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/s 2 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 F g = mg Weight depends on location, mass is independent of gravity Normal: a supporting force from a surface, always perpendicular to the surface F n Tension: the force supplied by a supporting rope, rod, cable, always in the same direction as the rope F t

Types of Forces Applied force: a general term for any pushing or pulling by some external agent F a Friction: a force that opposes motion or possible motion due to contact between surfaces (F f 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

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

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

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 (F s or f s ) prevents motion by an applied force As long as motion does not occur, f s = - F applied When applied force is maximum value without motion static friction is maximum value, f s,max

Kinetic Friction Opposes motion Always parallel to surface Less than static friction—once motion is started, less force is needed to continue motion f k < f s,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

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 2 nd 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 F W = mg F N = -mg F applied FfFf

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     FNFN F W = mg

Block on Plane with friction mg cos  mg sin     FNFN F W = mg FfFf

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.