ch. 4, motion & force: dynamics

Ch. 4, Motion & Force: DYNAMICS

Force

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!

Classes of Forces “Pulling” forces“Contact” Forces:

“Pushing” forces

“Field” Forces:

Physics I: Gravity Physics II: Electricity & Magnetism

• 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

Classes of 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!

The 4 Fundamental Forces of Nature

The 4 Fundamental Forces of NatureSources 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 Newton1642 – 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.– 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, this is 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 workNow, Newton’s 3 Laws, one at a time.

Newton’s First Law

• 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 wasborn the sameyear Galileo

died!

Newton’s First Law of MotionInertial Reference Frames

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

Newton’s First Law(Calvin & Hobbs)

A Mathematical Statement of Newton’s 1st LawIf v = constant, ∑F = 0

ORif 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?

• 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.

Newton’s First LawAlternative Statement

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 1st 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 2nd LawExperiments 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 2nd Law: Fnet = maFnet = 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, your text writes:

∑F = ma

∑ = a math symbol meaning sum (capital sigma)

The Vector Sumof all Forces on mass m!

• Newton’s 2nd Law: ∑F = ma

A VECTOR Equation!! It holds component by component.

∑Fx = max, ∑Fy = may, ∑Fz = mazll

THIS IS ONE OF THE MOST FUNDAMENTAL & IMPORTANTLAWS 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.• 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/s2

1N = 1 kg m/s2

NoteThe pound is a unit of force, not of mass, & can therefore be equated to Newtons but not to kilograms.

Laws or Definitions?

These are NOT Laws!

This is based onexperiment!

Not on math!!

• 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!

ExamplesExample 4-2:

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?