Download Objects in Motion

Lecture 2
Objects in Motion
• Aristotle and Motion
• Galileo’s Concept of Inertia
• Mass – a Measure of Inertia
• Net Force and Equilibrium
• Speed and Velocity
• Acceleration
Aristotle (384-322 BC)
• Believed that natural laws could
be understood by logical
reasoning.
• Divided motion into 2 categories:
– Violent motion – pushing or
pulling forces
– Natural motion – motion of
stars, falling rocks, rising
smoke, etc.
Aristotle (384-322 BC)
• Two of Aristotle’s assertions that were thought to
be correct for nearly 2,000 years:
– Heavy objects fall faster than lighter objects.
– Moving objects must have forces exerted upon them
to keep them moving.
Galileo (1564-1642)
• Revolutionized the laws
of motion and tested his
ideas by experiment.
• Experiment, not
philosophical
speculation, is the test
of truth.
Scientific Method: a process through which scientists
gather facts through observations and formulate scientific
hypotheses and theories.
1.
2.
3.
4.
5.
Observe – Recognize a question or a puzzle.
Question – Make an educated guess- a hypothesis to
answer the question.
Predict – Consequences that can be observed if
hypothesis is correct.
Test Predictions – Conduct experiments and make
observations to see if predicted consequences are
present.
Draw a Conclusion – The acceptance, modification,
or rejection of the hypothesis based on extensive
testing.
Galileo’s Concept of Inertia
• In the absence of a force, objects once set in motion
tend to continue moving indefinitely.
– Assuming there are no opposing forces such as
friction or air resistance.
• Force: a push or a pull that changes the motion of an
object.
• Inertia: the property by which objects resist changes in
motion.
Galileo’s Concept of Inertia
Galileo’s Concept of Inertia
No force is necessary to keep the cannonball
moving in the horizontal direction once it has left
the cannon.
Mass vs. Weight
• The inertia of an object
depends on its amount of
matter.
• Mass: the measure of the
inertia or the quantity of
matter in an object.
– Measured in Kilograms (kg)
• Weight of astronaut
on the Moon = 1/6
that of his weight on
Earth.
• However, mass
remains the same!
Mass vs. Weight
• Weight: the force upon an object due to
gravity.
– Measured in units of force such as pounds.
– Scientific unit is the Newton (N)
– 1 kg of any material at Earth’s surface has a
weight of 9.8 N (2.2 lb)
• Mass and Weight are directly proportional.
Mass and Volume
• An object’s size is not always a good
determination of its mass.
• Volume: the amount of space occupied by
an object.
• Density = mass / volume: amount of
matter per unit volume (g/cm3, kg/m3)
Net Force
• Net Force: the combination of all forces acting upon an
object.
• Forces are vector quantities.
– Vector Quantity: has both magnitude and direction.
Net Force
• When net force is zero, an object is at
mechanical equilibrium.
Equilibrium Rule:
ΣF = 0
• An object either remains at rest or moves at a
constant velocity (no change in motion).
If the scaffold is at rest, then the sum of the upward vectors
must equal the sum of the downward vectors.
ΣF = 0
F (pushing) = 20 N
F (friction) = 20 N
A desk is being pushed across the floor at a
constant velocity. What is the net force acting on it?
Net Force
• Support Force:
force that supports an
object against gravity,
often called the
normal force.
• Weight + Normal
Force = 0 (ΣF = 0)
Weight and Support Force
• What happens if
the supporting
surface undergoes
an acceleration?
Weight and Support Force
The Force of Friction
• Friction: the resistive force that opposes the
motion or attempted motion of an object past
another with which it is in contact.
• Friction occurs for all states of matter! (air
resistance for example).
Friction
• The force of friction
between 2 surfaces
depends on:
– The kind of materials.
– The force with which
they are pressed
together.
Speed
• Before the time of
Galileo, objects in motion
were described as “slow”
or “fast”.
• Speed: distance traveled
per amount of travel time.
• Examples of units of
speed: km/h, m/s, mi/h
Speed
• Instantaneous Speed vs. Average Speed
– Average Speed = Total distance covered
Travel time
– Total distance covered = Average speed X
Travel time
Velocity
• Velocity: both the speed and direction of an object.
• A quantity such as velocity that specifies both magnitude
and direction is known as a vector quantity.
• Constant velocity = constant speed and constant
direction.
Relative Motion: Are you standing still?
Relative to the Earth?
Relative to the Sun? The Earth is orbiting the Sun at
approximately 100,000 km/h!
Relative to the center of the galaxy? The Milky Way galaxy
is rotating at a speed of 965,600 km/h!
Relative to other galaxies? The Andromeda galaxy is
approaching the Milky Way at a velocity of 100 to 140 km/s!
Acceleration
• Acceleration: a rate of change of velocity.
Acceleration = Change in velocity = ΔV
T
Time interval
• Example of units of acceleration: m/s2
The velocity of a ball rolling down an inclined plane will gain
the same amount of velocity in equal intervals of time =
constant acceleration.
Acceleration
• A body experiences acceleration when
there is a change in its state of motion:
– Can either be an increase or a decrease in
velocity!
– Change in velocity = change in speed,
direction, or both.
Acceleration
• Decreasing Velocity = acceleration in
opposite direction of object’s motion.
• Increasing Velocity = acceleration in same
direction as object’s motion.
Falling Objects
• Acceleration due to gravity on Earth = 10 m/s2 (more
precisely 9.8 m/s2).
g = 10 m/s2
• Distance of free fall from rest is directly proportional to
the square of the time of the fall.
d = ½gt2
The rate at which
velocity changes each
second is the same.
g (acceleration due to
gravity) is always
constant.
Direction of velocity
Direction of velocity
Direction of g
Direction of g
Note: acceleration due to
gravity (g) is constant
(same quantity and same
direction).
• A penny is dropped from the top of the Empire
State Building (381 m). Ignoring the effect of air
resistance, the penny will fall for approximately 9
s. What will be its final velocity in m/s?
– Assume that the acceleration due to gravity
(g) is 10 m/s2 and that the penny starts from
rest.
Velocity will be 90 m/s or 324 km/h (203 mph)!