# Forces by zhangyun

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```									Forces and Newton’s
Laws

Remnants of supernova 1987A, a
cosmic display of forces
• For millennia, thinkers around the
world sought to incorporate the idea of
forces into a complete physical
description of motion:
Historical
Perspectives
• Circa 350 BCE: Aristotle proposes that
the “natural” state of an object is
stationary
• 1553: Galileo Galilei says that an
objects retain their velocity unless
acted upon by a force
• 1679: Isaac Newton incorporates
Galileo’s ideas into his Laws of Motion
Falling Apples or
Pure Genius?
• Isaac Newton was probably one   of the 3
smartest individuals in human   history
(at least mathematically)
• When he encountered a problem   he
couldn’t solve with current
mathematical techniques, he’d   invent
new branches of math
Unification, Part 1
• Newton’s work was very significant, as
it represented one of the first
attempts to unify natural phenomena
• Falling apples, rocks, and even the
motion of planets could all be
explained with one simple idea
• In a sense, this demystified nature
Interesting Tid-Bits
• Unfortunately, his social skills
weren’t on par with his intellect…
• He was a deeply religious individual
• After publishing Principia and Opticks,
he spent a large portion of life
working on Alchemy
• His autopsy revealed large amounts of
mercury in his body, which might
explain his eccentricity
Newton’s 1st Law
• An object moving at constant velocity
will stay that way unless acted upon by
an outside force
• Objects at rest will remain at rest
unless acted upon by a force
• In other words, objects are lazy…
Examples?
•   Hoop/ring
•   Penny Drop
•   Egg/Beaker
•   F4 Videos
• Why did Aristotle get it backwards?

• It’s likely that he didn’t think to
include how friction and air resistance
affect motion

• We’ve seen the clarity of Newton’s 1st
Law in the absence of air resistance
How Lazy Are Objects?
• An objects resistance to a change in
motion is called inertia
• We can also describe an object’s
inertia as its laziness
• Mass is actually a measure of an
object’s inertia
Rank the inertia of the following
in increasing order: a car, bug,
you, and NCSSM
•   1.   NCSSM, car, you, bug
•   2.   car, NCSSM, you, bug
•   3.   bug, car, you, NCSSM
•   4.   you, NCSSM, bug, car
•   5.   bug, you, car, NCSSM
Imagine sitting in a car at rest. If
you throw a tennis ball in the air, it
will land back in your hand. What
will happen if you throw it up, then
accelerate?
• 1. It will land in front of you

• 2. It will land back in your hand

• 3. It will hit you in the face
Which car accident would cause a
person to get thrown through
their windshield?
• 1. A car moving at high speeds hits
something in front of it
• 2. A car at rest is rear ended by a
fast moving car
• 3. A car moving at high speeds is hit
by a car behind going a few miles/hour
faster
• 4. A car loses control and spins out
If the sun were to disappear,
what would happen to Earth?

• 1. It would continue moving in its
normal orbit
• 2. It would move off in a straight line
• 3. It would spiral in towards the sun’s
previous location
• 4. It would stop
Reference Frames Are Key
• Your reference frame is essentially
your point of view
• A reference frame is inertial if it
does not accelerates
Which reference frame is
not inertial
• 1. A car moving at constant velocity
• 2. A rock, sitting at the edge of a
cliff
• 3. A car rounding a curve at constant
speed
• 4. A rock rolling down a hill at
constant velocity
Why is this so
Important?
• Imagine a baby, born on a bus with the
windows blacked out
• The baby spends its first few years on
the bus, learning about the world with
no knowledge of life outside the bus
• How would their ideas of motion
contrast with ours?
Types of Forces
•   Gravity
•   Tension
•   Friction
•   The “Normal” Force
•   Electrical and Magnetic Forces
•   Nuclear Forces
“Net” Forces
• What happens if more than one force
acts upon an object?
• Forces are vector quantities, so they
add like any other vectors
• The Net force is simply the vector sum
of all forces acting upon an object
• An object with a net force of 0 is said
to be in equilibrium
Which object is in equilibrium?

• 1. A car accelerates from rest
• 2. A sky diver falls at constant
velocity
• 3. An object is pulled upon by +200N
and -300N forces
• 4. An air puck slides across the air
table with the air supply turned off
Newton’s 2nd Law
• The Net Force Acting upon an object is
proportional to the resulting acceleration

• Net Force = mass x acceleration
• Fnet = ma
Mathematical Notation
•   Fnet = SF
•   a = SF/m
•   (Bold indicates a vector quantity)
•   This law holds for each direction
(x,y,z)
Units?
• kg m/s2
• We call these units Newton’s,
in honor of the man himself
A 10N forces pulls a 4kg box to the
left, while a 8N force pulls it to the
right. What is the box’s
acceleration?
Free-Body Diagrams
• With all the forces around us,
computing net force can get complicated
• We use the concept of free-body
diagrams to deal with this complexity
• A Free Body Diagram, or Force Diagram,
is simply a picture of object that
displays all the forces acting upon it
Rules of Force
Diagrams
• Forces vectors are drawn from the
application point of a force
• Most of our diagrams will involve point
masses (draw your vectors pointing away
from the COM)
• The length of a force vector indicates
the magnitude of the force
Rules, Part 2
• Include forces acting on an object
• Do not include forces produced by an
object
• Ex: Two skaters initially at rest push
off of one another. In the diagram for
skater 1, you would only include the
force from skater 2
The Jumbo Jet Revisited
• Fully loaded, a 747 jumbo jet has a
mass of 300,000kg. Assuming it needs
1900m of runway to reach a takeoff
speed of 100m/s, how much force does
each of 4 engines provide?
• Each engines provides 197kN of force
(thrust), for a total of 788kN
• Now, let’s think about the impact of
air resistance
• Imagine that at takeoff (v = 100m/s),
the plane encounters 450,000N of air
resistance
• How long will it take the plane to
reach its cruising speed of 250m/s?
• 133 seconds
A Falling Body (without
Air Resistance)
A Hanging Mass
• A rock hangs freely, held up by two
ropes
Which is the correct force
diagram for a mass hanging from
the ceiling by a rope?
Which is the correct diagram for a
block pushed along a rough surface at
constant velocity?
Same situation as before, but now the
object accelerates to the right
Weighing In
• What causes weight?
• How can weight change while mass
remains constant?
• It turns out that weight is simply a
measure of the gravitational force
acting upon an object

• Weight = mg
Force Diagram
Implications
• From now on, indicate an object’s
weight with mg on your force diagram
Falling Bodies
Revisited
• A hammer and a feather both accelerate
at little g
• Does that mean they experience the same
gravitational force?
• Definitely not; Earth has to pull
harder on the hammer to create the same
acceleration
Lift
• The force that keeps a plane in the air
is called lift. Imagine a plane,
flying perfectly level at constant
velocity. What is the magnitude of the
lift necessary to keep a 300,000kg
Boeing 747 in the air?

• Lift = 3,000,000 N (up)
Back to the F4…
•   Useful information
•   Force of wall on the plane = 13.3 MN
•   Force of thrust on the plane = .30 MN
•   Plane mass = 27,000 kg

• Find the plane’s acceleration while in
contact with the wall (express your
answer in “g”s)
Yoda’s Force?
• Yoda has an uncanny ability to make
things happen, despite his size
• I seem to recall a scene in Star Wars
where he accelerates a very massive
object (m = 30,000kg) straight up at a
rate of 5.0 m/s/s
In a Galaxy Far, Far
Away…
• Now, Star Wars does not occur on Earth,
which means g is not necessarily 10
m/s/s
• Let’s say Yoda is on a planet where g =
15 m/s/s (although is sure looks like g
= 10m/s/s when you watch Star Wars…)
• What force is necessary for Yoda to
accelerate this massive object (30,000
kg) upward at 5.0m/s/s?

• Just for comparison, how does this
force compare to Yoda’s body weight (m
= 15 kg)?
The Rising Box…
• Imagine a person with mass 65kg,
standing on a box
• If the box accelerates upwards at a
rate of 3 m/s/s, what is the normal
force of the box acting upon the
person?
• What would it feel like if you were
standing on the box?
• What would a scale read?
Apparent Weight
• Think of a situation in which you feel
heavier or lighter than normal
• Why do you feel this way?
• In such a situation, your apparent
weight is more or less than your actual
weight
• Why?
Feeling Weight
• The sensation of weight comes from
normal forces acting upon us
• Don’t believe me? Try standing in an
elevator in free fall
• At the bottom of a roller coaster loop,
the rider’s (mass 80kg) seat pushes him
up with a force of 900N. What is the
magnitude of the rider’s acceleration?
• a = 1.45 m/s/s (points up)
Newton’s 3rd Law
• This is likely the most familiar law
• For every action, there exists an equal
and opposite reaction
• In other words, nature always fights
back
• Forces always come in pairs
Examples
• Rockets
• Two Ice Skaters Push One Another
• Rifle Recoil
• 1) In a horse drawn carriage, the horse
pulls the cart forward. According to
Newton’s 3rd Law, the car pulls back
with an equal force. If that’s the
case, how does the horse or cart move?

• 2) A mack truck and bicycle collide.
Which experiences the greater force?

• 3) What happens if you use a fire
extinguisher in space?

• 4) What force actually moves a car
forward?
Forces in Space
• An astronaut (m = 120kg with gear)
working on the ISS needs to push a
massive object (m = 1500kg) forward
• If he pushes on it with 500N of force,
what happens
• How can he safely push it forward?
3 Block Problem
• Imagine three blocks of   different masses on a
table
• Find the force of block   one on block two
• Find the force of block   two on block one
• Find the force of block   two on block three
• Examine the Atwood’s machine below,
with m1 = 10kg and m2 = 30kg. If m2
rests upon a block, what is the normal
force acting upon it?

• Normal Force = 196N (up)
• Let’s return to the block/pulley
situation. If block one lies on a
frictionless surface, what is its
acceleration? (m1 = 5kg, m2 = 10kg)
• a = 6.5m/s/s (to the right)
• On the diagram below, two blocks are
connected by a rope. Block 1 has a
mass of 5kg, while block 2 has a mass
of 10kg. If block 1 is at rest, sitting
on a rough surface, what is the
magnitude of the frictional force
acting upon block one?
• Friction = 98N, pointing to the left
• A person’s weight is 600N, when
standing on a normal bathroom scale.
What would the scale read if this
person were in the Bryan elevator,
arriving at the 4th floor (a =
0.8m/s/s)?

• Normal Force/Apparent Weight   =
552N(up)
Tension: The Force
That Binds Us
• Tension is a very important force
• The magnitude of the tension force in
the same rope is always equal
• Why?
• Newton’s 3rd…
Pulley Problems
Variations
• We can ask a variety of questions about
the previous situation
• If the blocks are stationary or move at
constant velocity, what is the
frictional force?
• By how much do they accelerate?
• How much tension exists in the rope?
Tension in 2D
• Think about the situation below
•   Draw force diagrams for the block
•   Write net force equations
•   Find the tension in rope 1
•   Find the tension in rope 2
• T1 = 173N

• T2 = 87N
2D Tension, Part 2
• Now imagine a different block,
suspended from the ceiling by two ropes
• Find the mass of the hanging object

• m = 3.5kg
• Imagine a different box, suspended by
two different ropes

• Find the magnitude of the tension in
the second rope, and the angle the rope
makes w/ the horizontal
• Theta = 21.5 degrees
• T2 = 14.7N

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