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Chapter 4
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Goals for Chapter 4
• To understand force – either directly or as the
net force of multiple components.
• To study and apply Newton’s First Law.
• To study and apply the concept of mass and
acceleration as components of Newton’s
Second Law.
• To differentiate between mass and weight.
• To study and apply Newton’s Third Law.
• To open a new presentation of problem data in
a free body diagram.
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Dynamics, a new frontier
• Stated previously, the onset of physics
separates into two distinct parts:
– statics and
– dynamics.
• So, if something is going to be dynamic, what
causes it to be so?
– A force is the cause, it is either
• pushing or
• pulling.
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Types of Force Illustrated I – Figure 4.1
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Types of Force II – Figure 4.2
• Single or net
– Contact force
– Normal force
– Frictional force
– Tension
– Weight
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A force may be resolved into components – Figure 4.4
•Fx = F CosΘ
•Fy = F SinΘ
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Components and Resultants II – Figure 4.6
• An example of
component resolution.
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Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley
Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley
R = F1 + F2 + F3 + ……..= Σ F,
(resultant, and vector sum, of forces)
Rx = Σ Fx ,
Ry = Σ Fy
(components of vector sum of forces)
Once we have the components Rx and Ry, we can find the
magnitude and direction of the vector R.
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HOMEWORK
3; 5; 12; 13; 17; 18; 20; 22; 26; 28;
30; 31; 33; 35; 36; 37; 38
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Newton’s First Law – Figure 4.7
•“Objects at rest tend to
stay at rest and objects in
motion tend to stay in
motion in a straight line
unless it is forced to
change that state by forces
acting on it”
Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley
Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley
R = F1 + F2 = 0
• Zero resultant force is equal to no
force at all.
• When an object is acted on by no
forces or by several forces whose
vector sum (resultant) is zero, we say
that the object is in equilibrium,
R = Σ F = 0 (equilibrium under zero
resultant force)
Each component of R must be zero, so
Σ Fx = 0, Σ Fy = 0. (object in
equilibrium)
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We determine effect with the net force. – Figure 4.8
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Mass and Newton’s Second Law II – Figure 4.12
•Let’s examine some
situations with more than
one mass.
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INERTIA
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Newton’s Second Law of Motion (Vector Form)
The vector sum (resultant) of all the forces acting on an object
equals the object’s mass times its acceleration :
ΣF =
ma
The acceleration a has the same direction as the resultant force ΣF.
Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley
Newton’s Second Law of Motion (Components Form)
For an object moving in a plane, each component of the total force
equals the mass times the corresponding component of
acceleration:
ΣFx = max
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ΣFx = max
Definition of the newton
One newton is the amount of force that gives an
acceleration of 1 meter per second squared to an
object with a mass of 1 kilogram. That is,
1 N = (1 kg) ( 1 m/s2)
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ON THE MOON
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Measurement of mass – Figure 4.20
•Since gravity is
constant, we can
compare forces to
measure unknown
masses.
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Forces are the origin of motion
Forces
Acceleration a=F/m
Velocity
v= v0 + at
Position
x = x0 + v0t + ½ at2
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Forces and free body diagrams
• we account for the forces and draw a free body diagram.
•In this case, the net force is unbalanced.
•This is a good example of forces in dynamics.
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Newton’s Third Law
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Newton’s Third Law
•“For every action there is
an equal and opposite
reaction.”
•Rifle recoil is a wonderful
example.
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Newton’s Third Law
For two interacting objects A and B, the formal
statement of Newton’s third law is
FA on B = -FB on A
Newton’s own statement, translated from the latin of
the Principia, is
To every action there is always opposed an equal
reaction; or, the mutual actions of two objects upon
each other are always equal, and directed to contrary
parts.
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Free-Body Diagram
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Use free body diagrams in any situation – Figure 4.24
•Find the
object of
the focus
of your
study
and
collect all
forces
acting
upon it
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Homework
• 3, 9, 14, 20, 21, 23, 30, 34, 41, 52
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