Ch. 4, Motion & Force: DYNAMICS

1. Ch. 4, Motion & Force: DYNAMICS

2. Force Force: “A push or a pull”. F is a VECTOR! Vector Addition is needed vector to add Forces!

3. “Pushing” force Classes of Forces “Contact” forces: “Pulling” forces “Field” forces(Physics II):

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

5. 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. 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 and Optics

7. Newton’s Laws of Motion In the 21st Century, 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 FORCE is applied to an object moving at a constant speed in straight line, it will continuemoving at 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!

8. Newton’s Laws • Galileo laid the ground work for Newton’s Laws. • Newton: Built on Galileo’s work • Newton’s 3 Laws: One at a time

9. 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 aNET FORCE.”

10. Newton’s First Law of Motion Inertial Reference Frames Newton’s 1st lawdoesn’t hold in every reference frame, such as a reference frame that is accelerating or rotating. An inertial reference frame is one in which Newton’s first law is valid. 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!

11. Newton’s 1st Law:First stated by Galileo!

12. Newton’s First Law A Mathematical Statement of Newton’s 1st Law: If v = constant, ∑F = 0 OR if v ≠ constant, ∑F ≠ 0

13. 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 that?

14. 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 Law describes 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.

15. Inertia & Mass • InertiaThetendency of an object to maintain its state of rest or motion. • MASS:A measure of the inertia of an object • Quantity of matter in a body • Quantify mass by having a standard mass = Standard Kilogram (kg) (Similar to standards for length & time). • SI Unit of Mass = Kilogram (kg) • cgs unit = gram (g) = 10-3 kg • Weight: (NOT the same as mass!) • The force of gravity on an object (later in the chapter).

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

17. Experiment: The net force ∑F on a body and the acceleration aof that body are related. • HOW? Answer by EXPERIMENTS! • Thousands of experiments over hundreds of years find (for an object of mass m): a  ∑F/m(proportionality) • We choose the units of force so that this is not just a proportionality but anequation: a  ∑F/m OR:(total!) ∑F = ma

18. Newton’s 2nd Law:∑F = ma ∑F =the net (TOTAL!) force acting on mass m m =the mass (inertia) of the object. a =acceleration of the object. a is a description of the effectof ∑F ∑F is the cause of a. • To emphasize that the F in Newton’s 2nd Law is the TOTAL(net) force on the mass m, your text writes: ∑F = ma ∑ = a math symbol meaning sum (capital sigma) Vector Sum of all Forces!

19. Based on experiment! Not derivable mathematically!! • Newton’s 2nd Law: ∑F = ma AVECTOR equation!! Holds component by component. ∑Fx = max, ∑Fy = may, ∑Fz = maz ONE OF THE MOST FUNDAMENTAL & IMPORTANT LAWS OF CLASSICAL PHYSICS!!!

20. Summary Newton’s 2nd law is 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.

21. 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 unit of force is 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.

22. Laws or Definitions • When is an equation a “Law” & when is it just an equation? • Compare: The one dimensional, constant acceleration kinematic equations: v = v0 + at, x = x0 + v0t + (½)at2 v2 = (v0)2 + 2a (x - x0) Nothing general or profound. Constant a in one dimension only. Obtained from the definitions of a & v! • With:∑F = ma Based on EXPERIMENT.NOTderived mathematically from any other expression! Has profound physical content! Very general.  A LAW!! • Or definition of force! NOT Laws! Based on experiment! Not on math!!

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