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Chapter 4

The Laws of Motion

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Force

Force is associated with the change in the stat of motion of an object.

Force is required to make an object move from stationay.

What is the relation between the force on an object and the change in motion of that object?

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4.1 Classes of Forces Contact forces

involve physical contact between two objects

Field forces act through empty space No physical contact

is required

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Magnitudes of Forces A spring can be

used to calibrate the magnitude of a force

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Forces are vectors

Forces are vectors, so you must use the rules for vector addition to find the net force acting on an object

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Fundamental Forces All particles in nature are subject to four

fundamental forces Strong force Electromagnetic force Weak force Gravitational force

This list is in order of decreasing strength

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Nature of the four fundamental forces

Gravitational forces between objects with masses

Electromagnetic forces between electric charges

Strong nuclear forces between subatomic particles

Weak nuclear forces for certain radioactive decay processes

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Nuclear Force Holds nucleons together Strongest of all fundamental forces Very short-ranged

Less than 10-15 m (1fm) Negligible for separations greater than this

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31.1 Atoms as Elementary Particles

Atoms From the Greek for “indivisible” Were once thought to be the elementary

particles Atom constituents

Proton, neutron, and electron After 1932 (neutrons are found in this year)

these were viewed as elementary for they are very stable

All matter was made up of these particles

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Discovery of New Particles New particles

Beginning in 1945, many new particles were discovered in experiments involving high-energy collisions

Characteristically unstable with short lifetimes ( from 10-6s to 10-23s)

Over 300 have been cataloged and form a particle zoo

A pattern was needed to understand all these new particles

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Elementary Particles – Quarks Now, physicists recognize that most particles

are made up of quarks Exceptions include photons, electrons and a few

others The quark model has reduced the array of

particles to a manageable few Protons and neutrons are not truly

elementary, but are systems of tightly bound quarks

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Electromagnetic Force Responsible for binding atoms and

molecules together to form matter About 10-2 times the strength of the

nuclear force A long-range force that decreases in

strength as the inverse square of the separation between interacting particles

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Weak Force To account for the radioactive decay process

such as beta decay in certain nuclei Its strength is about 10-5 times that of the

strong force Short-range force Scientists now believe the weak and

electromagnetic forces are two manifestions of a single interaction, the electroweak force

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Gravitational Force A familiar force that holds the planets,

stars and galaxies together A long-range force It is about 10-41 times the strength of the

nuclear force Weakest of the four fundamental forces Its effect on elementary particles is

negligible

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Explanation of Forces Forces between particles are often

described in terms of the exchange of field particles or quanta The force is mediated by the field particles Photons for the electromagnetic force Gluons for the nuclear force W+, W- and Z particles for the weak force Gravitons for the gravitational force

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Forces and Mediating Particles

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Force and Motions:Isaac Newton (1642-1727)

Three Newton’s laws of motion

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4.2 Newton’s First Law: The Law of Inertia

A moving object can be observed from a number of reference frame.

Observers in different reference frames may describe the motion of the object differently.

If an object does not interact with other objects, it is possible to identify a reference frame in which the object has zero acceleration Such a reference frame is also called an inertial

frame of reference

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Inertial Frames Any reference frame that moves with constant

velocity relative to an inertial frame is itself an inertial frame

A reference frame that moves with constant velocity relative to the distant stars is the best approximation of an inertial frame We can consider the Earth to be such an inertial

frame although it has a small centripetal acceleration associated with its motion

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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 and an object in motion continues in motion with a constant velocity Newton’s First Law describes what

happens in the absence of a force When no force acts on an object, the

acceleration of the object is zero

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4.3 Inertia and Mass The tendency of an object to resist any

attempt to change its velocity is called inertia

Mass is the property of an object that specifies how much resistance an object exhibits to change in its velocity

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More About Mass An inherent property of an object Independent of the object’s

surroundings Independent of the method used to

measure it Mass is a scalar quantity The SI unit of mass is kg

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Mass vs. Weight Mass and weight are two different

quantities Weight is equal to the magnitude of the

gravitational force exerted on the object The weight of an object will vary with

location The mass of an object is the same

everywhere

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4.4 Newton’s Second Law The acceleration of an object is directly

proportional to the net force acting on it and inversely proportional to its mass Force is the cause of change in motion, as

measured by the acceleration Algebraically,

Fa

m

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More About Newton’s Second Law is the net force

This is the vector sum of all the forces acting on the object

Newton’s Second Law can be expressed in terms of components: Fx = m ax

Fy = m ay

Fz = m az

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Units of Force

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Fig 4.4

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4.5 Gravitational Force The gravitational force, , is the force

that the earth exerts on an object This force is directed toward the center

of the earth Its magnitude is called the weight of the

object Weight = Fg = mg

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More About Weight Because it is dependent on g, the

weight varies with location g, and therefore the weight, is less at

higher altitudes We can compare the masses of two

objects by measuring their weights. At a given location, the ratio of the weights of two objects equals the ratio of their masses.

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Gravitational Mass vs. Inertial Mass

In Newton’s first Law, the mass is the inertial mass and measures the resistance to a change in the object’s motion

In the gravitational force Fg=mg, the mass is determined by the gravitational attraction between the object and the Earth.

The mass of an object obtained in this way is called the gravitational mass.

Experiments show that gravitational mass and inertial mass have the same value

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4.6 Newton’s Third Law If two objects interact, the force

exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1

Note on notation: is the force exerted

by A on B

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Action-Reaction Examples, 1

The force exerted by object 1

on object 2 is equal in magnitude and opposite in direction to exerted by object 2 on object 1

Fig 4.5

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Fig 4.5

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Newton’s Third Law, Alternative Statements Forces always occur in pairs A single isolated force cannot exist The action force is equal in magnitude to the

reaction force but opposite in direction One of the forces is the action force, the other is

the reaction force It doesn’t matter which is considered the action

and which the reaction The action and reaction forces must act on

different objects and be of the same type

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Action-Reaction Examples, 2 The action force (table on

monitor) is the reaction of the force that the monitor exerts on the table

Normal means perpendicular, in this case

The action (Earth on monitor) force is equal in magnitude and opposite in direction to the reaction force (the monitor exerts on the Earth) Fig 4.6(a)

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Normal force The normal force is a contact force that

is perpendicular to the contact surface.

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Free Body Diagram

In a free body diagram, you want the forces acting on a particular object

The normal force and the force of gravity are the forces that act on the monitor

The normal force balances the gravitational force.

Fig 4.6(b)

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Fig 4.7

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4.7 Applications of Newton’s Law

Objects in equilibrium If the acceleration of an object is zero,

the object is said to be in equilibrium Mathematically, the net force acting on

the object is zero

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Fig 4.9

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Problem-Solving Hints Newton’s Laws Conceptualize the problem – draw a

diagram Categorize the problem

Equilibrium (F = 0) or Newton’s Second Law (F = m a)

Analyze Draw free-body diagrams for each object Include only forces acting on the object

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Equilibrium, Example 2a Example 4.2 Conceptualize the

traffic light Categorize as an

equilibrium problem No movement, so

acceleration is zero

Fig 4.10(a)

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Equilibrium, Example 2b

Analyze Need two free-body

diagrams Apply equilibrium

equation to the light and find

Apply equilibrium equations to the knot and find and

Fig 4.10(b)(c)

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Objects Experiencing a Net Force If an object that can be modeled as a

particle experiences an acceleration, there must be a nonzero net force acting on it.

Draw a free-body diagram Apply Newton’s Second Law in

component form

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Newton’s Second Law, Example 1a Forces acting on the

crate: A tension, the

magnitude of force The gravitational

force, The normal force, ,

exerted by the floor

Fig 4.8

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Newton’s Second Law, Example 1b Apply Newton’s Second Law in component

form:

Solve for the unknown(s) If is constant, then a is constant and the

kinematic equations can be used to more fully describe the motion of the crate

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Inclined Planes

Forces acting on the object: The normal force acts

perpendicular to the plane The gravitational force acts

straight down Choose the coordinate

system with x along the incline and y perpendicular to the incline

Replace the force of gravity with its components

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Fig 4.11

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Multiple Objects When two or more objects are

connected or in contact, Newton’s laws may be applied to the system as a whole and/or to each individual object

Whichever you use to solve the problem, the other approach can be used as a check

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Multiple Objects, Example 1 Forces acting on the

objects: Tension (same for both

objects, one string) Gravitational force

Each object has the same acceleration since they are connected

Draw the free-body diagrams

Apply Newton’s Laws Solve for the unknown(s)

Fig 4.12

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Multiple Objects, Example 2

First treat the system as a whole:

Apply Newton’s Laws to the individual blocks

Solve for unknown(s) Check: |P21| = |P12|

Fig 4.13

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Fig 4.14

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Exercises of Chapter 4

7, 14, 17, 25, 29, 31, 33, 46, 49, 51, 56

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Exercise 49

What horizontal force must be applied to the cart shown in Figure on the right so that the blocks remain stationary relative to the cart? Assume that all surfaces, wheels, and pulley are frictionless. (Suggestion: Note that the force exerted by the string accelerates m1.)