Transcript Foundations of Physical Science

Foundations of Physical Science
Unit One: Forces and Motion
Chapter 3: Forces and Motion
• 3.1 Force, Mass and Acceleration
• 3.2 Weight, Gravity and Friction
• 3.3 Equilibrium, Action and Reaction
Learning Goals
• Explain the meaning of force.
• Show how force is required to change the motion of an
object.
• Use a graph to identify the relationships between variables.
• Explain and discuss Newton's second law and the
relationship between force, mass and acceleration.
• Describe how changing the mass of the car affects its
acceleration.
Learning Goals (continued)
• Draw conclusions from experimental data.
• Demonstrate qualitatively how friction can affect motion.
• Explain Newton's third law of motion.
• Identify action-reaction pairs of forces.
• Recognize how Newton's third law of motion explains the
physics behind many common activities and useful objects.
Vocabulary
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air friction
equilibrium
force
friction
gravity
inertia
law of conservation of
momentum
• mass
• momentum
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newton
Newton's 1st law of motion
Newton's 2nd law of motion
Newton's 3rd law of motion
pounds
rolling friction
sliding friction
viscous friction
weight
3.1 Force, Mass, and
Acceleration
Sir Isaac Newton’s
Laws of Motion
• Sir Isaac Newton (1642-1727), an English
physicist and mathematician, is one of
the most brilliant scientists in history.
• Before the age of 30, he formulated the
basic laws of mechanics, discovered the
universal law of gravitation, and invented
calculus!
Newton’s Laws
Force
• A push or a pull, or any action that has the
ability to change motion
• Two units of force commonly used
– Pounds (lb)
– Newtons (N)
• The force that will give an object of mass 1 kg an
acceleration of 1 m/s2
Force
• Force is a push or
pulling action that can
change motion
• Force is measured in
newtons
Mass
• Mass is the amount of
“stuff” or matter in an
object.
• Mass is measured in
kilograms.
Newton’s 1st Law
• Law of Inertia: every
object continues in a
state of rest, or in a
state of motion in a
straight line at
constant speed, unless
it is compelled to
change that state by
forces exerted upon it
Newton’s
nd
2
Law
Key Question:
What is the relationship between force, mass and acceleration?
Force Causes Acceleration
• Acceleration is
directly proportional
to net force!
• Double the net force = acceleration doubles
• Triple the net force = acceleration triples
Mass Resists Acceleration
• More massive objects are more
difficult to accelerate
• 2x the mass  1/2 the acceleration
• 3x the mass  1/3 the acceleration
• Therefore, acceleration is inversely
proportional to mass
• As one gets bigger, the other gets
smaller
Newton’s Second Law
• In other words:
a = F/m
m = F/a
• Or most commonly:
F = ma
Balanced and Unbalanced Forces
• Net Force: the total of all forces acting on an
object
• Vector: an arrow drawn to scale that
represents the magnitude and direction of a
quantity having both magnitude and direction
• In this case the quantity is force
Adding and Subtracting Forces
Equilibrium
• Mechanical equilibrium: when the
net force on something is zero
• ΣF=0
• Static Equilibrium: objects at rest
• Dynamic Equilibrium: objects
moving at constant velocity
Example
• Consider the gymnast hanging from the
rings. If she hangs with her weight evenly
divided between the two rings, how
would scale readings in both support
ropes compare with her weight?
• The reading on each scale will be half her
weight. The sum of the readings on both
scales then equals her weight.
The Support ForceWhy We Don’t Fall Through The Floor
• Support Force = Normal Force
• Upward force that is equal and opposite to the
force of gravity
• Σ F=0
Example
• An airplane flies at constant velocity. In other words, it is in
equilibrium. Two horizontal forces act on the plane. One is the
thrust of the propeller that pushes it forward. The other is the
force of air resistance that acts in the opposite direction.
Which force is bigger?
• Both forces have the same magnitude. Call the forward force
exerted by the propeller positive. Then the air resistance is
negative. Since the plane in in equilibrium, can you see that
the two forces combine to equal zero?
3.2 Weight, Gravity,
and Friction
Gravity
• A force that pulls every mass toward
every other mass
• Earth is the biggest mass; gravity pulls
everything toward the center of Earth
• Depends on mass
• More mass, more gravity pulls on you
Mass
Weight
• The quantity of matter in an
object
• Measured in kilograms (kg)
• The gravitational force
exerted on an object by the
nearest most-massive body
(locally, by Earth)
• Measured in Newtons (N)
• Mass is directly proportional to weight
– large mass = large weight
– small mass = small weight
• 1 kg (mass) = 9.8 N (weight)
Weight
Weight force (N)
Fw = mg
gravity (9.8 m/sec2)
mass (kg)
Weight and Galileo
• A legend has it that, around
1587, Galileo dropped two balls
from the Leaning Tower of Pisa
to see which would fall faster
• Objects in free fall have equal
acceleration
• But, why are accelerations equal
between objects of greater and
lesser mass?
Free Fall and Equal Acceleration
• One object relates to the other:
F/m = F/m
F/m = g
C/D = 
F/m = g
C/D = 
Free Fall and Equal Acceleration
• A falling 10 kg boulder “feels” 10x
the force of gravity (weight) as a 1
kg stone
• 10x as much force acting on 10x as
much mass produces the same
acceleration as the smaller force on
the smaller mass
Free Fall without Friction (Air Drag)
Friction
• Occurs when one object rubs against
something else
• Occurs for solids, liquids and gases
• It always acts in a direction OPPOSITE to
motion
Friction
• Push crate right, friction is left
• Object falls down through the air, AIR FRICTION
(drag) acts upward
• The amount of friction depends on the kind of
material and how much they press together
Example
• Suppose a high-flying jumbo jet flies at constant
velocity when the thrust of its engines is a constant
80,000 N. What is the acceleration of the jet? What
is the force of air drag acting on the jet?
• Zero acceleration because the velocity is constant.
The net force has to be zero if a = F/m. Air drag must
be equal and opposite to the thrust: 80,000 N.
Air Drag
• We know that a feather drops more
slowly than a coin when dropped in
air
• Air drag affects the feather more
• In a vacuum the feather and coin
drop at the same time
• With no air drag the force/mass ratio
is the same for both
Free Fall with Friction (Air Drag)
Air Drag
• In reality, air drag is usually NOT negligible for falling
objects
• Acceleration of fall is less
• Air drag depends on:
– Speed
– Surface area
Air Drag
• Free fall = downward net
force is weight
• Air drag therefore reduces
the net force
• With air present the net
force is:
• Reduced net force 
reduced acceleration
Weight – Air Drag
So the equation becomes:
a = (weight-air drag)/m
• Eventually the net force
becomes zero
• The falling object no longer
accelerates but has reached
TERMINAL VELOCITY
What is the acceleration in each diagram?
(The skydiver has a mass of 100 kg)
10m/s2
6m/s2
2m/s2
0m/s2
Example
• Consider two parachutists, a heavy person
and a light person, who jump from the
same altitude with parachutes of the
same size.
• Which person reaches terminal speed
first? Which person has the greatest
terminal speed?
• The lighter person reaches terminal speed
first. The heavy person falls faster and
reaches a higher terminal speed.
Example
• Which person gets to the ground first? If
there were no air drag, like on the moon,
how would your answers to these questions
differ?
• The heavier person falls faster and will reach
the ground first.
• If there were no air drag, there would be no
terminal speed at all.
• Both would be in free fall and hit the ground
at the same time.
Gravity (again)
• The attractive force from gravity between objects of
ordinary mass is incredibly small.
• You feel weight because the mass of Earth is large
enough to create significant gravity forces.
Legend has it…
• Newton saw an apple fall
• He realized that the force pulling
on the apple was the same force
pulling on the moon
• Earth’s gravity reaches the moon!
Tangential Velocity
• Velocity parallel to the Earth’s
surface
• The orbit of the moon around the
Earth
• Keeps the moon constantly falling
around the Earth instead of
directly into it
• Similar to the paths of the planets
around the sun
Centripetal Force
• A force that makes a
body follow a curved
path
• “center seeking”
force
Newton’s Law of Universal Gravitation
• The force of attraction between two objects is
directly related to the masses of the objects
and indirectly related to the distance between
them
Newton's Law of Universal Gravitation
gravity constant
mass 1 (kg)
Force (N)
F = G m1m2
R2
mass 2 (kg)
distance (m)
between m1 and m2
Example
• What happens to the force between two
bodies if the mass of one body is doubled?
• When one mass is doubled, the force
between them doubles
Gravity and Distance
• Gravity gets weaker with distance
• This is like how light gets dimmer
as you move farther away from it
• As the light spreads out, its
brightness decreases
• When you are 2X as far away, it
appears ¼ as bright
Inverse-Square Law
• The intensity gets less as the inverse square of
the distance
• The greater the distance from Earth’s center,
the less the gravitational force on an object
3.3 Equilibrium,
Action and Reaction
What has Force?
• Does a speeding baseball have force?
• NO
• Force is not something an object possesses, like mass
• A speeding baseball exerts force when it hits something
• How much force?
• Depends on how quickly the ball decelerates
Forces
• Equal in strength
• Opposite in direction
• Occur exactly the same time
Newton’s Third Law of Motion
• For every action force, there is a reaction force
equal in strength and opposite in direction
• Action-Reaction Pairs
• To every action there is always an
equal yet opposite reaction
Example
• When a heavy football player and a light one
run into each other, does the light player
really exert as much force on the heavy player
as the heavy player exerts on the lighter one?
• Yes, the forces have equal strength
Example
• Is the damage to the heavy player the same as
the damage to the lighter one?
• No! Although the forces are the same on
each,the effects of these equal forces are
quite unequal!
Cannon-Cannonball Example
• Cannonball: F/m = a
• Cannon: F/m = a
• Cannonball: smaller mass, greater acceleration
Momentum
• Inertia in motion
• momentum = mass x velocity
• P = mv
• When direction is not an important factor:
• momentum = mass x speed, still P = mv
Momentum
Momentum (kg-m/sec)
P = mv
velocity (m/sec)
mass (kg)
Momentum
• A compact car traveling at 20 mph has
less momentum than a large truck
traveling at the same velocity
• Why? The truck has more mass
Example
• When would a car and a truck with 2X car’s
mass have the same momentum?
• They’d have the same momentum if the car
were traveling 2x as fast as the truck
• (m x 2v) car = (2m x v) truck
How Does Momentum Change?
• mass changes
• velocity changes
• both mass and velocity change
• Usually-velocity changes (it accelerates!)
Impulse
• “force x time”
• Change in
momentum
• Ft  change in mv
• Ft = ∆ mv
Impulse = ∆ Momentum
Ft = ∆ mv
2
(Kg)(m/s )(s)
= (kg)(m/s)
Example: Long-Range Cannons
• Long barrels
• Longer the barrel, the greater the
velocity of the emerging
cannonball or shell
• The force of exploding gunpowder
in a long barrel acts on the
cannonball for a longer time
• Increased impulse  greater
momentum
Momentum Over a Long Time
• The brakes in your car fail! Do
you aim the car at the
concrete wall or at the
haystack?
• Either way your momentum
decreases the same-you come
to rest
• Hitting the haystack extends
your contact time-the time
during which your momentum
is brought to zero
Momentum Over a Long Time
• Reduces the force
• Decreases the resulting deceleration
• Time of contact is extended 10x  force of
contact is reduced 10X
• When you jump you bend your knees before
you make contact with the ground: increases
the amount of time in the collision
Examples
Extending the time in which momentum is being reduced
Bungee Jumping
The long stretch of the
cord results in a small
average force to bring the
jumper to a safe halt
before hitting the ground
Catching A Fastball The
hand is initially forward
so it can move
backward after contact
with the ball
Momentum and Airbags
• Airbags expand from the steering
wheel/dashboard
• A sensor has been triggered due to a
sudden IMPULSE or CHANGE IN
MOMENTUM
• The airbag fills with nitrogen gas in 1/20th
of a second
• The airbag expands before the person hits
it
• After 0.3 sec, the collision should be
complete and the airbags empty
What is the function of an airbag?
• During front-end collisions the driver and
passengers have inertia and will continue
forward until the dashboard, seatbelt, or
airbag forces them to stop
• Airbags were created to cushion the impact by
increasing the time to stop, resulting in a
smaller force
Momentum Over a Short Period
• Short contact time = large force
• Momentum is quickly reduced
• Example: Karate Expert…The impulse is the force of his hand
against the bricks multiplied by the time his hand makes
contact
• Therefore the force is huge!
• If his hand bounces, the force is even greater
Conservation of Momentum
• There is a fixed amount of momentum for the
entire universe
• Additional momentum cannot be gained or
lost, but only transferred from one object to
another
• Momentum is a vector quantity (magnitude
and direction)
Law of Conservation of Momentum
• In the absence of an external force, the
momentum of a system remains unchanged
Mgvg = mbVb
(4kg) vg = (0.010kg) (300 m/s)
4vg = 3
vg = 3/4
vg = 0.75 m / s
Momentum is Conserved in Collisions
Net momentum
before collision
=
Net momentum
after collision
mvbefore = mvafter
Elastic Collisions
• A collision in which colliding objects rebound without lasting
deformation or the generation of heat
• The first ball comes to rest and the
second ball moves away at the
velocity of the first ball.
• Momentum is transferred from the
first ball to the second one!
• [m1v1 + m2v2]before = [m1v1 + m2v2]after
Inelastic Collisions
• A collision in which the colliding objects
become distorted, generate heat, and
possibly stick together
• [m1v1 + m2v2]before = [(m1 + m2)v]after
FORMULAS
•
force --> F = ma
weight --> F = mg
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acceleration --> a = F/m
Newton’s Law of Gravitation --> F = G m1m2
r2
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Impulse = force x time
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Conservation of Momentum --> mvbefore = mvafter
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Elastic Collision
[m1v1 + m2v2]before = [m1v1 + m2v2]after
mass --> m = F/a
Momentum = mass x velocity
Impulse = change in momentum --> Ft = Δ mv
Inelastic Collision
[m1v1 + mBvB]before = [(m1 + m2)v]after