Applied Building Science I (ABC105D)

By: F.V. Molefe (molefefv@tut.ac.za)

2022
 Contents
❑ Introduction
❖ Learning Outcome 5
❖ The concept of Force and Mass
❖ Newton’s First Law of Motion
❖ Newton’s Second Law of Motion
❖ The Vector Nature of Newton’s second Law
❖ Newton’s Third Law of Motion
❖ Types of Forces: an overview
❖ The gravitational Force
❖ The Normal Force
❖ Static and Frictional Forces
❖ The Tension Force
❖ Equilibrium Application of Newton’s Laws of Motion
❖ Non-equilibrium Application of Newton’s Laws of Motion
 Introduction
In science and engineering various forces are investigated to show that they
can change either the shape of an object or its motion. Both balanced and
unbalanced forces are considered. Force can be defined as any action that
tends to maintain or alter the motion of a body or to distort it. The concept of
force is commonly explained in terms of Isaac Newton's three laws of motion.
Because a force is a vector quantity, it is said to have both magnitude and
direction. The representation of forces by vectors implies that they are
concentrated either at a single point or along a single line. Physicists use the
newton which is the International System (SI) unit for measuring force. A
newton is the force needed to accelerate a body weighing one kilogram by
one metre per second. The formula F = ma is employed to calculate the
number of newtons required to increase or decrease the velocity of a given
body.
4.1 The Concepts of Force and Mass

What is force ?
A force is a push or a pull.

Contact forces arise from physical

contact .

Action-at-a-distance forces do not

require contact and include gravity and
electrical forces.
4.1 The Concepts of Force and Mass

Arrows are used to represent forces. The length of the arrow

is proportional to the magnitude of the force.

15 N

5N
4.1 The Concepts of Force and Mass

Mass is a measure of the amount

of “stuff” contained in an object.
4.2 Newton’s First Law of Motion
Newton’s First Law
An object continues in a state of rest or in a state
of motion at a constant speed along a straight
line, unless compelled to change that state by a
net force. If no net force acts on a body, the
body’s velocity cannot change that is the body
cannot accelerate
The net force is the vector sum of all of the
forces acting on an object.
4.2 Newton’s First Law of Motion

The net force on an object is the vector sum of all forces

acting on that object.

The SI unit of force is the Newton (N).

Individual Forces Net Force

4N 10 N 6N
4.2 Newton’s First Law of Motion

Individual Forces Net Force

3N 5N
64

4N

The net force is

obtained using the 5N 3N
tail to head method
4N
4.2 Newton’s First Law of Motion

Inertia is the natural tendency of an object to

remain at rest or in motion at a constant speed
along a straight line.
It is the resistance of any physical object to any
change in its velocity. This includes changes to
the object speed or direction of motion.
4.2 Newton’s First Law of Motion

This occurs because of Newton’s First Law. Thus, an

object at rest or in motion will continue to be in the
same state unless acted upon by an external force.

The mass of an object is a quantitative measure of

inertia.
SI Unit of Mass: kilogram (kg)
4.2 Newton’s First Law of Motion

An inertial reference frame is one in which Newton’s

Law of Inertia is valid.
All accelerating reference frames are non-inertial. It
takes a net force >0 to cause anything to accelerate.
An object at rest v= 0 𝑚/𝑠(constant velocity) will
remain at rest and an object in motion v= 3𝑚/𝑠 will
continue in motion at a constant velocity unless acted
upon by a net force >0.
4.3 Newton’s Second Law of Motion

Mathematically, the net force is

written as 

F

where the Greek letter sigma

denotes the vector sum.
4.3 Newton’s Second Law of Motion
Newton’s Second Law
When a net external force acts on an object of mass m, the
acceleration that results is directly proportional to the net force
and has a magnitude that is inversely proportional to the mass.
The direction of the acceleration is the same as the direction of
  
F
the net force.

a=
m
 F = ma
Net Force and acceleration always act in the same direction. If
you double the Force, acceleration will increase by factor of 2,
but if you triple the mass the acceleration will be reduced by
factor of 3.
4.3 Newton’s Second Law of Motion
SI Unit for Force
 m  kg  m
(kg )  2  = 2
s  s
This combination of units is called a newton (N).

In a figure presented below, what would be the magnitude and

direction of acceleration when the indicated force is applied on
the 5kg object?

𝐹Ԧ = 40𝑁 𝑎Ԧ = 8𝑚/𝑠 2
5kg
4.3 Newton’s Second Law of Motion
4.3 Newton’s Second Law of Motion

Two people are pushing a stalled car, as shown in the figure.

The mass of the car is 1850 kg. One person applies a force of
275 N to the car, while the other applies a force of 395 N.
Both forces act in the same direction. A third force of 560 N
also acts on the car, but in a direction opposite to that in
which the people are pushing. This force arises because of
friction and the extent to which pavement opposes the
motion of the tires. Find the acceleration of the car.
4.3 Newton’s Second Law of Motion

A free-body-diagram is a diagram that represents the object

and the forces that act on it.
4.3 Newton’s Second Law of Motion

The net force in this case is:

275 N + 395 N – 560 N = +110 N

and is directed along the + x axis of the coordinate system.

4.3 Newton’s Second Law of Motion
If the mass of the car is 1850 kg then, by N’s 2𝑛𝑑 law, the acceleration
is:
a=
 F + 110 N
= = +0.059 m s 2
m 1850 kg
(a) Use a diagram and calculate the net force and give magnitude of
force (b) Calculate the acceleration and determine its direction.

𝐹Ԧ = 19𝑁 𝐹Ԧ = 35𝑁
8kg

𝐹Ԧ 𝑛𝑒𝑡 = −16𝑁 𝑚𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑖𝑠 16 𝑁

𝑎Ԧ = −2𝑚/𝑠 2 to the left
4.4 The Vector Nature of Newton’s Second Law
The direction of force and acceleration vectors can be taken into
account by using x and y components.
 
 F = ma

is equivalent to

F y = may  Fx = max
4.4 The Vector Nature of Newton’s Second Law
A man is stranded on a raft (mass of man and raft is 1300 kg), as
shown in the figure. By paddling, he causes an average force P, of
17 N to be applied to the raft in a direction due east. The wind
also exerts a force A on the raft. This force has a magnitude of 15
N and points 67° north of east. Ignoring any resistance from the
water, find the x and y components of the raft’s acceleration.
4.4 The Vector Nature of Newton’s Second Law
4.4 The Vector Nature of Newton’s Second Law

The net force on the raft can be calculated in the following way:

Force x component y component

+17 N 0N

P
 +(15 N) cos67 +(15 N) sin67
A
+23 N +14 N
4.4 The Vector Nature of Newton’s Second Law

ax =
 F x
=
+ 23 N
= +0.018 m s 2

m 1300 kg

ay =
 F y
=
+ 14 N
= +0.011 m s 2

m 1300 kg
4.5 Newton’s Third Law of Motion

Newton’s Third Law of Motion

Whenever one body exerts a force on a second body, the
second body exerts an oppositely directed force of equal
magnitude on the first body.

Action and Reaction.

4.5 Newton’s Third Law of Motion

Suppose that the magnitude of the force is 36 N. If the mass of

the spacecraft is 11,000 kg and the mass of the astronaut is 92 kg,
what are the accelerations?
4.5 Newton’s Third Law of Motion
 
On the spacecraft 
F = P.

On the astronaut  F = −P.


 P + 36 N
as = = = +0.0033 m s 2

ms 11,000 kg


 − P − 36 N
aA = = = −0.39 m s 2

mA 92 kg
4.6 Types of Forces: An Overview

In nature there are two general types of forces,

fundamental and non-fundamental.

Fundamental Forces

1. Gravitational force

2. Strong Nuclear force

3. Electroweak force
4.6 Types of Forces: An Overview

Examples of non-fundamental forces:

friction

tension in a rope

normal or support forces

4.7 The Gravitational Force
Newton’s Law of Universal Gravitation
Every particle in the universe exerts an attractive force on every
other particle.

A particle is a piece of matter, small enough in size to be

regarded as a mathematical point.

The force that each exerts on the other is directed along the
line joining the particles.

All objects accelerates at the same rate due to gravitational

attraction.
4.7 The Gravitational Force
For two particles that have masses m1 and m2 and are
separated by a distance r, the force has a magnitude given by
m1m2
F =G 2 G = 6.673 10 −11
N  m kg
2 2

r
G represents a very small number called a gravitational constant.
4.7 The Gravitational Force

m1m2
F =G 2
r
(
= 6.67 10 −11
N  m kg
2 2
) (12 kg )(25 kg )
(1.2 m )2

−8
= 1.4 10 N
4.7 The Gravitational Force
4.7 The Gravitational Force
Definition of Weight

The weight of an object on or above the earth is the

gravitational force that the earth exerts on the object. The
weight always acts downwards, toward the center of the earth.

On or above another astronomical body, the weight is the

gravitational force exerted on the object by that body.

SI Unit of Weight: newton (N)

4.7 The Gravitational Force
Relation Between Mass and Weight
From Newton’s second law
F= 𝑚𝑎, now when the net M Em
force acting on an object is W =G 2
r
coming from gravity the
acceleration is equal to mass
of bigger object mass (M) of W = mg
the earth times the
Gravitational constant ME
g =G 2
r
4.7 The Gravitational Force

On the earth’s surface:

ME
g =G 2
RE

(
= 6.67 10 −11
N  m kg
2 2 () 5.98 10 kg )
24

(6.38 10 m)
6 2

= 9.80 m s 2
4.8 The Normal Force
Definition of the Normal Force
The normal force is one component of the force that a surface
exerts on an object with which it is in contact – namely, the
component that is perpendicular to the surface.
4.8 The Normal Force

FN − 11 N − 15 N = 0

FN = 26 N

FN + 11 N − 15 N = 0

FN = 4 N
4.8 The Normal Force

Apparent Weight
The apparent weight of an object is the reading of the scale.

It is equal to the normal force the man exerts on the scale.

4.8 The Normal Force

F y = + FN − mg = ma

FN = mg + ma

true
apparent weight
weight
4.9 Static and Kinetic Frictional Forces
When an object is in contact with a surface there is a force
acting on that object. The component of this force that is
parallel to the surface is called the frictional force.

Frictional force opposes

motion and is caused by the
interaction between two
objects. Friction is said to slow Imperfections seen when probing using
microscope
down objects.
4.9 Static and Kinetic Frictional Forces

When the two surfaces are not

sliding across one another the
friction is called static friction.

When an object is in motion

on the surface, surface exerts
force on the object such as
normal force (perpendicular
to surface) and the frictional
force (parallel to the surface).
4.9 Static and Kinetic Frictional Forces

The magnitude of the static frictional force can have any value
from zero up to a maximum value.

fs  f s
MAX

f s
MAX
= s FN

0  s is called the coefficient of static friction.

4.9 Static and Kinetic Frictional Forces

Note that the magnitude of the frictional force does not depend
on the contact area of the surfaces.
4.9 Static and Kinetic Frictional Forces
Static friction opposes the impending relative motion between
two objects.

Kinetic friction opposes the relative sliding motion.

f k = k FN

0  k is called the coefficient of kinetic friction.

4.9 Static and Kinetic Frictional Forces
4.9 Static and Kinetic Frictional Forces

A sled and its rider are moving at a speed of 4.0 m/s along a
horizontal stretch of snow as shown in the figure below.
The snow exerts a kinetic frictional force on the runners of
the sled, so the sled slows down and eventually comes to a
stop.
4.9 Static and Kinetic Frictional Forces

The sled comes to a halt because the kinetic frictional force

opposes its motion and causes the sled to slow down.
4.9 Static and Kinetic Frictional Forces

Suppose the coefficient of kinetic friction is 0.05 and the total

mass is 40kg. What is the kinetic frictional force?
f k =  k FN =  k mg =
(
0.05(40kg ) 9.80 m s = 20 N
2
)
4.10 The Tension Force

Cables and ropes transmit

forces through tension.
4.10 The Tension Force

A massless rope will transmit

tension undiminished from one end
to the other.

If the rope passes around a

massless, frictionless pulley, the
tension will be transmitted to the
other end of the rope
undiminished.
4.11 Equilibrium Application of Newton’s Laws of Motion

Definition of Equilibrium
An object is in equilibrium when it has zero acceleration.

 Fx = 0

 Fy = 0
4.11 Equilibrium Application of Newton’s Laws of Motion
Reasoning Strategy

• Select an object(s) to which the equations of equilibrium are to

be applied.
• Draw a free-body diagram for each object chosen above.
Include only forces acting on the object, not forces the object
exerts on its environment.
• Choose a set of x, y axes for each object and resolve all forces
in the free-body diagram into components that point along these
axes.
• Apply the Newton’s laws equations and solve for the unknown
quantities.
4.11 Equilibrium Application of Newton’s Laws of Motion
Figure here shows a traction device used with a foot injury. The weight
of the 2.2 object creates a tension in the rope that passes around the
pulleys. Therefore, tension forces 𝑇1 and 𝑇2 are applied to the pulley
on the foot. The foot pulley is kept in equilibrium because the foot also
applies a force 𝐹Ԧ to it. This force arises in reaction (Newton’s third law)
to the pulling effect of the forces 𝑇1 and 𝑇2 . Ignoring the weight of the
foot, find the magnitude of 𝐹. Ԧ
4.11 Equilibrium Application of Newton’s Laws of Motion
Solving for F and letting T = 𝑇1 = 𝑇2 .
We find that F = 2Tcos35°.
However, the tension T in the
rope is determined by the
weight of the 2.2 kg object:
T =mg, where m is its mass
and g in the acceleration due
to gravity. Therefore, the
magnitude of F is
F=2Tcos35° = 2mgcos35° + T1 sin 35 − T2 sin 35 = 0
 

F= 2(2.2)(9.8)cos35° =35N.
+ T1 cos 35 + T2 cos 35 − F = 0
 
4.11 Equilibrium Application of Newton’s Laws of Motion
An automobile engine
has weight 𝑊=
3150𝑁 and it is
positioned above
compartment using
rope as shown in the
Figure. To position the
engine, a worker is
using a rope. Find the
tension 𝑇1 in supporting
cable and 𝑇2 in
positioning rope.
4.11 Equilibrium Application of Newton’s Laws of Motion
Force x component y component


T1 − T1 sin 10.0 + T1 cos 10.0 


T2 + T2 sin 80.0 − T2 cos 80.0 


W 0 −W

W = 3150 N
4.11 Equilibrium Application of Newton’s Laws of Motion

 Fx = − T1 sin 10.0 + T2 sin 80.0 = 0

F y = + T1 cos 10.0 − T2 cos 80.0 − W = 0

 

 sin 80.0 
The first equation gives T1 =  T
  2
 sin 10.0 
Substitution into the second gives

 sin 80.0 
 T
  2
cos 10.0 
− T2 cos 80.0 
−W = 0
 sin 10.0 
4.11 Equilibrium Application of Newton’s Laws of Motion

W
T2 =
 sin 80.0 
 
 
cos 10.0 
− cos 80.0 

 sin 10.0 

T2 = 582 N T1 = 3.30 10 N 3

4.12 Non-equilibrium Application of Newton’s Laws of Motion

When an object is accelerating, it is not in equilibrium.

 Fx = max

 Fy = may
4.12 Non-equilibrium Application of Newton’s Laws of Motion
A super tanker of mass 𝑚 = 1.50 × 108 𝑘𝑔 is being towed by two tugboats,
as shown in the Figure. The tensions in the towing cables apply forces 𝑇1 and
𝑇2 at equal angles of 30° with respect to the tankers axis. In addition, the
tankers engines produce a forward drive force and 𝐷 whose magnitude is
D = 75.0 × 103 N. Moreover, the water applies an opposing force 𝑅, whose
magnitude is R = 40.0 × 103 N. The tanker moves forward with an
acceleration that points along the tanker’s axis and has a magnitude of 2.00×
10−3 𝑚. 𝑠 −2 . Find the magnitude of the tensions 𝑇1 and 𝑇2 .
4.12 Non-equilibrium Application of Newton’s Laws of Motion

The acceleration is along the x axis so ay = 0

4.12 Non-equilibrium Application of Newton’s Laws of Motion
Force x component y component


T1 + T1 cos 30.0 
+ T1 sin 30.0 


T2 + T2 cos 30.0 
− T2 sin 30.0 


D +D 0
 −R 0
R
4.12 Non-equilibrium Application of Newton’s Laws of Motion

F y = + T1 sin 30.0 − T2 sin 30.0 = 0



 T1 = T2

F x = + T1 cos 30.0 + T2 cos 30.0 + D − R



= max
(mass = 1.50 x10 kg) 8
4.12 Non-equilibrium Application of Newton’s Laws of Motion

T1 = T2 = T

max + R − D
T= 
= 1.53 10 N
5

2 cos 30.0
 Summary

• Forces are investigated to show that they can change either the shape
of an object or its motion.
• Force can be defined as any action that tends to maintain or alter the
motion of a body or to distort it.
• Force as a vector quantity is said to have both magnitude and
direction.
• Physicists use the newton which is the International System (SI) for
measuring force.
• Investigation of equilibrium and non-equilibrium applications of
forces has been carried out.
End!