Motion & Force: DYNAMICS

Obviously, vector addition is needed to add forces! 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!

Electricity & Magnetism Classes of Forces “Pushing” Forces “Pulling” Forces 1. “Contact” Forces: 2. “Field” Forces: Physics II: Electricity & Magnetism Physics I: Gravity

Contact Forces involve physical contact between two objects 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 Note: These are all field forces! Gravitational Forces Between masses Electromagnetic Forces Between electric charges Nuclear Weak Forces 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 a 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. The “natural” state of an object is at rest. In the 21st Century, its still a common MISCONCEPTION!! THE CORRECT VIEW (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.

Newton’s Laws of Motion THE CORRECT VIEW (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 Experiments Show 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!

Now, Newton’s 3 Laws, one at a time. 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’s First Law (“Law of Inertia”): 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 1st Law: Doesn’t hold in every reference frame. In particular, it doesn’t work in 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 1st Law Was actually stated first stated by Galileo!

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

What force causes them to do this? Conceptual Example 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? 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.

Inertia & Mass Inertia  The tendency of an object to maintain its state of rest or motion. MASS  A measure of the inertia of a mass. The quantity of matter in an object. As we already discussed, the SI System quantifies mass by having a standard mass = Standard Kilogram (kg). (Similar to 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.

Newton’s Second Law (Lab) Newton’s 1st Law: If no net force acts, an object remains at rest or in uniform motion in a straight line. What if a net force acts? That 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 mass produces an Acceleration!!! ∑F  a

 Fnet  ∑F = ma Newton’s 2nd Law Experiments Show That: EXPERIMENTS! The net force ∑F on an object & the acceleration a of that object 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 2nd Law: Fnet = ma ∑F = ma  Vector Sum of all Forces 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 2nd Law is the TOTAL (net) force on the mass m, some texts write: ∑F = ma  Vector Sum of all Forces on mass m! ∑ = a math symbol meaning sum (capital sigma)

MOST FUNDAMENTAL & IMPORTANT LAWS OF CLASSICAL PHYSICS!!! Newton’s 2nd 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!!! Based on experiment! Not derivable mathematically!!

It takes a force to change either the direction 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. Figure 4-5. Caption: The bobsled accelerates because the team exerts a force.

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

v = v0 + at, x = x0 + v0t + (½)at2, v2 = (v0)2 + 2a (x - x0) Laws or Definitions? 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 NOT derived mathematically from any other expression! It has profound physical content & is very general. It is A LAW!! Also it is a definition of force! These are NOT Laws! This is based on experiment! Not on math!!

Example: The force to stop a car. Example: Estimate the net force needed to accelerate (a) a 1000-kg car at a = (½)g = 4.9 m/s2 (b) a 200-g apple at the same rate. Example: The 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.