PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 6 Last Lecture Gravity Normal forces Strings ropes and Pulleys Today Friction Work and Kinetic Energy Potential Energy Conservation of Energy Frictional Forces RESISTIVE force between object and neighbors or the medium Examples Sliding a box Air resistance Rolling resistance Sliding Friction Parallel to surface opposing direction of motion independent of the area of contact Depends on the surfaces in contact Object at rest Static friction Object in motion Kinetic friction Static Friction s fs sN Just enough force to keep object at rest s is coefficient of static friction N is the normal force f F Kinetic Friction k f k k N k s k is coefficient of kinetic friction Friction force opposes direction of motion N is the normal force f F Coefficients of Friction f sN f kN s k 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 the acceleration child 59 N is a 3 80 m s2 of the 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 is the tension of the rope 2 a c What 0 5 b a 1 96 m s 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 Chapter 5 Work and Energy Forms of Energy Mechanical Kinetic gravitational Thermal Microscopic mechanical Electromagnetic Nuclear Energy is conserved Work Relates force to change in energy r r r W F xf xi F xcos Scalar quantity Independent of time Units of Work and Energy W F x SI unit Joule 1 J 1 N m 1 kg m2 s2 Example 5 0 A man holds a 50 lb box at waist level for 10 minutes Has he done any work during this time 120 m Work can be positive or negative Man does positive work lifting box Man does negative work lowering box Gravity does positive work when box lowers Gravity does negative work when box is raised Work and friction A block is pulled a distance x N by constant force F fk F mg Work Work Work Work of of of of F 0 N 0 mg 0 fk 0 Work of kinetic frictional force is always 0 It removes mechanical energy from system Kinetic Energy 1 2 KE mv 2 Same units as work Remember the Eq of motion v 2f vi2 a x 2 2 Multiply both sides by m 1 2 mv mv ma x 2 f 1 2 2 i KE f KE i Fnet x KE f KE i W net Work Energy Theorem Example 5 1 A skater of mass 60 kg has an initial velocity of 12 m s He slides on ice where the frictional force is 36 N How far will the skater slide before he stops 120 m Potential Energy If force depends on distance we can define Potential Energy PE F x This must be independent of Path Conservative Force For gravity near Earth s surface PE mgh Conservation of Energy PE f KE f PEi KEi KE PE Conservative forces Gravity electrical Non conservative forces Friction air resistance Non conservative forces still conserve energy Energy just transfers to thermal energy heat Example 5 2 A diver of mass m drops from a board 10 0 m above the water surface as in the Figure Find his speed 5 00 m above the water surface Neglect air resistance 9 9 m s Example 5 3 A skier slides down the frictionless slope as shown What is the skier s speed at the bottom start H 40 m finish L 250 m 28 0 m s Example 5 4 Three identical balls are thrown from the top of a building with the same initial speed Initially Ball 1 moves horizontally Ball 2 moves upward Ball 3 moves downward Neglecting air resistance which ball the1 fastest speed A has Ball B when Ballit2 hits the ground C Ball 3 D All have the same speed Example 5 5 Two blocks A and B mA 50 kg and mB 100 kg are connected by a string as shown If the blocks begin at rest what will their speeds be after A has slid a distance s 0 25 m Assume the pulley and incline are frictionless 1 51 m s s Example 5 6 Tarzan swings from a vine whose length is 12 m If Tarzan starts at an angle of 30 degrees with respect to the vertical and has no initial speed what is his speed at the bottom of the arc 5 61 m s
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