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Transcript
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.