Forces and The Laws of Motion Newton’s Laws. Force Simply a push or a pull Forces can change the...
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Transcript of Forces and The Laws of Motion Newton’s Laws. Force Simply a push or a pull Forces can change the...
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
amF
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
n
kk F
f
n
ss F
f max,
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
FW = mg
FN = -mg
FappliedFf
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)
mg cos
mg sin
FN
FW = mg
Block on Plane with friction
mg cos
mg sin
FN
FW = mg
Ff
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.