Ch 4 Motion Force DYNAMICS Force A Force

Ch. 4, Motion & Force: DYNAMICS

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

Classes of Forces “Contact” Forces: “Pulling” forces “Pushing” forces “Field” Forces: Physics I: Gravity Physics II: Electricity & Magnetism

Classes of Forces • Contact Forces involve physical contact between 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

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!

The 4 Fundamental Forces of Nature Sources of 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.

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.

Newton’s Laws of Motion • The ancient (& wrong!) view (of Aristotle): – A force is needed to keep an object in motion. In the 21 st Century, this is still a common – The “natural” state of an object is at rest. MISCONCEPTION!!! • THE CORRECT VIEW (of Galileo & Newton): – It’s just as natural for an object to be in motion at constant Proven by Galileo speed in a straight line as to be at rest. – At first, imagine the case of NO FRICTION in the 1620’s! – Experiment: If NO NET FORCE is applied to an object moving at a constant speed in straight line, it will continue moving 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!

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.

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. ”

Newton’s First Law of Motion Inertial Reference Frames Newton’s 1 st 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!

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

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

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?

Newton’s First Law Alternative 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 1 st 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.

Inertia & Mass • Inertia The tendency 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.

Newton’s Second Law (Lab) • Newton’s 1 st 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 The velocity 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 body produces an acceleration! ∑F a

Newton’s 2 nd Law Experiments Show That: The net force ∑F on a body & the acceleration a 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 mass m): 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

Newton’s 2 nd 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 2 nd Law is the TOTAL (net) force on the mass m, your text writes: ∑F = ma The Vector Sum of all Forces on mass m! ∑ = a math symbol meaning sum (capital sigma)

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

Summary • Newton’s 2 nd 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.

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/s 2 1 N = 1 kg m/s 2 Note The pound is a unit of force, not of mass, & can therefore be equated to Newtons but not to kilograms.

Laws or Definitions? • When is an equation a “Law” & when is it just an equation? Compare These are NOT Laws! • The one dimensional constant acceleration equations: v = v 0 + at, x = x 0 + v 0 t + (½)at 2, v 2 = (v 0)2 + 2 a (x - x 0) 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 NOT derived mathematically from any other expression! It has profound This is based on physical content & is very general. experiment! It is A LAW!! Not on math!! Also it is a definition of force!

Example 4 -2: Examples Estimate the net force needed to accelerate (a) a 1000 -kg car at a = (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 a 1500 -kg car to rest from a speed of 100 km/h (27. 8 m/s) within a distance of 55 m?