Motion Force Dynamics Force A Force is A

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 1. “Contact” Forces: “Pulling” Forces “Pushing” Forces

Classes of Forces • Contact Forces involve physical contact between two objects – Examples (in the pictures): spring forces, pulling force, pushing force

Classes of Forces 1. “Contact” Forces: “Pulling” Forces “Pushing” Forces 2. “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 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.

Sir Isaac Newton 1642 – 1727 Also • Research on Alchemy! • Biblical Research! Was NOT a nice man! Bad Treatment of Scientific Colleagues! • Never Married • Entered Politics Late in Life

Newton’s Laws of Motion • The ancient (& 100% 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 21 st 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!

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 (“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 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 st 1 Law • Was actually stated first stated by Galileo!

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

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?

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 at constant velocity continues in motion with 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 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 1 st 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

Newton’s 2 nd Law Experiments Show That: • 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 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, some texts write: ∑F = ma 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 & 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 & ΣF = ma 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 physical content & is very general. It is A LAW!! Also it is a definition of force! This is based on experiment! Not on math!!

Simple Example: Estimate the net force needed to accelerate (a) a 1000 -kg car at a = (½)g = 4. 9 m/s 2 (b) a 200 -g apple at the same rate. Solutions: F = ma.

Simple Example: Estimate the net force needed to accelerate (a) a 1000 -kg car at a = (½)g = 4. 9 m/s 2 (b) a 200 -g apple at the same rate. Solutions: F = ma. (a) F = (1000)(4. 9) = 4. 9 4 10 N

Simple Example: Estimate the net force needed to accelerate (a) a 1000 -kg car at a = (½)g = 4. 9 m/s 2 (b) a 200 -g apple at the same rate. Solutions: F = ma. (a) F = (1000)(4. 9) = 4. 9 (b) F = (0. 2)(4. 9) = 0. 98 N 4 10 N

Another Simple Example: Estimate the net force needed to stop a car. • What average net force is needed to bring a 1500 -kg car to rest from a speed of 100 km/h (27. 8 m/s) in distance 55 m?

Another Simple Example: Estimate the net force needed to stop a car. • What average net force is needed to bring a 1500 -kg car to rest from a speed of 100 km/h (27. 8 m/s) in distance 55 m? Solution: A 2 step problem! 1. Calculate the acceleration a. Use a kinematic equation for constant a: v 2 = v 02 + 2 ax = 0. So a = - (v 02)/(2 x) = - (27. 8)2/[(2)(55)] = - 6. 9 m/s 2

Another Simple Example: Estimate the net force needed to stop a car. • What average net force is needed to bring a 1500 -kg car to rest from a speed of 100 km/h (27. 8 m/s) in distance 55 m? Solution: A 2 step problem! 1. Calculate the acceleration a. Use a kinematic equation for constant a: v 2 = v 02 + 2 ax = 0. So a = - (v 02)/(2 x) = - (27. 8)2/[(2)(55)] = - 6. 9 m/s 2 2. Use Newton’s 2 nd Law: F = ma = (1500)(-6. 9) = -1. 04 104 N