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, 8.
1
example uses
•
•
•
•
•
design crumple zones (cars & barriers)
power requirements for cars
parachute design
elevator design
/
2
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”)
3
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
4
Effect of a Net Force
•
•
•
•
•
•
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.
5
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.
7
Ex. Net Force Rightward
• Car moving to right
• net force is to right
• Speed increases
8
Ex. Net Force Leftward
• Car moving to right
• net force is directed left
• Car slows down
9
Ex. Net Force Downward
• Ball is tossed to right
• net force is down
• object turns downward
10
Mass and Weight
•
•
•
•
•
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
11
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.
12
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”.
13
Direction of Frictional Forces
• Frictional forces oppose the direction of
motion of object if it is moving.
14
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.
15
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
16
Question
In a vacuum, a coin and feather fall side by side, at the
same rate. Is it true to say that, in vacuum, equal forces
of gravity act on both the coin and the feather?
NO! They accelerate together
because the ratio
weight/mass for each are
same (=g)
17
Non Free Fall
• Whenever air drag is significant compared
to weight the object will fall with
acceleration less than 10m/s/s.
18
Terminal Speed/Velocity
•
•
•
•
•
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.
19
20
Fnet (mg  R)
a

m
m
21
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
22
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)
23
4 agenda
• lecture
• practicing physics: pages 11, 12-16, 17
• lab: acceleration on an air-track
• lab: Newton’s 2nd Law on air-track
24
Which encounters
the greater force
of air resistance—
1. A falling
elephant, or
2. A falling
feather?
25
air drag ~ size and speed
26
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.
27
Size of Frictional Force:
• proportional to the force holding the
objects in contact, e.g. weight of a box.
• does not depend on the area of contact.
Box on different sides will have similar
frictional forces.
• Static friction > Sliding friction
28
Example of Objects at
Terminal Velocity
29
Fluid Friction
• Gases and Liquids are both “Fluids”
• Motion through air is a “fluid-drag” and is
called “air resistance” or “air drag”.
• Fluid-drag usually proportional to velocity
or velocity squared.
• Air-drag ~ v2.
30
Ex. Falling Motion
•
•
•
•
•
•
M = 1kg, speed is small, f = 0.
Weight of 1kg is about W = 10N.
Net force = W – f = W – 0 = W.
Acceleration, a = Net Force/Mass
a = Weight/Mass = 10N/1kg = 10 m/s/s
N/kg = m/s/s
Ex. Falling Motion
• M = 1kg, speed is large, e.g. f = 1/3
weight = 10N/3 =3.33N
• Weight of 1kg is about W = 10N.
• Net force = W – f = W – W/3 = (2/3)W.
• Acceleration, a = Net Force/Mass
• a = (2/3)W/Mass = 6.67N/1kg = 6.67m/s/s
• N/kg = m/s/s