imagine the case of NO FRICTION Experiments Show • If NO NET FORCEis appliedto an object moving at a constant speed in straight line, it will continuemovingat the same speed in a straight line! • If I succeed in having you overcome the wrong, ancient misconception & understand the correct view, one of the main goals of the course will have been achieved!

13. Newton’s Laws • Galileo laid the ground work for Newton’s Laws. • Newton: Built on Galileo’s work • Now, Newton’s 3 Laws, one at a time.

14. Newton’s First Law Newton was born the same year Galileo died! • Newton’s First Law (“Law of Inertia”): “Every object continues in a state of rest or uniform motion (constant velocity) in a straight line unless acted on by a net force.”

15. Newton’s First Law of Motion • Inertial Reference Frames • Newton’s 1st Law: • Doesn’t hold in every reference frame. In particular, it doesn’t work in a reference frame that is accelerating or rotating. • An Inertial Reference frame is one in which Newton’s first law is valid. • This excludes rotating & accelerating frames. • How can we tell if we are in an inertial reference frame? • By checking to see if Newton’s • First Law holds!

16. Newton’s 1st Law • Was actually stated first stated by Galileo!

17. Newton’s First Law(Calvin & Hobbs) Mathematical Statement of Newton’s 1st Law: If v = constant, ∑F = 0 OR if v ≠ constant, ∑F ≠ 0

18. Conceptual Example Newton’s First Law. A school bus comes to a sudden stop, and all of the backpacks on the floor start to slide forward. What force causes them to do this?

19. Newton’s First LawAlternative Statement • In the absence of external forces, when viewed from an inertial reference frame, an object at rest remains at rest & an object in motion at constant velocity continues in motion with constant velocity • Newton’s 1st Lawdescribes what happens in the absence of a net force. • It also tells us that when no force acts on an object, the acceleration of the object is zero.

20. Inertia & Mass • InertiaThetendency of an object to maintain its state of rest or motion. • MASS A measure of the inertia of a mass. • The quantity of matter in an object. • As we already discussed, the SI System quantifies mass by having a standard mass = Standard Kilogram (kg). (Similar to standards for length & time). • The SI Unit of Mass = The Kilogram (kg) • The cgs unit of mass = the gram (g) = 10-3 kg • Weight is NOT the same as mass! • Weight is the force of gravity on an object. • Discussed later.

21. Newton’s Second Law(Lab) • Newton’s 1st Law: If no net force acts, an object remains at rest or in uniform motion in a straight line. • What if a net force acts? That is answered by doing Experiments! • It is found that, if the net force ∑F  0  Thevelocity v changes (in magnitude, in direction or both). • A change in the velocity v (Δv). There is an acceleration a = (Δv/Δt) OR A net force acting on a mass produces an Acceleration!!! ∑F  a

22. Newton’s 2nd Law Experiments Show That: • The net force ∑F on an object & the accelerationa of that object are related. • How are they related? Answer this by doing more EXPERIMENTS! Thousands of experiments over hundreds of years find (for an object of massm):a  ∑F/m (proportionality) • The SI system chooses the units of force so that this is not just a proportionality but an Equation:a  ∑(F/m) OR(total force!)  Fnet ∑F = ma

23. Newton’s 2nd Law:Fnet = ma • Fnet =the net (TOTAL!) force acting on mass m m =mass (inertia) of the object. a = acceleration of the object. OR, a = a description of the effect of F. OR, F is the cause of a. • To emphasize that F in Newton’s 2nd Lawis the TOTAL(net) force on the mass m, some texts write: ∑F = ma  Vector Sum of all Forces on mass m! ∑ = a math symbol meaning sum (capital sigma)

24. Based on experiment! Not derivable mathematically!! • Newton’s 2nd Law: ∑F = ma(A VECTOREquation!) It holds component by component. ∑Fx = max, ∑Fy = may, ∑Fz = maz ll THIS IS ONE OF THE MOST FUNDAMENTAL & IMPORTANT LAWS OF CLASSICAL PHYSICS!!!

25. Summary • Newton’s 2nd Lawis the relation between acceleration & force. • Acceleration is proportional to force & inversely proportional to mass. • It takes a force to change either the direction of motion or the speed of an object. • More force means more acceleration; the same force exerted on a more massive object will yield less acceleration.

26. Now, a more precise definition of Force: Force  An action capable of accelerating an object. Force is a vector & ΣF = ma is true along each coordinate axis. The SI unitof forceis The Newton (N) ∑F = ma,unit = kg m/s2  1N = 1 kg m/s2 Note The pound is a unit of force, not of mass, & can therefore be equated to Newtons but not to kilograms.

27. Laws or Definitions? These are NOT Laws! • When is an equation a “Law” & when is it just an equation? Compare • The one dimensional constant acceleration equations: v = v0 + at, x = x0 + v0t + (½)at2, v2 = (v0)2 + 2a (x - x0) • These are nothing general or profound. They are valid for constant a only. They were obtained from the definitions of a & v! With∑F = ma. • This is based on EXPERIMENT. It is NOTderived mathematically from any other expression! It has profound physical content & is very general. It is A LAW!! Also it is a definition of force! This is based on experiment! Not on math!!

28. Simple Example: Estimate the net force needed to accelerate (a) a 1000-kgcar at a = (½)g = 4.9 m/s2 (b) a 200-g appleat the same rate. Solutions: F = ma.

29. Simple Example: Estimate the net force needed to accelerate (a) a 1000-kgcar at a = (½)g = 4.9 m/s2 (b) a 200-g appleat the same rate. Solutions: F = ma. (a) F = (1000)(4.9) = 4.9  104 N

30. Simple Example: Estimate the net force needed to accelerate (a) a 1000-kgcar at a = (½)g = 4.9 m/s2 (b) a 200-g appleat the same rate. Solutions: F = ma. (a) F = (1000)(4.9) = 4.9  104 N (b) F = (0.2)(4.9) = 0.98 N

31. Another Simple Example: • Estimatethe net force needed to stop a car. • What average net force is needed to bring a1500-kgcar to rest from a speed of 100 km/h (27.8 m/s)in distance 55 m?

32. Another Simple Example: • Estimatethe net force needed to stop a car. • What average net force is needed to bring a1500-kgcar to rest from a speed of 100 km/h (27.8 m/s)in distance 55 m? Solution: A 2 step problem! 1. Calculate the acceleration a. Use a kinematic equation for constant a:v2= v02 + 2ax = 0. Soa = - (v02)/(2x) = - (27.8)2/[(2)(55)] = - 6.9 m/s2

33. Another Simple Example: • Estimatethe net force needed to stop a car. • What average net force is needed to bring a1500-kgcar to rest from a speed of 100 km/h (27.8 m/s)in distance 55 m? Solution: A 2 step problem! 1. Calculate the acceleration a. Use a kinematic equation for constant a:v2= v02 + 2ax = 0. Soa = - (v02)/(2x) = - (27.8)2/[(2)(55)] = - 6.9 m/s2 2. Use Newton’s 2ndLaw: F = ma = (1500)(-6.9) = -1.04 104 N