Download Chapter 3 - "Patterns of Motion"

• Patterns of Motion
In a moving airplane, you feel forces in many
directions when the plane changes its motion. You
cannot help but notice the forces involved when there
is a change of motion.
• Laws of Motion
Among other accomplishments, Sir Isaac Newton
invented calculus, developed the laws of motion, and
developed the law of gravitational attraction.
• Newton's First Law of Motion
– Every object remains in its state of rest or motion
unless acted upon by an unbalanced force.
– Objects tend to remain either at rest or in straight
line motion.
– This tendency to resist changes in motion is
inertia.
– Mass is a measure of the amount of inertia an
object has.
Top view of a person standing in the aisle of a bus. (A)
The bus is at rest, and then starts to move forward.
Inertia causes the person to remain in the original
position, appearing to fall backward.
(B) The bus turns to the right, but inertia causes the
person to retain the original straight line motion until
forced in a new direction by the side of the bus.
This marble can be used to demonstrate inertia.
• Newton's Second Law of Motion
– The acceleration of an object is directly
proportional to the net force acting on it and
inversely proportional to the mass of the object.
– This law describes the relationship between net
force, acceleration, and mass
This bicycle rider knows about the relationship
between force, acceleration, and mass.
At a constant
velocity the force
of tire friction (F1)
and the force of air
resistance (F2)
have a vector sum
that equals the
force applied (Fa).
The net force is
therefore 0.
More mass results in less
acceleration when the same
force is applied. With the
same force applied, the
riders and the bike with
twice as much mass will
have half the acceleration,
with all other factors
constant. Note that the
second rider is not pedaling.
– The acceleration of an object is directly
proportional to the net force acting on it and
inversely proportional to the mass of the object.
– The unit of force used in the SI system is the
Newton (N)
– N= kgm/s2
– Force is equal to mass times acceleration
• F=ma
– Weight is equal to the mass of an object times the
force of gravity
• w=mg
• Newton's Third Law of Motion.
– Whenever two objects interact, the force exerted
on one object is equal in size and opposite in
direction to the force exerted on the other object.
• FA due to B = FB due to A
Forces occur in matched pairs that are equal in
magnitude and opposite in direction.
The football
player's foot is
pushing against the
ground, but it is
the ground pushing
against the foot
that accelerates the
player forward to
catch a pass.
Both the astronaut and the satellite received a force of
30.0 N for 1.50 s when they pushed on each other.
Both then have a momentum of 45.0 kg m/s in the
opposite direction. This is an example of the law of
conservation of momentum.
• Momentum
• Momentum () is the product of the mass of an
object (m) and its velocity (v).
–  = mv
• The law of conservation of momentum
– The total amount of momentum remains constant
in the absence of some force applied to the
system.
• Two unusual aspects of momentum
– The symbol for momentum does not indicate what
the quantity if measures is.
– The units for momentum (kgm/s) has no name.
According to the law of
conservation of
momentum, the
momentum of the expelled
gases in one direction
equals the momentum of
the rocket in the other
direction in the absence of
external forces.
Forces and Circular Motion.
• Centripetal force.
– This is the force that keeps an object in its straight
line path
• Centrifugal force.
– The imaginary force that is thought to force
objects toward the outside of an object moving in
a circular pattern.
– Actually the force is simply the tendency of the
object to move in a straight line.
• The acceleration of an object moving in a circular
path (ac) is
– ac = v2/r
• m = mass
• v = velocity
• r = the radius of the circular path.
– This can be substituted into the Force equation F
= ma
• F = mv2/r
Centripetal force on the ball causes it to change
direction continuously, or accelerate into as circular
path. Without the unbalanced force acting on it, the
ball would continue in a straight line.
• Newton's Law of Gravitation.
• Objects fall due to the force of gravity (g) on them.
– This force is 9.8 m/s2
– It is this force that gives objects weight
• w = mg
• Universal Law of Gravitation
– Every object in the universe is attracted to every
other object in the universe by a force that is
directly proportional to the product of their
masses and inversely proportional to the square of
the distances between them.
• F = G(m1m2)/d2
• G is a proportionality constant and is equal to
6.67 X 10-11 Nm2/kg2
– Usually the objects in our environment that we
interact with on an everyday basis are so small
that the force is not noticed due to the large force
of attraction due to gravity.
The variables involved in gravitational attraction. The
force of attraction (F) is proportional to the product of the
masses (m1, m2) and inversely proportional to the square
of the distance (d) between the centers of the two masses.
The force of
gravitational
attraction
decreases
inversely with the
square of the
distance from the
earth's center.
Note the weight of
a 70.0 kg person at
various distances
above the earth's
surface.
Gravitational attraction
acts as a centripetal
force that keeps the
Moon from following
the straight-line path
shown by the dashed
line to position A. It
was pulled to position
B by gravity (0.0027
m/s2) and thus "fell"
toward Earth the
distance from the
dashed line to B,
resulting in a
somewhat circular
path.