phy 130 - chapter 4 - dynamics -newton’s law of motion
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chapter 4 physics phy130TRANSCRIPT
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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
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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Chapter 4 Newtons third law of motion
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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Chapter 4 Newtons third law of motion
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 Newtons third law of motion
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Chapter 4 Newtons third law of motion
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
Application of Newtons Law of Motions Case 3 : Motion of a lift
Consider a person standing inside a lift as shown in figures.
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
Application of Newtons Law of Motions Case 3 : Motion of a lift
Consider a person standing inside a lift as shown in figures.
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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Chapter 4 4.4. Static Equilibrium Under Concurrent Force
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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Chapter 4 4.4. Static Equilibrium Under Concurrent Force
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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Chapter 4 Example 2:
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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Chapter 4 Example 3:
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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Chapter 4 Example 4:
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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Chapter 4 Example 5:
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)