Ch. 4, Motion & Force: DYNAMICS

1. Ch. 4, 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. Classes of Forces “Pushing” forces “Contact” Forces: “Pulling” forces “Field” Forces: Physics II: Electricity & Magnetism Physics I: Gravity

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

5. The 4 Fundamental Forces of Nature • Gravitational Forces • Between objects • Electromagnetic Forces • Between electric charges • Nuclear Weak Forces • Arise in certain radioactive decay processes • Nuclear Strong Forces • Between subatomic particles Note: These are all field forces!

6. 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.

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

8. Newton’s Laws of Motion In the 21st Century, this is still a common MISCONCEPTION!!! • The ancient (& wrong!) view (of Aristotle): • A force is needed to keep an object in motion. • The “natural” state of an object is at rest. • THE CORRECT VIEW(of 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 • Experiment: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! Proven by Galileo in the 1620’s!

9. 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.

10. Newton’s First Law Newton was born the same year Galileo died! • Newton’s First Law(The “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.”

11. 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 such 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!

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

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

14. Conceptual Example 4-1: 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?

15. 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 continues in motion with a 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.

16. Inertia & Mass • InertiaThetendency of a body to maintain its state of rest or motion. • MASSA measure of the inertia of a body. • The quantity of matter in a body. • The SI System quantifies mass by having a standard mass = Standard Kilogram (kg) (Similar to the 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 in the chapter.

17. Newton’s Second Law(Lab) • Newton’s 1st Law: If no net force acts, an object remains at rest or in uniform motion in straight line. • What if a net force acts? That question 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 velocityv (Δv). There is an accelerationa = (Δv/Δt)OR A net force acting on a body produces an acceleration!∑F  a

18. Newton’s 2nd Law Experiments Show That: The net force ∑F on a body & the accelerationa of that body 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

19. 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 2ndLawis the TOTAL(net) force on the mass m, your text writes: ∑F = ma ∑ = a math symbol meaning sum (capital sigma)  The Vector Sum of all Forces on mass m!

20. 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!!!

21. Summary • Newton’s 2nd Lawis the relation between acceleration & force. • Acceleration is proportional to force and 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.

22. Now, a more precise definition of Force: Force  An action capable of accelerating an object. Force is a vector & 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.

23. 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!!

24. Examples Example 4-2: Estimate the net force needed to accelerate (a) a 1000-kgcar at a = (½)g (b) a 200-g appleat the same rate. Example 4-3: Force to stop a car. What average net force is required to bring a1500-kgcar to rest from a speed of 100 km/h (27.8 m/s) within a distance of 55 m?