Chapter 4 Forces and Mass Newton s First Law If the net force F exerted on an object is zero the object continues in its original state of motion That is if F 0 an object at rest remains at rest and an object moving with some velocity continues with the same velocity Classical Mechanics does not apply for very tiny objects atomic sizes objects moving near the speed of light Forces Usually a push or pull Vector Either contact or field force Contrast with Aristotle Contact and Field Forces Fundamental Field Forces Types Strong nuclear force Electromagnetic force Weak nuclear force Gravity Electromagnetic Forces Strong Nuclear Force QCD Quantum chromodynamics confines quarks by exchaning gluons Nuclear force binds protons and neutrons by exchanging pions Opposites attract like signs repel Electric forces bind electrons in atoms Magnetic forces arise from moving charges Weak Nuclear Force Gravity Involves exchange of heavy W or Z particle Attractive force between any two bodies Responsible for decay of neutrons Proportional to both masses Inversely proportional to square of distance F G Inertia Newton s First Law Tendency of an object to continue in its original motion m 1 m2 r2 Mass A measure of the resistance of an object to changes in its motion due to a force Scalar SI units are kg Newton s Second Law Units of Force Acceleration is proportional to net force and inversely proportional to mass F ma SI unit is Newton N F ma 1 N 1 US Customary unit is pound lb Weight kg m s2 1 N 0 225 lb Weight vs Mass Weight is magnitude of gravitational force mass w mg weight M earth m r2 GM earth g 2 Rearth w G Newton s Third Law F12 F21 Single isolated force cannot exist For every action there is an equal and opposite reaction Mass is inherent property Weight depends on location Newton s Third Law cont Force on 1 due to 2 F12 is action force F21 is reaction force You can switch action reaction Action reaction forces act on different objects Action Reaction Pairs Define the OBJECT free body n n Fg Fg Newton s Law uses the forces acting ON object n and Fg act on object n and Fg act on other objects Assumptions for F ma Definition of Equilibrium F 0 Objects behave as particles ignore rotational motion for now Consider only forces acting ON object neglect reaction forces Example 4 1a Example 4 1b A Ford Pinto is parked in a parking lot A Ford Pinto is parked in a parking lot There is no net force on the Pinto A True B False The contact force acting on the Pinto from the parking lot surface A Points upwards B Is zero C Points downward Example 4 1c Example 4 1d A Ford Pinto drives down a highway on the moon at constant velocity where there is no air resistance A Ford Pinto drives down a highway on the moon at constant velocity where there is no air resistance The Pinto s acceleration is The force acting on the Pinto from the contact with the highway is vertical A Less than zero B Equal to zero C Greater than zero Mechanical Forces A True B False Some Rules for Ropes and Pulleys Strings ropes and Pulleys Force from rope points AWAY from object Gravity Normal forces Magnitude of the force is tension Friction Tension does not change when going over frictionless pulley Springs later Example 4 2 a Find acceleration b Find T the tension above the bowling ball c Find T3 the tension in the rope between the pails d Find force ceiling must exert on pulley a a g 6 1 635 m s2 b T 57 2 N Example 4 3a 2 Which statements are correct Assume the objects are static T1 is T2 A Less than B Equal to C Greater than c T3 24 5 N d Fpulley 2T 114 5 N cos 10o 0 985 sin 10o 0 173 Example 4 3b Example 4 3c 2 Which statements are correct Assume the objects are static 2 Which statements are correct Assume the objects are static T2 is T3 T1 is Mg A Less than B Equal to C Greater than A Less than B Equal to C Greater than cos 10o 0 985 sin 10o 0 173 cos 10o 0 985 sin 10o 0 173 Example 4 3d Example 4 4 2 Which statements are correct Assume the objects are static T1 T2 is Mg A Less than B Equal to C Greater than cos 10 0 985 sin 10o 0 173 o Given that Mlight 25 kg find all three tensions T3 245 3 N T1 147 4 N T2 195 7 N Cable Pull Demo Inclined Planes Choose x along the incline and y perpendicular to incline Replace force of gravity with its components Fg x mgsin Fg y mg cos Example 4 5 Example 4 6 Skip M Find the acceleration and the tension Find M such that the box slides at constant v a 4 43 m s2 T 53 7 N M 15 6 kg Forces of Friction Sliding Friction RESISTIVE force between object and neighbors or the medium Examples Sliding a box Air resistance Rolling resistance Coefficients of Friction f s N f k N s k Parallel to surface opposite to other forces independent of the area of contact Depends on the surfaces in contact Static Friction s fs s N f s N f k N s k s is coefficient of static friction f N is the normal force F Friction Demo Kinetic Friction k f k n f k is coefficient of kinetic friction Friction force opposes F n is the normal force F Example 4 7 Example 4 8 The man pushes pulls with a force of 200 N The child and sled combo has a mass of 30 kg and the coefficient of kinetic friction is 0 15 For each case What is the frictional force opposing his efforts What is the acceleration of the child f 59 N a 3 80 m s2 f 29 1 N a 4 8 m s2 Example 4 9 Given m1 10 kg and m2 5 kg a What value of s would stop the block from sliding b If the box is sliding and k 0 2 what is the acceleration c What is the tension of the rope a s 0 5 b a 1 96 m s2 Other kinds of friction Air resistance F Area v2 Rolling resistance F v Terminal velocity What is the minimum s required to prevent a sled from slipping down a hill of slope 30 degrees s 0 577 Fresistance CAv 2 mg at terminal velocity c 39 25 N Coffee Filter Demo Example 4 9 An elevator falls with acceleration a 8 0 m s2 If a 100 kg person stood on a bathroom scale during the fall what would the scale read 18 45 kg Accelerating Reference Frames Fictitious Force Derivation Equivalent to Fictitious gravitational force g fictitious a frame 1 x v0 t …
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