Note - Chapter 04

8/11/2019 Note - Chapter 04

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Chapter 4

Newtons Laws of Motion

4.1 Forces and Interactions

Aforceis a push or a pull. It is that which causes an

object to accelerate. The unit of force in the metric system

is the Newton. Force is a vector quantity.

Superposition of Forces

Any number of external forces applied to an object has

the same effect as a single force equal to the vector sum

of the external forces.


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4.2 Newtons First Law of Motion

Every body continues in its state of rest or of uniform

motion in a straight line unless it is compelled by a forceto change that state.

That is, a body acted on by NO NET EXTERNAL

FORCE moves with constant velocity (which may be

zero) and zero acceleration.

r

F =0"

When the net external force acting on an object is zero,

the object is said to be in a state of translational

equilibrium.

4.3 Newtons Second Law of Motion

The netforce !Fr

acting on an object of mass m is

equal to the product of the objects mass with its

acceleration ar

.

! = amF r

r


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Note that the netforce (or resultantforce)!Fr

is in the

same direction as the acceleration vector ar

. This is

illustrated in the following picture.

4.4 Mass and Weight

The massof an object is that property that specifies howmuch resistance the object exhibits to changes in its

velocity (a measure of the inertia of the object).

Mass is ascalarquantity.

The unit of mass in the metric system is the kilogram.

Weight is aforceexerted on a body by the earth. Weight

is thus a vectorquantity.


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Newtons Law of Universal Gravitation:

Every particle (with non-zero mass) in the universe

attractsevery other particle (with non-zero mass) with a

force that is directly proportional to the product of theirmasses and inversely proportional to the square of the

distance between them. That is,

2

21

r

mmGF =

r

where

G= 6.67x10-11

Nm2/kg

2= the universal gravitational

constant.

r= distance from the center of mass of one particle to thecenter of mass of the other particle.

The attractive force exerted by the Earth on an object is

called thegravitational forcer

Fg orr

W . This force is called

the weightof the object, and its directionis toward the

center of the Earth. The weightof an object of mass monthe Earth has a magnitudeequal to:

r

Fg =Weight=GMEm

RE2


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The quantity2

E

E

R

MG appears so often that it is given the

name gr

or simply g. This quantity is also called thegravitational fieldgenerated by the Earth at locations near

its surface. The gravitational field gr

is a vectorquantity

with a directiontoward the center of the Earth, and with a

magnitudedefined as

2

E

E

RMGgg ==

r

using

G = 6.67x10-11

Nm2/kg

2

ME= 5.98x1024

kg (mass of the Earth)

RE= 6.37x106

m (radius of the Earth)

yields a value of g = 9.8 m/s2. One can thus say that the

weightof an object of mass mon the surface of the Earth

is

r

W = mr

g

where gr

= the acceleration due to gravity (or the

gravitational field), always directed toward the center of

the Earth.


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Mass and weight are thus related quantities. The

magnitudeof a bodys weight Wis directly proportional

to its mass m.

4.5 Newtons Third Law (Action-Reaction Law)

If body A exerts a forcer

FAonB

on body B, then body

B exerts an equal (magnitude) and opposite (direction)forcer

FBon A

on body A.

r

FAonB

= "

r

FBon A

Forces always occur in pairs.

Essentially, you cannot touch without being touched!


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4.6 Solving Problems with Newtons Laws: Free-Body

Diagrams

Objects in Equilibrium:An object is said to be in mechanical equilibrium when

twoconditions are met:

(1) The net forceacting on the object is equal tozero.

This ensures translational equilibrium.

From ! = amF r

r

we see that if ! =0Fr

, then

ttanconsv0a =!=!rr

That is, the object is

(i) at rest and stays at rest or

(ii) the object moves in a straight line with constantspeed.

(2) The net torqueacting on the object iszero.

This ensures rotational equilibrium. The object is

(i) at rest and stays at rest or

(ii) the object spins about a fixed axis with constant

angular speed.

We will discuss rotational equilibrium in chapter 10.


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Strategy for applying Newtons laws of motion:

(1) Isolate (consider) a part of the system or the entire

system and draw the forces acting ON it. This iscalled afree-body diagram.

(2) Apply Newtons 2nd

law of motion in component

form. That is, solve

!! == yyxx maFmaF

(3) Solve for any unknown quantities.

(4) If the acceleration of the object is constant, then you

may also apply the kinematic equations of motion.

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Note - Chapter 04