4 outline
• Newton’s 2nd Law
• friction
• dynamics of falling objects
• RQ: 1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 16, 18, 20, 21,
24, 26, 27, 30, 31, 33.
• Ex: 2, 3, 20, 31, 32, 33, 42, 43, 44.
• Problems: 2, 3, 5.
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example uses
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design crumple zones (cars & barriers)
power requirements for cars
parachute design
elevator design
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force & acceleration
• Net force  acceleration
• acceleration ~ net force
• e.g. The net force on a car is doubled. The
acceleration of the car will then also
double in size.
(“~” means “directly proportional to”)
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Newton’s Second Law: the acceleration of an
object is proportional to the Net External Force
acting on it, and inversely proportional to the
object’s mass.
acceleration
net force

mass
change in speed / direction
time
net force

mass
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Effect of a Net Force
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•
•
•
•
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object at rest begins to move
moving object changes its:
speed
or direction
or both.
change in velocity is in the same
direction as the net force on the object.
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Finding Net Force Using Diagrams
• Example of adding two perpendicular
Forces A = 3, B = 4:
• A) Walk 3 steps forward.
• B) Turn left or right, walk 4 steps in this
direction.
• C) Walk directly between the starting and
ending locations counting your steps.
• Distance in “steps” in (C) is the Net of the
two forces.
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Ex. Net Force Rightward
• Car moving to right
• net force is to right
• Speed increases
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Ex. Net Force Leftward
• Car moving to right
• net force is directed left
• Car slows down
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Ex. Net Force Downward
• Ball is tossed to right
• net force is down
• object turns downward
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Mass and Weight
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•
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•
•
Mass is the quantity of matter.
Mass measures “inertia”.
Mass is measured in kilograms (kg)
Weight is the force on mass due to gravity.
Weight is measured in newtons (N) or
pounds (lb).
• Weight ~ Mass
• 1 kg of mass has a weight of 2.2 lbs
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Comparing Accelerations of
Objects in Free Fall.
• Downward force is weight.
• a = weight/mass
• but an object with twice the mass will have
twice the weight…
• so the accelerations are the same…
• We call this acceleration “g”.
• g is about 10m/s/s downward.
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Friction
• Objects in contact “like each other”, i.e.
they form a “bond”.
• They resist being moved when in contact.
• Ex. A Chest sitting on a wood floor seems
“glued” down. It is harder to get it moving
than it is to keep it moving.
• These resistance forces are called
“frictional forces”.
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Direction of Frictional Forces
• Frictional forces oppose the direction of
motion of object if it is moving.
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Direction of Frictional Forces
(cont.)
• If the object is at rest there still may be a
frictional force. If there is a frictional force
then it is in a direction opposite to the
direction of the net applied force due to
other causes.
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Categories of Friction
• Sliding Friction: exists when one object
slides against a second object, e.g. box
along floor.
• Static Friction: exists when a force is
applied to an object, but that force is not
large enough to break the frictional bond.
• Air friction force ~ (speed of object)2.
• /
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Weight Force
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•
•
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Weight (N) = mass (kg) x (10N/kg)
Weight = mg
g = 10 m/s/s = 10 N/kg
Acts at all times, e.g. object is falling,
sitting, etc.
• Ex: A 2kg object weighs 20N.
• Weight = (2kg)(10N/kg) = 20N
• /
Free-Fall
• only force is object’s weight
• air drag is negligible in size
• Ex. A solid steel ball falling a short
distance is in free-fall.
• Ex. A falling feather is not in free-fall since
air drag is equal to its weight
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Non Free Fall
• Whenever air drag is significant compared
to weight the object will fall with
acceleration less than 10m/s/s.
• Example: A 5kg object weighs 50N but an
air drag force of 10N acts on it.
• Acceleration = NetForce/mass
•
= (50-10)N/5kg
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= 40/5 m/s/s
•
= 8 m/s/s
• /
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Ex. Falling Motion 1
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M = 1kg, speed is small, air friction = 0.
Weight is 10N.
Net force = 10N – 0 = 10 N
Acceleration = Net Force/Mass
= 10N/1kg
= 10 m/s/s
N/kg = m/s/s
/
Ex. Falling Motion 2
• M = 1kg, speed is large and air friction is
1/3 the weight = 10N/3 =3.33N
• Net force = 10N – 3.33N = 6.67N
• Acceleration = Net Force/Mass
•
= 6.67N/1kg
•
= 6.67m/s/s
• /
Ex. Falling Motion 3
• M = 1kg, speed is larger and air friction is
equal to the object weight = 10 N
• Net force = 10N – 10N = 0N
• Acceleration = Net Force/Mass
•
= 0N/1kg
•
= 0 m/s/s
• /
Terminal Speed/Velocity
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•
•
•
•
Air drag on falling objects increases…
until equal to the objects weight…
… resulting in balanced forces
acceleration = 0, speed no longer changes
This top speed is called the “terminal
velocity” of the object…
• … and varies from object to object.
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4 summary
• Newton’s 2nd Law relates net force, mass,
and acceleration. It also covers the 1st
Law.
• frictional forces are proportional to the
forces holding objects together
• falling objects accelerate until air drag
equals their weight
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p.11 practicing physics
• Mass is fundamental, does not depend on
location
• Mass is not a vector and not a force, it is
simply a number
• 1kg mass “weighs” 10N on earth (2.2lbs),
less on the moon
• Weight = mg (earth g = 10m/s/s)
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