Ch 4 Motion Force DYNAMICS Force A push

Ch. 4, Motion & Force: DYNAMICS

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

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

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

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!

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

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, 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 speed in a straight line as to be at rest. Proven by Galileo in the 1620’s! – 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 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 • Newton’s 3 Laws: One at a time

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. ”

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

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

Newton’s First Law 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 that?

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 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).

Newton’s Second Law (Lab) • 1 st 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? Do Experiments. • Find, 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

• Experiment: The net force ∑F on a body and the acceleration a of 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 an equation: a ∑F/m OR: (total!) ∑F = ma

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

• Newton’s 2 nd Law: ∑F = ma Based on experiment! Not derivable mathematically!! A VECTOR equation!! Holds component by component. ∑Fx = max, ∑Fy = may, ∑Fz = maz 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: The one dimensional, constant acceleration kinematic equations: v = v 0 + at, x = x 0 + v 0 t + (½)at 2 NOT Laws! v 2 = (v 0)2 + 2 a (x - x 0) Nothing general or profound. Constant a in one dimension only. Obtained from the definitions of a & v! • With: ∑F = ma Based on EXPERIMENT. NOT derived mathematically from any other expression! Has profound physical content! Very general. A LAW!! Based on experiment! Not on math!! – Or definition of force!

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