Forces - handout.pdf

(1)

(2)

At the end of this chapter, you should be able to

• Comprehend the origins and reasons of motion

DYNAMICS

• Define FORCE based on different situations and conditions • Distinguish an inertial and a non-inertial reference frame

FORCES AND NEWTON’S LAWS

• Enumerate and define different forces based on

(3)

Two Schools:

• Kinematics and Dynamics

Kinematics: The study of motion

Dynamics: The study of forces (those who give rise to motion)

Mechanics also cover work, energy, power and momentum!

(4)

Push a piece of ice on a counter top!

• It slides then it stops. • If the counter is wet,

the ice will travel

further before stopping.

• Galileo, later Newton, recognized that slowing of objects in everyday experience is due to

friction (a type of force) • Before Galileo, it was

thought that a force

(5)

 The water in this case

reduced the friction. This allowed the ice to travel further with little change in its velocity.

• Remove all external forces on an object,

Galileo reasoned, and its velocity will never

change-- a property of matter he described as inertia.

• This conclusion,

restated by Newton as his first law, is

also called the law of inertia.

(6)

If no forces act on an object, it continues in its original state of motion; that is, unless

something exerts an external force on it, an object at rest remains at rest and an object

moving with some velocity continues with that same velocity.

0

F

(7)

Two Statements:

STATIC EQUILIBRIUM:

• An object at rest stays at rest unless acted on by an

external force.

DYNAMIC EQUILIBRIUM:

• An object in motion continues to travel with constant

velocity unless acted upon by an external force.

(8)



Elementary Definition:

• A force is simply a push or a pull.



Fundamental Definition #1 (1

st

Law):

• A force is any external influence that causes a

(9)

Vector quantity

May be contact

or field force

(10)

You are driving along a straight road at a

(11)



Answer: Neither! Since both cars

have constant velocities, they are in

equilibrium, meaning the net force on

both cars is

zero

(12)

Newton's First Law:

• There is NO distinction between a body at rest and a

body moving at constant velocity.

Whether an object is at rest or moving with

(13)

A reference frame is a set of coordinate systems at rest relative to each other.

A reference frame in which the law of inertia holds exactly is termed as an inertial reference frame.

“Any reference frame moving with constant

velocity relative to an inertial reference frame is also an inertial reference frame.”

(14)

A reference frame accelerating relative to an

inertial reference frame is NOT an inertial reference frame.

(15)



Newton's first law thus gives us the

criterion for determining if a reference

frame is an inertial frame or not.

(16)

If we attach a coordinate system to each one

of the following, which is an inertial reference frame?

a) An apple falling from a tree

b) A girl riding on a Merry Go Round moving at constant velocity

c) A car rounding a sharp curve

(17)

Inertia is the tendency of an object to continue in its original motion

Mass is a measure of the inertia, i.e resistance of an object to changes in its motion due to a force

Recall: mass is a scalar quantity

(18)

1. If an object has no acceleration, can you

conclude that no forces are acting on it?

2. If the velocity of a body is zero, is there any

force acting on it?

3. Is it possible for an object to round a curve

(19)

A spacecraft engine dies when it is moving in the vacuum of outer space far from any planet (We assume that no force is acting on the system). Will the spacecraft stop? What does Newton’s first law say about this?

(20)

(21)

 Fundamental Definition #2

 Force is a vector.

 The magnitude of the force is the product of the

mass of the object and the magnitude of its acceleration

 The direction of the force is the direction of the

acceleration it causes if it is the only force acting on the body.

 Newton's Second Law-- The Law of Acceleration  |F_net| = m |a|

(22)

 It is found experimentally that two or more

forces acting on a single object accelerates it as if the object were acted on by a single force equal to the vector sum of the individual

forces.

 That is, forces combine as vectors. Newton's

2nd Law is thus



ΣF =

_F

net = m a

(23)

F



:

x x

y y

z z

F

ma

F

ma

F

ma

F

ma

(24)

Magnitude of the force is the product of mass and acceleration.

We know what acceleration is, don’t we? However, what is mass?

Mass is an intrinsic property of an object that measures its resistance to acceleration...

(25)

 The ratio of two masses is defined qualitatively

by applying the same force to each mass and comparing their accelerations.

 If a force F produces acceleration a

1 when

applied to an object of mass m₁,

 And the same force F produced an acceleration a

2

when applied to an object of mass m₂, then the ratio of the masses is defined by

(26)

The definition agrees with our intuitive idea

of mass.

If the same force is applied to two objects, the

(27)

A car rounds a curve while maintaining a constant

speed. Is there a net force on the car as it rounds the curve?

1. No—its speed is constant. 2. Yes.

3. It depends on the sharpness of the curve and the speed of the car.

4. It depends on the driving experience of the driver.

Note: Acceleration is a change in the speed

and/or direction of an object. Thus, because its direction has changed, the car has

(28)

An object experiences an acceleration of

3m/s2 when a force F acts on it

(a) What is the acceleration when the force is

doubled?

(b) A second object experiences an acceleration of

9m/s2 _{under the influence of the same force.}

What is the ratio of the mass of the 2 objects?

(c) If the two objects are tied together, what

(29)

 What net force is needed to uniformly

stop an automobile whose mass is 1500 kg, from a velocity of 100 km/h to rest, on a distance of 55 m?

(30)

 Fundamental Definition #3:

 Force, is used to describe the interaction

(31)

 Newton's Third law states that these forces

are equal in magnitude and opposite in direction.

 If object A exerts a force F on object B, object B exerts a force on A that is equal in

magnitude and opposite in direction.  F

BA = - FAB

(32)



Thus, forces always occurs in

pairs

.



It is common to refer to one force in the

pair as an

action

and the other as

reaction

.



This terminology is unfortunate because

it sounds like one force

“

reacts

”

to the

other, which is

NOT TRUE.

• Because both of the forces occur simultaneously!

(33)

(34)

 A boy stated that “if I exert a force on a box by

kicking it, then by Newton’s third law, the box will also kick me with a force equal in magnitude but in the opposite direction.

 Thus, since there are two forces with equal in

magnitude and opposite in direction, by vector addition these forces will just cancel and the net force will be zero.

 If the net force acting on the box is zero, then the

(35)



Action

and

Reaction

forces can

NEVER

BALANCE

each other because they act on

different bodies!

(36)

 Consider collision of two

spheres

 F₁₂ may be called the

action force and F₂₁ the reaction force

• Actually, either force can be the action or the

reaction force

 The action and reaction

(37)

A. The small guy.

B. The football player.

(38)

(39)

 Elementary Definition:

• A force is simply a push or a pull.

• Fundamental Definition #1 (1st _Law):

– A force is any external influence that causes a change in the state of motion of a particle or systems of particles

(40)

• Fundamental Definition #2

• Force is a vector.

• The magnitude of the force is the product of the mass of the object and the magnitude of its

acceleration

• The direction of the force is the direction of the

(41)

41

Fundamental Definition #3

(42)

Physical Properties:

Dimensions:

• Mass Times Length over Time over Time (ML/T2)

Type: Derived SI Unit:

(43)

1. If an object has no acceleration in an inertial reference frame, can you conclude that no forces are acting on it? Why?

2. If an object is accelerating in an inertial

reference frame, can you say that there is a force acting on it? Why?

3. If an object is acted upon a single known force, can you tell in which direction the

object will move using no other information? Why?

(44)

There are two ways to classify forces:

1. Nature of the Force

(45)

All the different forces observed in nature can be explained in terms of four basic interactions

that occur between elementary particles

• 1. The gravitational force • 2. The weak nuclear force • 3. The electromagnetic force

• 4. The strong nuclear force (hadronic force)

(46)

 Contact Forces

(47)

 Force At-A-Distance

47

• Forces that are found between two particles separated in space.

• This creates a philosophical problem.

(48)

 A diagram that shows schematically all the forces acting on a body in a system.

 Constraints: Conditions on the motion of an object, such as

• If the object/system is to remain at rest

• If the object/system is to remain in uniform motion • If the object/system is accelerating/decelerating • Getting angles of repose

(49)

1. Applied Force 2. Weight

3. Tensile (Tension) 4. Normal Force

5. Frictional

6. Hookean Spring Forces

• A. Compressive Spring Force • B. Extensive Spring Force

(50)

 These are forces that are applied to systems by

force loads, and can't be classified as other types of forces

 Classification can not be carried out since

simplicity is maintained

(51)

 This is the force due to gravity exerted by a

heavenly object on a small object in its field.  It is always directed

downwards (or towards the center of the

heavenly object

 Symbol and Formula:  w = mg

(52)

 It is a force that

arises from pulling using strings.

 It is always directed

away from the

(53)

 This force is always directed perpendicular to the surface of contact.

 This force arises due to the resistance of the materials from being penetrated or

compressed. (Law of Material Impenetrability)

 The normal force acts as a balancer or support.

 Symbol: η (Greek Letter ETA)

(54)

(55)

 This force is always directed

parallel to the surface of contact.

 This force acts as a

motion-retarder (or motion stopper), thus it is always directed

against the direction of motion

 Two types: Static and Kinetic  Symbol: f: f_s and f_k

 Formula: f = μη ; μ is the

coefficient of friction

(56)

 It is a force that arises when a system has springs in it.

 Springs are materials that are capable of compression and extension.

 When a spring is compressed or extended at a certain displacement (Δx) a “restoring force” tends to return the spring system to its original state.

(57)

(58)

Conventions:



Hooke’s Law: Defining Law for Spring

Systems

• F_Δx = -k Δx

 Symbols used:

F_Δx : hookean spring force

(59)

(60)

(61)

(62)

Draw the FBD of the following. Identify all

forces acting on the system: 1. A book is at rest on a table top

2. A girl is suspended motionless from the ceiling by two ropes

3. An egg is free-falling from a nest in a tree