Download Forces and The Laws of Motion

Forces and The Laws of Motion
Newton’s Laws
Force
• Simply a push or a pull
• Forces can change the state of an object’s
motion
• A vector quantity with magnitude and
direction
• Unit is the newton (N) :1 N = 1 kg·m/s2
• Forces can be due to contact or from the
action of a field such as gravity
Types of Forces
• Weight: the force on a mass caused by gravity,
direction is down Fg = mg
• Weight depends on location, mass is independent
of gravity
• Normal: a supporting force from a surface,
always perpendicular to the surface Fn
• Tension: the force supplied by a supporting rope,
rod, cable, always in the same direction as the
rope Ft
Types of Forces
• Applied force: a general term for any
pushing or pulling by some external agent
Fa
• Friction: a force that opposes motion or
possible motion due to contact between
surfaces (Ff or f)
Free-body Diagrams
• Forces are represented by vector arrows
• Objects are represented by simplified
diagrams with all forces acting on the object
drawn from its center
• Other objects not directly involved are not
shown
• Used to analyze forces and motion of single
object
Early Motion Ideas
• Aristotle (~ 350 BC) taught continuing
motion requires constant force because
objects naturally come to a stop
• Galileo (~ 1630) first to understand that
moving objects will continue moving and
stop due to a force
• Isaac Newton restated ideas in Principia
Mathematica (1684 – 1686)
Galileo’s Experiment
Galileo’s Experiment
First Law of Motion
• When the net external force on an object is
zero, its acceleration is zero
• Conversely, an object that is not
accelerating has no net force acting on it
• Net force is vector sum of all forces:
• Bodies at rest will stay at rest and bodies in
motion will stay in straight-line motion at a
constant speed if no net force is present

F

F
First Law of Motion
• Inertia: the property of a body that resists
any change in motion
• The measure of inertia is mass
• Seat belts & air bags protect us from our
inertia
Equilibrium
• If net force equals zero, object is said to be
in equilibrium
• Can be at rest or moving at constant
velocity
Equilibrium Problems
• Draw free body diagram
• Resolve all forces not aligned with x – y
coordinate system into x and y components
• Sum of x forces and components = 0 and
sum of y forces and components = 0
• Ups = downs; lefts = rights
Second Law of Motion
• A net force on an object creates an
acceleration
• The acceleration is directly proportional to
the net external force and inversely
proportional to the object’s mass


F  ma
Third Law of Motion
• If two objects interact, they exert equal and
opposite forces on each other
• Forces always exist in pairs
• For every action there is an equal and
opposite reaction
• action/reaction forces act on different
objects, don’t cause equilibrium
Friction
• Can be desirable (gripping, traction, etc.) or
undesirable (causes heat and wear from
moving parts)
• Caused by adhesion due to intermolecular
forces and irregularities of surfaces
• On microscopic scale, even smooth-feeling
surfaces are rough
Static Friction
• Static friction (Fs or fs) prevents motion by an
applied force
• As long as motion does not occur, fs = - Fapplied
• When applied force is maximum value
without motion static friction is maximum
value, fs,max
Kinetic Friction
• Opposes motion
• Always parallel to surface
• Less than static friction—once motion is
started, less force is needed to continue
motion
• fk < fs,max
Coefficient of Friction
• Ratio of normal force to the friction force
• Depends on the type of surfaces in contact
• Different coefficients for static and kinetic
friction
fk
k 
Fn
s 
f s ,max
Fn
Friction in Fluids
• Friction is created by fluids (liquids and gases)
as well as solids
• Called drag, it depends on density of fluid,
cross-sectional area of moving object, and
speed
• Drag force is proportional to the square of the
speed
• When drag force equals weight, net force is
zero, acceleration is zero, and terminal
velocity is reached
Using the Second Law
• Define the boundaries of the system
• Draw a free body diagram of the situation
• Resolve all forces not aligned with
coordinate system into x and y components
• For each direction, find the sum of all forces
and write the 2nd law
Laws of Motion Applications
• Statics: analyze forces where no motion
occurs
• Dynamics: analyze forces with motion and
acceleration with or without friction
• Examples include blocks on planes, pulley
systems, slippery slopes
Statics
• No motion so net force = 0
• Can have forces from
supporting surfaces, ropes,
beams, girders, etc.
• important in building
structures where no motion is
desired: bridges, buildings,
etc.
Block on level surface
• Normal force equal in
magnitude to weight
• Friction force = weight x

• Applied force - friction
force = net force
• If applied force > friction
force, block accelerates
FN = -mg
Ff
Fapplied
FW = mg
Blocks and Inclined Planes
• Use coordinate system aligned with plane
• Find weight components of block parallel to and
perpendicular with plane
• Perpendicular component equals normal force between
surfaces
• Parallel component is force that causes motion down
the plane
• Component magnitudes depend on elevation angle of
plane
Block on Plane (no friction)
FN
mg sinq
q
q
q
FW = mg
mg cosq
Block on Plane with friction
FN
Ff
mg sinq
q
q
q
FW = mg
mg cosq
Block - Plane with friction
• Parallel component of weight - friction
force = net force
• If net force > 0, block accelerates down
plane
• If net force = 0, block is at rest or moves
down plane at constant speed.