Chapter 4
Force; Newton’s Laws of
Motion
Classical Mechanics


Describes the relationship between
the motion of objects in our
everyday world and the forces acting
on them
Conditions when Classical Mechanics
does not apply
• very tiny objects (< atomic sizes)
• objects moving near the speed of light
Forces



Usually think of a force as a push or pull
Vector quantity
May be a contact force or a field force
• Contact forces result from physical contact
between two objects: pushing, pulling
• Field forces act between disconnected objects


Also called “action at a distance”
Gravitational force: weight of object
Contact and Field Forces

F
Force as vector


Magnitude + Direction
Components Fx, Fy
Fy
tan  
Fx
Fx  F cos
Fy  F sin 


Units: Newton (N),
pound(lb)
1lb=4.45N
F  Fx2  Fy2
y

F
Fy

x
Fx
Addition of Forces

A



A
Tail-to tip method


B
Parallelogram method
Components method

A

B

B
  
C  A B
Examples

Parallel forces

F1=150N, F2=100N and 53° to F1
Newton’s First Law

An object moves with a velocity that
is constant in magnitude and
direction, unless acted on by a
nonzero net force
• The net force is defined as the vector
sum of all the external forces exerted on
the object
External and Internal Forces

External force
• Any force that results from the
interaction between the object and its
environment

Internal forces
• Forces that originate within the object
itself
• They cannot change the object’s
velocity
Inertia

Is the tendency of an object to
continue in its original motion
Mass



A measure of the resistance of an
object to changes in its motion due
to a force
Scalar quantity
SI units are kg
Condition for Equilibrium


Net force vanishes
No motion
F  F  F
1

F
F
2
 F3  ...  0
x
F1x  F2 x  F3 x  ...  0
y
F1 y  F2 y  F3 y  ...  0
Newton’s Second Law

The acceleration of an object is
directly proportional to the net force
acting on it and inversely
proportional to its mass.
F  ma
• F and a are both vectors
Units of Force

SI unit of force is a Newton (N)
kg m
1N  1 2
s

US Customary unit of force is a
pound (lb)
• 1 N = 0.225 lb
Sir Isaac Newton





1642 – 1727
Formulated basic
concepts and laws
of mechanics
Universal
Gravitation
Calculus
Light and optics
Weight

Falling object
F  mg


Weight w=mg
Object on a table?
Weight

The magnitude of the gravitational
force acting on an object of mass m
near the Earth’s surface is called the
weight w of the object
• w = m g is a special case of Newton’s
Second Law


g is the acceleration due to gravity
g can also be found from the Law of
Universal Gravitation
More about weight

Weight is not an inherent property of
an object
• mass is an inherent property

Weight depends upon location
Newton’s Third Law

If object 1 and object 2 interact, the
force exerted by object 1 on object 2
is equal in magnitude but opposite in
direction to the force exerted by
object 2 on object 1.
•
F12  F21
• Equivalent to saying a single isolated
force cannot exist
Newton’s Third Law cont.

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 forces act
on different objects
Example: Force Table
Three forces in equilibrium!
Find tension in each cable supporting
the 600N sign
Examples


Calculate the acceleration of the box
A 50 kg box is pulled across a 16m
driveway
Projectile Motion(Ch. 5)


Example of motion in 2-dim
An object may move in both the x
and y directions simultaneously
• It moves in two dimensions


The form of two dimensional motion
we will deal with is called projectile
motion
vo and o
Assumptions of Projectile
Motion



We may ignore air friction
We may ignore the rotation of the
earth
With these assumptions, an object in
projectile motion will follow a
parabolic path
Rules of Projectile Motion


The horizontal motion (x) and vertical of
motion (y) are completely independent of
each other
The x-direction is uniform motion
• ax = 0

The y-direction is free fall
• ay = -g

The initial velocity can be broken down
into its x- and y-components
•
vOx  vO cos  O
vOy  vO sin  O
Projectile Motion
Projectile Motion at Various
Initial Angles

Complementary
values of the
initial angle result
in the same range
• The heights will be
different

The maximum
range occurs at a
projection angle
of 45o
Some Details About the Rules

Horizontal motion
• vx =vxo =vo coso
• x = xo+vxot
v xo  v o cos o  v x  constant

This is the only operative equation in the xdirection since there is uniform velocity in
that direction
More Details About the Rules

Vertical motion-- free fall problem
• vy=vosino-gt
v y o  v o sin o
• y=yo+ (vosino)t-(1/2)gt2
• the positive direction as upward
• uniformly accelerated motion, so the
motion equations all hold
Velocity of the Projectile

The velocity of the projectile at any
point of its motion is the vector sum
of its x and y components at that
point
2
x
v  v v
2
y
and
  tan
1
vy
vx
• Remember to be careful about the
angle’s quadrant
Example

Superman hits a home run with
vo=15m/s and o=60°
Some useful results

Trajectory
g
2
y  (tan  o ) x  2
x
2
2vo cos  o

Maximum Height
v sin  o
h
2g
2
o

Range
2
vo2 sin( 2 o )
R
g
Example
A daredevil jumps a canyon 15m wide
by driving a motorcycle up an incline
sloped at an angle of 37° with the
horizontal. What minimum speed
must she have in order to clear the
canyon? How long will she be in the
air?