Ch 5 Newton`s 2nd Law

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Transcript Ch 5 Newton`s 2nd Law

Chapter 5
Newton’s Second Law of Motion-Force and Acceleration
Force Causes Acceleration
In order to make an object at rest move, it must
Suppose you hit a hockey puck
• as it is struck it experiences acceleration, but as it travels
off at constant velocity (assuming no friction) the puck is
not accelerating
• if the puck is struck again, then it accelerates again; the
force the puck is hit with causes the acceleration
Acceleration depends on net force
• to increase acceleration—increase net force
• double acceleration—double the force
Force ~ Acceleration
• directly proportional
Mass Resists
Acceleration depends on mass
to decrease acceleration—increase mass
 to increase acceleration—decrease mass
 double the mass = ½ the acceleration
Acceleration ~ 1/mass
• inversely proportional
Newton’s Second Law
Newton was the first to realize that acceleration
produced when something is moved is
determined by two things
• how hard or fast the object is pushed
• the mass of the object
Newton’s 2nd Law
The acceleration of an object is directly
proportional to the net force acting on the object
and is inversely proportional to the object’s mass
Newton’s Second Law
Second Law Video
Newton’s Second Law
a = F/m
F = ma
Robert and Laura are studying across from each other at a
wide table. Laura slides a 2.2 kg book toward Robert. If
the net force acting on the book is 1.6 N to the right, what
is the book’s acceleration?
A = F/m
= 1.6N / 2.2kg
= .73m/s2
Newton’s Second Law
2. An applied force of 50 N is used to accelerate an object to the right
across a frictional surface. The object encounters 10 N of friction. Use
the diagram to determine the normal force, the net force, the mass, and
the acceleration of the object. (Neglect air resistance.)
3. Rose is sledding down an ice-covered hill inclined at an angle of 15.0°
with the horizontal. If Rose and the sled have a combined mass of
54.0 kg, what is the force pulling them down the hill?
Newton’s 2nd Law &
A 4.60 kg sled is pulled across a smooth ice
surface. The force acting on the sled is of
magnitude 6.20 N and points in a direction 35.0°
above the horizontal. If the sled starts at rest,
what is its velocity after being pulled for 1.15 s?
V = 1.265 m/s
The fire alarm goes off, and a 97 kg fireman
slides 3.0 m down a pole to the ground floor.
Suppose the fireman starts from rest, slides with
a constant acceleration, and reaches the ground
floor in 1.2 s. What was the force exerted by the
pole on the fireman?
F = 201.76N
Acts on materials that are in contact with each other
Always acts in a direction to oppose motion
Depends on type of surfaces
• Rubber against concrete produces more friction than steel
against steel
Occurs in liquids and gases
• Air resistance, running in water
When friction is present an object can still move at a constant
• The friction force must balance outside force—net force
would be zero (no acceleration)
Does friction act on an object at rest?
• No, there must be movement
Suppose a biker cruises with a constant velocity
but the thrust from his pedaling is 10 N. What is
the acceleration of the bike?
• 0 m/s2; the bike is moving at a constant
What is the force of air resistance (friction) acting
on the bike?
• 10 N in the direction opposite the motion of
the bike; these forces must balance or the
bike would be accelerating
Types of Friction
• The resistance force that must be overcome to start
an object in motion
• The resistance force between two surfaces already
in motion
• The resistance force between a surface and a
rolling object
• The resistance force between and object and a
fluid/gas (air resistance)
Sliding Friction
Ffriction = µFnormal
µ = the coefficient of sliding friction (has no units)
1. Ben is walking through the school cafeteria but
does not realize that the person in front of him
has just spilled his glass of chocolate milk. As
Ben, who weighs 420 N, steps in the milk, the
coefficient of sliding friction between Ben and the
floor is suddenly reduced to 0.040. What is the
sliding force of friction between Ben and the
slippery floor?
While redecorating her apartment, Kelly slowly pushes an
82 kg china cabinet across the wooden dining room floor,
which resists motion with a force of 320 N. What is the
coefficient of sliding friction between the china cabinet and
the floor?
A rightward force is applied to a 10-kg object to move it
across a rough surface at constant velocity. The coefficient
of friction, µ, between the object and the surface is 0.2. Use
the diagram to determine the gravitational force, normal
force, applied force, frictional force, and net force.
(Neglect air resistance.)
Applying Force—Pressure
Pressure – the amount of force per unit area
P = F/A
• Units are Pascal’s (Pa) = N/m2
• We usually use kPa
Suppose you are standing on the ground. Do
you exert more pressure when you stand on both
feet or stand on one foot?
• The force, your weight, is the same in both
cases. Two feet have more area than one foot,
therefore, there will be more pressure exerted if
you are standing on one foot.
Brooke comes home from school and puts her books down
on the kitchen table. The books have a combined weight of
25 N and the area in contact is 0.19 m by 0.24 m. What
pressure do the books apply on the table?
2. A full coffee mug has a mass of 0.60 kg and an empty mug
has a mass of 0.30 kg. a.) Which mug, the full or empty
one, applies a greater pressure on the table? b.) If the full
mug applies a pressure of 1200 N/m2, what is the area of
the circular ring of coffee left on the table by the bottom of
the mug?
Free Fall Explained
Do heavy objects always fall faster than
light objects?
• Only in the presence of air resistance
Newton’s Second Law (F = ma)
• Mass is only a factor in the force; not in the
• A heavier object will strike the ground with a
much greater force than a lighter object, but
they will have the same acceleration and drop
Falling & Air Resistance
Air resistance obviously affects the amount of
time it takes an object to drop.
Think of an elephant and a feather; if we
dropped both off the school, which would land
Without air resistance, they land at the same
With air resistance, the elephant lands first
Falling & Air Resistance
For the elephant:
• net force is only slightly decreased by the air
resistance because the elephant has a large
weight (downward force)
For the feather:
• the net force is greatly decreased by the air
resistance because the feather has a small
weight (downward force)
Falling & Air Resistance
Does the elephant or the feather experience a greater
force due to air resistance?
Air resistance of a falling body depends on
1.How big the body is
2.How fast the body is falling
Air resistance is the result of an object plowing through a
layer of air and colliding with air molecules.
• The more air molecules which an object collides with, the
greater the air resistance force. Subsequently, the
amount of air resistance is dependent upon the speed of
the falling object and the surface area of the falling
• Based on surface area alone, it is safe to assume that
(for the same speed) the ELEPHANT would encounter
more air resistance than the feather.
Falling & Air Resistance
Why does the elephant fall faster if it
experiences more air resistance than the
• Objects accelerate when forces are unbalanced
• The feather has a smaller force of gravity,
therefore its air resistance (even though it is
smaller than the elephant’s) equals its force of
gravity much faster than for the elephant.
• When these forces are equal, the feather has
stopped accelerating and therefore reached its
terminal speed.
Falling & Air Resistance
Terminal Speed – the speed reached when the
acceleration stops
Terminal Velocity – the terminal speed with its
Ping pong ball = 9 m/s; baseball = 20 m/s
When the force of air resistance of a falling object
is equal to the object’s weight, what will the net
force be?
What will the acceleration be?
Does this mean that the object stops falling?
Falling & Air Resistance
With air resistance, Newton’s Second
Law becomes
a = Fnet/m = (weight – air resistance)/m
a = (mg – R)/m = g – R/m
R = resistance force
This is actually a much simplified version of the formula so we won’t
be doing actual air resistance problems.
Falling & Air Resistance
A skydiver jumps. As she falls faster through
the air, does air resistance increase, decrease,
or remain the same?
Does net force increase or decrease?
As she falls faster and faster does her
acceleration increase, decrease, or remain the
How can a skydiver control his/her velocity?
Falling & Air Resistance
For each case, use the diagram to find the
net force and the acceleration of the