Download Chapter 3: Newton*s Second Law of motion

CHAPTER 3: NEWTON’S
SECOND LAW OF MOTIONFORCE AND
ACCELERATION
3.1 GALILEO DEVELOPED THE CONCEPT
OF ACCELERATION
• Founded the concept of acceleration
• A ball rolling down a hill speeds up
• Velocity increased by a given amount each second
• Acceleration: change in speed, a change in direction, or a
change in both speed and direction
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =
𝑡𝑖𝑚𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙
• Speeding up in a car
• The car is changing direction = change in velocity
3.1 ACCELERATION CONTINUED
• Example Problems:
• In 1 second, we steadily increase our velocity from
30 km/h to 35 km/h. In the next second, we go
from 35 km/h to 40 km/hr, and so on. What is the
acceleration?
• You do an experiment and drop an apple from
your head. The object is in free fall and you
determine that the free fall’s velocity if 10 m/s in
one second. What is the accerleration?
3.2 FORCE CAUSES ACCELERATION
• Any object that accelerates is acted on by a push or pull of some kind
• Suppose you pull a toy wagon with a net force of 20N. Then you
doubled the net force with 40 N. What happens with the
acceleration?
• If net force doubled, then so is acceleration
• Acceleration is directly proportional to the net force.
• Acceleration ~ net force
Means: Directly proportional
• The direction of acceleration is always in the direction of the net force
• Force in same direction as motion = speed increase
• Force in opposite direction as motion = speed decrease
• Force at right angles, change direction of the object
CONCEPT CHECK
1.If you push on a shopping cart, it will
accelerate. If you apply four time the net
force, how much greater will the
acceleration be?
2.If the net force acting on a sports car is
reduced to half, how will the
acceleration change?
MASS IS A MEASURE OF INERTIA
• Mass of an object relates to inertia
• EX: full can of rocks vs. empty can
• Greater the mass, the greater its inertia
• Mass is also a measure of how much material an object
measures
• Mass depends on the number and kinds of atoms making
up the object
• Lead: made up of many tightly packed atoms so it has a
greater volume
MASS IS NOT VOLUME
• Volume: measure of space
• Measured in cubic centimeters, cubic
meters, or liters
• Mass is measured in kilograms
• Ex: equal-size bags of popcorn and jelly beans
may have equal volumes but very unequal
masses
MASS IS NOT A WEIGHT
• Mass: measure of the amount of matter in an object and
depends in its number and kind of atoms
• Also measure of inertia that an object shows when trying
to change its state of motion
• Weight: Force that depends on gravity
• Mass doesn’t change depending on gravity
• Although they are different they are directly proportional to
one another
• Object with great mass has a great weight
CONCEPT CHECK
• Does a 2-kilogram iron block have twice as much
inertia as a 1-kilogram iron block? Twice as much
mass? Twice as much volume? Twice as much
weight when weighed in the same location?
• Does a 2-kilogram iron block have twice as much
inertia as a 1-kilogram bunch of bananas? Twice as
much mass? Twice as much volume? Twice as much
weight when weighed in the same inertia?
• How does mass of a bar of gold vary with location?
1 KILOGRAM WEIGHS 10 NEWTONS
• Standard unit of mass is kilograms
• A 1 kilogram bag of material has a weight of about 10
Newtons
• Want to know how much something weighs, do 10 times
the kg
• Weight and mass are proportional
• Precision is needed sometimes
• EX: 1 kilogram of matter actually weighs 9.8 N.
• 1 kilogram weighs 2.2 lbs.
• 2.2 lbs. = 4.45 N
CONCEPT CHECK
•Why is it okay to say a 1 kg bag of
sand weighs 10 N, but a 1 kg. bag
of gold weighs 9.8 N? Don’t they
weigh the same?
MASS RESISTS ACCELERATION
• Massive objects are more difficult to accelerate
• Same force and twice as much mass = half as much
acceleration
• Acceleration produced by a given force is inversely
proportional to the mass
1
Acceleration ~
𝑚𝑎𝑠𝑠
• Inversely: Two values change in opposite ways
• One value gets larger, the other gets smaller
CONCEPT CHECK
• Suppose you are offered either ¼ of an apple pie or
1/8 of the pie. Which piece is larger?
• Suppose you apply the same amount of force to
two carts, one cart with a mass of 4 kg and the other
with a mass a 8 kg.
• Which cart will accelerate more?
• How much greater will the acceleration be?
NEWTON’S SECOND LAW LINKS
FORCE, ACCELERATION, AND MASS
• Isaac Newton was the first to realize the connection
between force and mass when creating acceleration
• Newtons Second Law states: “The acceleration produced
by a net force on an object is directly proportional to the
net force, is in the same direction as the net force, and is
inversely proportional to the mass of the object.”
𝑁𝑒𝑡 𝐹𝑜𝑟𝑐𝑒
𝐹
Acceleration =
a=
𝑀𝑎𝑠𝑠
𝑚
CONCEPT CHECK
• Consider a 1000 kg car pulled by a cable with 2000 N of
force. What will be the acceleration of the car?
• Suppose the force were 4000 N. What would be the
acceleration of the car?
• If you push on a shopping cart, it will accelerate.
• If you push the same, but the cart is loaded with
groceries so it has five times as much mass, what
happens to the acceleration?
• If you push five times harder on the loaded cart, what
happens to the acceleration?
FRICTION IS A FORCE THAT AFFECTS
MOTION
• Friction: an object tends to rub or rubs against
something else
• Occurs for solids, liquids, and gases
• Acts in a direction to oppose motion
• Friction in the air is known as drag
• Amount of friction depends on the material and
how much they are pressed together
• Ex: sliding a book on the floor vs. down a ramp
OBJECTS IN FREE FALL HAVE EQUAL
ACCELERATION
• Galileo found that planes were tipped to
effectively slow down acceleration is greater
• Free Fall: falling only under the influence of
gravity, where other forces such as air drag is
neglected
• Any incline has the same acceleration no
matter the mass
NEWTONS SECOND LAW EXPLAINS
WHY OBJECTS IN FREE FALL HAVE
EQUAL ACCELERATION
• All free falling objects have the same force/mass ratio and
undergo the same acceleration at the same location
• Acceleration due to gravity is represented by (g)
• Ex:
𝐹 10𝑁
𝑚
𝑎= =
= 10 = 𝑔
𝑚 1 𝑘𝑔
𝑠
𝐹
a=
𝑚
=
100 𝑁
10 𝑘𝑔
=
𝑚
10
𝑠
=𝑔
ACCELERATION OF FALL IS LESS WHEN
AIR DRAG ACTS
• Air drag depends on two things: speed and surface
area
• Increase surface area
• Slow down speed
• Terminal Speed: stop accelerating
• Terminal Velocity: stop accelerating in a certain
direction