Forces Prof. Yury Kolomensky Feb 9/12, 2007 - Hooke s law - String tension - Gravity and Weight - Normal force - Friction - Drag -Review of Newton s laws
Today s Plan Catalog common forces around us What you will use in problems But also what you experience every day So that you can sound sophisticated when you tell your mom what you learned Remember Newton s laws Computational techniques: will use today again Review (again) on Monday
Spring Force Hooke s law: force is proportional to extension Demo: suspended block Mathematically F =! kx Warning: this cannot continue to x Max tension
String Tension Force exerted by a rope, string, or cable on an object it is attached to Always directed along the string Always points away from contact (pulls the object) Approximations: Un-stretchable string: tension T constant along length Massless string: does not sag, has no weight Common pulley approximations (until Ch.10): frictionless, massless
Gravity F g Newton s law of gravity: F g = G N Mm/r 2 G N =6.6742(10)*10-11 N*m 2 /kg 2 is the Newton s constant Plug in Earth mass and radius: M earth =6*10 24 kg R earth =6400 km F g =mg, where g=g N M earth /R earth2 =9.8 m/s 2
My pet peeve Weight I think the book defines it incorrectly Should not be equal to gravity Depends on acceleration, since, according to Einstein, can t distinguish gravity and acceleration Physicists define weight as force an object exerts on support Have to be careful about this one and read carefully! g W y mg
Friction Force that resists relative motion of dry surfaces Three kinds Static friction Kinetic friction Rolling friction Demo on Friday
Static friction Properties of Friction No relative motion: static friction balances externally applied force Directed opposite to external force along the surface 0 F static F max Maximum friction force proportional to normal force at the surface F max =µ s N Kinetic friction Once the motion starts, friction force is equal to F kin = µ k N Direction is opposite to velocity vector (opposes motion) Rolling friction For rolling motion over surface F roll = µ r N 0 µ r µ k µ s Coefficients of friction: property of materials and surface F fr mg N F ext
Coefficients of Friction Steel on steel Al on steel Rubber on concrete Wood on wood Glass on glass Ice in ice Teflon on teflon Synovial joints in humans Measuring friction: demo µ s 0.7 0.6 1.0 0.25-0.5 0.9 0.1 0.04 0.01 µ k 0.6 0.5 0.8 0.2 0.4 0.03 0.04 0.003
When an object moves through a fluid (gas or liquid) it experiences an opposing force known as drag. Under certain conditions (turbulent, as opposed to laminar, flow) the magnitude of the drag force is given by the expression: 1 D C Av 2 Drag Force and Terminal Speed 2 =! C is a constant (depends on shape), A is the effective Object at terminal speed cross sectional area of the moving object, ρ is the density of the surrounding fluid, and v is the object s speed. Consider an object (a cat of mass m in this case) start moving in air. Initially D = 0. As the cat accelerates D increases and at a certain speed v t D = mg At this point the net force and thus the acceleration become zero and the cat moves with constant speed v t known the the terminal speed (velocity) 1 2 D = C! Avt = mg 2 v t = 2mg C! A
Object Car Smooth sphere Human body Parachute Terminal Speed ρ air =1.2 kg/m 3 C 0.3-0.5 0.5 ~1 ~1-1.2 Object v t (m/s) Shotput 145 Skydiver 60 Baseball 42 Basketball 20 Ping-pong ball 9 Raindrop 7 Parachutist 5
Newton s Laws: Summary 1st law: Relationship between inertial systems v = v + V a=a v is velocity in fixed frame, v is velocity in moving frame, V is velocity of moving frame wrt fixed V=const : inertial frames 2nd law: F = ma (remember vector form) 3rd law F 12 =-F 21 for two interacting bodies
Relationships
Problem-Solving Strategy 1. Visualize (draw a picture) 2. Write down knowns and unknowns 3. Split system into objects 4. Draw free-body diagrams for each object List and draw all forces: contact, long-distance 5. 2nd law in vector form and projections 2 or 3 equations per object 6. Write down constraints Additional equations 7. Solve for unknowns 8. Plug in numbers Demo: system of pulleys, mechanical advantage