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”

Forces1. “Contact” Forces:

“Pushing” Forces

Physics I: GravityPhysics II:

Electricity & Magnetism

2. “Field” 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

Classes of 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

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 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!

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 (“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 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 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’sFirst 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 ORif 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?

• 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 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)

ORA net force acting on a mass produces

an Acceleration!!! ∑F a

Newton’s 2nd LawExperiments 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 moreEXPERIMENTS!

Thousands of experiments over hundreds ofyears 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 anEquation: a ∑(F/m) OR (total force!)

Fnet ∑F = ma

Newton’s 2nd 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 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)

• 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 &

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.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/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.

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!

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?