Chapter 4 Forces and Mass Classical Mechanics does not apply for very tiny objects atomic sizes objects moving near the speed of light 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 Contrast with Aristotle Forces Usually a push or pull Vector Either contact or field force Contact and Field Forces Fundamental Field Forces Types Strong nuclear force Electromagnetic force Weak nuclear force Gravity Strong Nuclear Force QCD Quantum chromodynamics confines quarks by exchaning gluons Nuclear force binds protons and neutrons by exchanging pions Electromagnetic Forces Opposites attract like signs repel Electric forces bind electrons in atoms Magnetic forces arise from moving charges Weak Nuclear Force Involves exchange of heavy W or Z particle Responsible for decay of neutrons Gravity Attractive force between any two bodies Proportional to both masses Inversely proportional to square of distance F G m1m2 r2 Inertia Newton s First Law Tendency of an object to continue in its original motion 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 Acceleration is proportional to net force and inversely proportional to mass r r F ma Units of Force SI unit is Newton N F ma kg m 1 N 1 2 s US Customary unit is pound lb 1 N 0 225 lb Weight Weight is magnitude of gravitational force mass w mg weight M earthm w G r2 GM earth g 2 Rearth Weight vs Mass Mass is inherent property Weight depends on location Newton s Third Law r r F12 F21 Force on 1 due to 2 Single isolated force cannot exist For every action there is an equal and opposite reaction Newton s Third Law cont F12 is action force F21 is reaction force You can switch action reaction Action reaction forces act on different objects Action Reaction Pairs r r n n Fg Fg Define the OBJECT free body 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 Objects behave as particles ignore rotational motion for now Consider only forces acting ON object neglect reaction forces Definition of Equilibrium r F 0 Example 4 1a A Ford Pinto is parked in a parking lot There is no net force on the Pinto A True B False Example 4 1b A Ford Pinto is parked in a parking lot The contact force acting on the Pinto from the parking lot surface A Points upwards B Is zero C Points downward Example 4 1c A Ford Pinto drives down a highway on the moon at constant velocity where there is no air resistance The Pinto s acceleration is A Less than zero B Equal to zero C Greater than zero Example 4 1d A Ford Pinto drives down a highway on the moon at constant velocity where there is no air resistance The force acting on the Pinto from the contact with the highway is vertical A True B False Mechanical Forces Strings ropes and Pulleys Gravity Normal forces Friction Springs later Some Rules for Ropes and Pulleys Force from rope points AWAY from object Magnitude of the force is tension Tension does not change when going over frictionless pulley 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 c T3 24 5 N d Fpulley 2T 114 5 N Example 4 3a Which statements are correct ssume the objects are static T1 is T2 A Less than B Equal to C Greater than cos 10o 0 985 sin 10o 0 173 Example 4 3b Which statements are correct ssume the objects are static T2 is T3 A Less than B Equal to C Greater than cos 10o 0 985 sin 10o 0 173 Example 4 3c Which statements are correct ssume the objects are static T1 is Mg A Less than B Equal to C Greater than cos 10o 0 985 sin 10o 0 173 Example 4 3d Which statements are correct ssume the objects are static T1 T2 is Mg A Less than B Equal to C Greater than cos 10o 0 985 sin 10o 0 173 Example 4 4 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 F mgsin g x Fg y mgcos Example 4 5 Find the acceleration and the tension a 4 43 m s2 T 53 7 N Example 4 6 M Find M such that the box slides at constant v M 15 6 kg Forces of Friction RESISTIVE force between object and neighbors or the medium Examples Sliding a box Air resistance Rolling resistance Sliding Friction f sN f kN s k Parallel to surface opposite to other forces independent of the area of contact Depends on the surfaces in contact Coefficients of Friction f sN f kN s k Static Friction s fs sN s is coefficient of static friction N is the normal force f F Kinetic Friction k f kn k is coefficient of kinetic friction Friction force opposes F n is the normal force f F Friction Demo Example 4 7 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 8 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 a What the tension of them s rope 2 is0 5 b a 1 96 c 39 25 N s Example 4 9 What is the minimum s required to prevent a sled from slipping down a hill of slope 30 degrees s 0 577 Other kinds of friction Air resistance F Area v2 Rolling resistance F v Terminal velocity Fresistance CAv2 mg at terminal velocity Coffee Filter Demo Example 4 9 An elevator falls with acceleration a 8 0 m s2 If a 200 lb person stood on a bathroom scale during the fall what would the scale read 36 9 lbs Accelerating Reference Frames Equivalent to Fictitious gravitational force g fictitious aframe Fictitious Force Derivation 1 2 x v0t at 2 1 F 2 Eq of motion in fixed …
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