Ch. 4, Motion & Force: DYNAMICS

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

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

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. gravitation, electrostatic, magnetic

Fundamental Forces of Nature Note: These are all field forces! 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!

Basic Laws of Mechanics Law of Universal Gravitation 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. 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 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! In the 21st Century, still a common MISCONCEPTION!!! Proven by Galileo in the 1620’s!

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’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 was born the same year Galileo died!

Newton’s First Law of Motion Inertial Reference Frames Newton’s 1st 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 1st Law: First stated by Galileo!

Newton’s First Law A Mathematical Statement of Newton’s 1st 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? Answer: No force; the backpacks continue moving until stopped by friction or collision.

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 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.

(Similar to standards for length & time). 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) 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? 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

HOW? Answer by EXPERIMENTS! 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

∑F = ma 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 effect of ∑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!

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

Summary Newton’s 2nd law is the relation between acceleration & force. Acceleration is proportional to force and inversely proportional to mass. Figure 4-5. Caption: The bobsled accelerates because the team exerts a force. 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.

The SI unit of force is the Newton (N) ∑F = ma, unit = kg m/s2 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.

The one dimensional, constant acceleration kinematic equations: 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. NOT derived 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!!

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? Figure 4-6. 4-2. Use Newton’s second law: acceleration is about 5 m/s2, so F is about 5000 N for the car and 1 N for the apple. 4-3. First, find the acceleration (assumed constant) from the initial and final speeds and the stopping distance; a = -7.1 m/s2. Then use Newton’s second law: F = -1.1 x 104 N.