Forces & the Laws of Motion
Chapter 4
4.1 Changes in Motion
• Objectives:
• I can explain how force affects the motion
of an object
• I can distinguish between contact forces
and field forces
• I can interpret and construct free-body
diagrams
Force
• What is a force?
• A push or pull that can change the motion of an
object
• SI unit is the newton (N)
• One newton is the force required to accelerate a
1-kg mass at 1 m/s2
• 1N = 1 kg·m/s2
1N = 0.225 lbf
• 1lbf = 4.448 N
Forces act through contact or at a
distance
• Contact forces:
• Forces that affect an object through
physical contact with another object
• Example: a baseball bat hitting a baseball
• Field forces:
• Forces that affect an object without
physical contact
• Examples: gravitational, magnetic, and
electrostatic forces
Field Theory
• Explains how forces can affect an object
without physical contact
• Explanation of field forces…
• An object affects the space surrounding it
so that a force is exerted on other objects
in that space.
• The “field” is the region of space in which
the force is exerted
• Example: magnetic field
Electrostatic Forces
• Example of a field force
• Stream of ethanol is
attracted to an electrically
charged probe
Force Diagrams
• Force is a vector
• Force diagrams:
– Diagram the objects involved in a situation
and the forces acting on the objects
• Free-body diagrams:
– Diagram the forces acting on a single object
– i.e. diagram the object “free” from influence of
other objects and their forces
Representing Forces
• Force is a vector
• Free-body diagrams illustrate forces acting on
an object isolated from its surroundings
Free-body Diagrams
• Free-body diagrams are diagrams used to
show the relative magnitude and direction
of all forces acting upon an object in a
given situation
• Represent object as a box with forces
originating from center of box
Common Forces in Force
Diagrams
•
•
•
•
•
•
•
Applied force
Weight
Normal force
Friction
Air resistance
Tension
Spring force
Fapp
Fg
FN
Ff
Fair
FT
Fsp
(mg)
┴ to surface
Example of a Free-Body Diagram
4.2 Newton’s First Law:
Law of Inertia
• Galileo noted that things tend to slide
further on smoother surfaces
• Concluded that an object would slide
forever on a perfectly smooth surface in
the absence of any applied force
• This led to Newton’s First Law of Motion
Newton’s First Law of Motion
• An object at rest remains at rest, and an
object in motion continues in motion in a
straight line, with a constant velocity,
unless acted upon by a net external force
• Inertia: the tendency of an object to
maintain its state of uniform linear motion
• When net force on an object is zero,
acceleration is zero (∆v/∆t = 0)
Newton’s First Law of Motion
• An object at rest remains at rest, and an
object in motion continues in motion with a
constant velocity unless acted upon by a
net external force
• A net force is required to change the state
of motion of an object
• Net external force
– Resultant force produced from combination of
all forces acting on an object
Net Force
• A net force is the resultant force of two or
more forces
• Since forces are vectors, the net
(resultant) force is determined as any
other resultant vector.
• Example: A student pushes a book across
a table with a force of 5 N
Net Force
• Example: A student pushes a book across
a table with a force of 5 N. Frictional
forces of 2 N act in the opposite direction.
What is the net force acting on the book?
Forces Acting on
Inclined Planes
1.
2.
3.
4.
5.
FN, normal force, surface acting on object
Fg, weight = mg
Fgx, component of g, ║ to surface
Fgy, component of g ┴ surface
Ff, friction
Inertia
• Inertia is tendency of an
object to maintain its
state of motion unless
acted upon by a net force
• Mass is a measurement
of inertia
• ↑ mass → ↑ inertia
• As the same speed, a
rolling car is more difficult
to stop than a rolling
basketball
Equilibrium
• The state of a body in which
there is no change in motion
• Net force acting on a body is
zero
4.3 Newton’s 2nd & 3rd Laws
Learning objectives
1. Describe acceleration of an object in
terms of its mass and the net external
force acting on it
2. Predict direction & magnitude of
acceleration caused by a known net
external force
3. Identify action-reaction force pairs
4. Explain why action-reaction pairs do not
result in equilibrium
Newtons 2nd Law
• The acceleration of an object is directly
proportional to the net external force
acting on the object and inversely
proportional to the mass of the object
• a = ΣF /m , where Σ means “sum of”
• ΣF = ma
Conceptual Question
A grain truck filled with soy beans
accelerates along the highway at 0.50
m/s2. If the driving force on the truck
remains the same, what happens to the
acceleration of the truck if soybeans leak
from it at a constant rate?
Answer: The loss of soy beans is a
decrease in mass. Since a = ΣFnet /m ,
acceleration increases.
Newton’s 3rd Law
• "For every action, there is an equal and
opposite reaction." equal magnitude and
opposite direction
• In every interaction, there is a pair of
forces acting on the two interacting
objects.
• Action-reaction force pairs: equal in
magnitude, but opposite in direction.
Action-Reaction Force Pairs
• Since force pairs are equal in magnitude, but opposite in
direction, why do they not result in equilibrium?
• Because they act on different objects.
• If equal but opposite forces acted on the same object,
there would be equilibrium, i.e. no net force.
4.4 Everyday Forces
• Weight
Force of gravity acting on a mass
Fg = mg
W = mg
Fw = mg
• Normal Force
contact force exerted by one object on
another in a direction ┴ surface of contact
• Friction
contact force that opposes motion….
opposes applied force
Weight & Normal Force
• Fg = mg
• Always ┴ surface of
earth
• Directed toward
center of earth
• FN = Fgcos (θ)
• Always ┴ surface of
contact
• Always opposes Fg
Identify Forces
Acting on Inclined
Planes
1.
2.
3.
4.
5.
FN, normal force, surface acting on object
Fg, weight = mg
Fgx, component of g, ║ to surface
Fgy, component of g ┴ surface
Ff, friction
Force of Friction
• Ff opposes applied force
• Static friction Ffs ….
force exerted by environment on motionless body to
resist applied force
• Kinetic friction Ffk ….
force exerted by environment on moving
object to resist applied force
• Ffs > Ffk
• Depends on surfaces in contact….
Types and smoothness
• Proportional to FN
Static vs. Kinetic Friction
Relationship of Ff and Fn
• Ff is proportional to FN
• Proportionality constant is the coefficient
of friction, μ
• μ = Ff / FN
• Depends on types of surfaces in contact
• Depends on static or kinetic friction
μs = Fs / FN
μk = Fk / FN
Problem 4D
• A crate of mass 24 kg is set in motion on a
horizontal surface with a horizontal force
of 75 N. Find the coefficient of static
friction, μs
• μs = Fs / FN
•
= Fs / mg
•
= 75 N / (24 kg x 9.81 m/s2)
•
= 0.32
Coefficients of Friction
(Approximate)
Materials
μs
μk
Steel on steel
0.74
0.57 Waxed wood on wet
Materials
μs
μk
0.14
0.10
----
0.04
0.15
0.06
snow
Aluminum on steel
0.61
0.47 Waxed wood on dry
snow
0.80 Metal on metal
Rubber on dry
concrete
1.00
Rubber on wet
concrete
----
0.50 Ice on ice
0.10
0.03
Wood on wood
0.40
0.20 Teflon on Teflon
0.04
0.04
Glass on glass
0.90
0.40 Synovial joints in
0.01
0.003
(lubricated)
humans
Role of Surface in Friction
• Static friction increases
with increasing force
until overcome
• Kinetic friction is less
than the maximum
static friction
Frictional Forces &
Applied Force
Air Resistance
• When an object passes through a fluid….
• The fluid has to be pushed out of the way
for the object to pass through it
• i.e., Motion of objects through a fluid is
hindered by the fluid
Air Resistance
•
•
•
•
At low speeds FR is proportional to v
At higher speeds FR is proportional to v2
When FR = FA, constant speed
Terminal speed
– For free falling object
– When FR up = Fg down
– Fnet = 0
Four Fundamental Forces
• All are field forces
• Strong nuclear force
– Holds nucleus together
• Weak nuclear force
– Involved in radioactive decay
• Electromagnetic force
• Gravitational force
– weakest