phy 130 - chapter 4 - dynamics -newton’s law of motion

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PHY130

Chapter 4

Dynamics: Newtons Law of Motion

Assoc. Prof. Dr. Ahmad Taufek Abdul Rahman PhD (Medical Physics), University of Surrey, UK

M.Sc. (Radiation Health Physics), UTM

B.Sc. Hons. (Physics & Math), UTM

[email protected]

[email protected]

https://www.facebook.com/DR.ATAR.UiTM

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4.0 Dynamics: Newtons Law of Motion

4.1 Definition of force

4.2 Types of forces

4.2.1 Gravitational force

4.2.2 Normal force

4.2.3 Frictional force

4.2.4 Tensional force

4.3 Newtons Law of Motion and its application

4.3.1 Newtons First Law

4.3.2 Newtons Second Law

4.3.3 Newtons Third Law

4.4 Static equilibrium under concurrent force

Chapter 4

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Chapter 4

4.1. Definition of Force

The concept of Force

A force is an action exerted upon a body in order to change its

state, either rest, or of uniform motion in a straight line.

A force can change the motion of a body, for example its

causing a body to start moving or stop a body is already

moving. Its also can squeeze, stretch or tear an object.

Force is a vector quantity, so its must be stated by the

magnitudes with the direction of the force action.

Unit of force ~ Newton (N) or kg ms-2.

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Chapter 4

Force, Weight and Mass

Force = mass acceleration

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Chapter 4

Weight and Mass Mass, m

is defined as a measure of a bodys inertia.

is a scalar quantity.

The S.I. unit of mass is kilogram (kg).

The value of mass is independent of location.

If the mass of a body increases then its inertia will increase.

Weight,

is defined as the force exerted on a body under gravitational field.

It is a vector quantity.

It is dependant on where it is measured, because the value of g varies at

different localities on the earths surface.

It always directed toward the centre of the earth or in the same direction of acceleration due to gravity, g.

The S.I. unit is kg m s-2 or Newton (N).

inertiamass

gmW

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Chapter 4

4.2. Types of Force

Gravitational Force

is the force with which the gravity pulls

downward upon it

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Chapter 4

4.2. Types of Force

Normal Force

is the perpendicular component of the

force exerted by the supporting surface on

the surface being supported

is defined as a reaction force that exerted

by the surface to an object interact with it

and the direction always perpendicular to

the surface.

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Chapter 4

4.2. Types of Force

Frictional Force

is defined as a force that resists the

motion of one surface relative to another

with which it is in contact.

is independent of the area of contact

between the two surfaces..

is directly proportional to the reaction

force

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Chapter 4

4.2. Types of Force

Tensional Force

is the force with which the strings pulls

upon the object to which it is attached.

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Chapter 4 4.3 Newtons Law of Motion and its Application Newtons first law of motion

states an object at rest will remain at rest, or continues to move with uniform velocity in a straight line unless it is acted upon by a external forces

The first law gives the idea of inertia.

0FFnett

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Chapter 4 Newtons first law of motion

Inertia is defined as the tendency of an object to resist any change in its state of rest or motion.

is a scalar quantity.

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Chapter 4 Newtons second law of motion

The acceleration of an object is directly proportional to the nett force acting on it and inversely proportional to its mass.

Also states as

the rate of change of linear momentum of a moving body is proportional to the resultant force and is in the same direction as

the force acting on it

dt

pdF

amF

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Chapter 4 Newtons second law of motion

One Newton (1 N) is defined as the amount of net force that gives an acceleration of one meter per second squared to a body with a mass of

one kilograms.

OR 1 N = 1 kg m s-2

Notes:

is a nett force or effective force or resultant force.

The force which causes the motion of an object.

If the forces act on an object and the object moving at uniform acceleration (not at rest or not in the equilibrium) hence

amFFnett

F

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Chapter 4 Newtons third law of motion

states every action force has a reaction force that is equal in magnitude but opposite in direction.

For example : When the student push on the wall it will push back with the

same force. (refer to figure)

BAAB FF

is a force by the hand on the wall (action)

is a force by the wall on the hand (reaction) BAF

ABF

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When a book is placed on the table.

If a car is accelerating forward, it is because its tyres are pushing backward on the road and the road is pushing forward on the tyres.

A rocket moves forward as a result of the push exerted on it by the exhaust gases which the rocket has pushed out.

In all cases when two bodies interact, the action and reaction forces act on different bodies.

Force by the book on the table (action)

Force by the table on the book (reaction)

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Every action must have

a reaction where the

action and reaction

force are acting on the

different direction with

a same magnitude.

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Every action must have

a reaction where the

action and reaction

force are acting on the

different direction with

a same magnitude.

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Chapter 4

Force and Motion

An Equilibrium of Force

Consider two situation happened when the sum of all the

forces acting on an object is zero

v = 0

FR

FW

v

F fs

Constant

Velocity

Static

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Chapter 5

Application of Newtons Law of Motions

A. Reaction (normal) force,

is defined as a reaction force that exerted by the surface to an object interact with it and the direction always perpendicular to

the surface.

Case 1: Horizontal surface

An object lies at rest on a flat horizontal surface as shown in figure.

0mgNFy mgN

Action: weight of an object is exerted on the

horizontal surface

Reaction: surface is exerted a force, N on the object .

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Chapter 5

Application of Newtons Law of Motions Case 2 : Inclined plane

An object lies at rest on a rough inclined plane as shown in figure.

mgWx sin mgWy cos

0yy WNF

Component of the weight :

cosmgN

Action: y-component of the objects weight is exerted

on the inclined surface.

Reaction: surface is exerted a force, N on the object.

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Chapter 5

Application of Newtons Law of Motions Case 3 : Motion of a lift

Consider a person standing inside a lift as shown in figures.

a. Lift moving upward at a uniform velocity

Since the lift moving at a uniform velocity, thus

0ya

0yF0mgN

mgN

amF

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Chapter 5



b. Lift moving upwards at a constant acceleration, a

By applying the Newton's 2nd law of motion, thus

yy maF

mamgN

gamN

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Chapter 5



c. Lift moving downwards at a constant acceleration, a

By applying the Newton's 2nd law of motion, thus

yy maF

maNmg

agmN

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Chapter 5

Application of Newtons Law of Motions

B. Frictional force, is defined as a force that resists the motion of one surface relative to another with which it is in contact.

is independent of the area of contact between the two surfaces..

is directly proportional to the reaction force.

OR

Coefficient of friction,

is defined as the ratio between frictional force to reaction force.

OR

is dimensionless and depends on the nature of the surfaces.

Nf

Nf force frictional:f

friction oft coefficien :

forcereaction : N

where

N

f

f

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Chapter 5 There are three types of frictional force :

Static, fs (frictional force act on the object before its move)

Kinetic, fk (frictional force act on the object when its move)

Rolling, fr (frictional force act on the object when its rolling)

Caution:

The direction of the frictional force exerted by a surface on an object is always in the opposite direction of the motion.

The frictional and the reaction forces are always perpendicular.

Nf kk Nf ss

Nf rr skr fff where

thus skr

Can be ignored

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Case 1 : Horizontal surface

Consider a box of mass m is pulled along a horizontal surface

by a horizontal force, F as shown in figure.

x-component :

y-component :

maFF nettxmafF

0yFmgN

Chapter 5

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Case 2 : Inclined plane

Consider a box of mass m is pulled along an inclined plane by a force, F as shown in figures.

fmgmaF

mafWF

maF

x

x

sin

x-component

(parallel to the inclined plane) :

y-component

(perpendicular to the inclined plane:

mgN

WN

maF

y

y

cos

0

Chapter 5

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Chapter 4 4.4. Static Equilibrium Under Concurrent Force

Definition Concurrent forces:

Are forces whose lines of action all pass through a

common point.

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What are the equilibrium conditions under the

action of concurrent forces?

The resultant of all forces acting on an object

must be zero. or

The sum of all x-components is zero.

The sum of all y-components is zero.

The sum of all z-components is zero.

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When an object is in equilibrium

If it is at rest and remains at rest. or if it is in motion

with constant vector velocity

What are the types of equilibrium

Static-Equilibrium: The object it is at rest and remains

at rest.

Translational-Equilibrium: The object is in motion

with constant vector velocity

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Chapter 4

Problem Solving There are five steps in applying the force equation to solve problems in

mechanics:

Identify the object whose motion is considered.

Determine the forces exerted on the object.

Draw a free body diagram for each object.

is defined as a diagram showing the chosen body by itself, with vectors drawn to show the magnitude and directions of all the forces applied to the body by the other bodies that interact with it.

Choose a system of coordinates so that calculations may be simplified.

Apply the equation above,

Along x-axis:

Along y-axis:

xxmaF

yy maF

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Chapter 4 Example 1:

Three wooden blocks connected by a rope of negligible mass are being dragged

by a horizontal force, F in figure.

Suppose that F = 1000 N, m1 = 3 kg, m2 = 15 kg and m3 = 30 kg. Determine

a)the acceleration of blocks system.

b)the tension of the rope, T1 and T2.

Neglect the friction between the floor and the wooden blocks.

1T

m1 m2 m3 2T

F

2s m 20.8 a N 9361T N 6242T

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Two objects of masses m1 = 10 kg and m2 = 15 kg are connected by a light string

which passes over a smooth pulley as shown in figure. Calculate

a)the acceleration of the object of mass 10 kg.

b)the tension in the each string.

(Given g = 9.81 m s2)

m1

m2

2s m 1.96 a N 118 TTT 21

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Two blocks, A of mass 10 kg and B of mass 30 kg, are side by side and in contact

with each another. They are pushed along a smooth floor under the action of a

constant force F of magnitude 200 N applied to A as shown in figure. Determine

a)the acceleration of the blocks,

b)the force exerted by A on B.

A B

F

2s m 5.0 a N 150 BAAB FF N 150ABF

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A box of mass 20 kg is on a rough horizontal plane. The box is pulled

by a force, F which is applied at an angle of 30 above horizontal as

shown in figure 3.28. If the coefficient of static friction between the box

and the plane is 0.3 and the box moves at a constant speed, calculate

a. the normal reaction force,

b. the applied force F,

c. the static friction force.

(Given g = 9.81 m s-2)

N 167N N 57.9F N 50.1sf

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A block of mass 200 kg is pulled along an inclined plane of 30 by a

force, F = 2 kN as shown in figure. The coefficient of kinetic friction of

the plane is 0.4. Determine

a. the normal force,

b. the nett force,

c. the acceleration of the block,

d. the time taken for the block to travel 30 m from rest.

(Given g = 9.81 m s-2)

N 1015N N 492nettF2s m 2.46 a s 4.94t

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Thank You & All the Best

Peace cannot be kept by force; it can only be achieved by

understanding.

(Albert Einstein)

phy 130 - chapter 4 - dynamics -newton’s law of motion

Documents

mass force

types of force normal

types of force tensional

unit of force

definition of force

force action

reaction force

concept of force