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, ƒ s f s! µ s N Just enough force to keep object at rest. µ s is coefficient of static friction N is the normal force f F
Kinetic Friction, ƒ k f k = µ k N µ k < µ s µ k is coefficient of kinetic friction Friction force opposes direction of motion N is the normal force f F
Coefficients of Friction f! µ s N f = µ k N µ s > µ 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 is the acceleration of the child? f=59 N, a=3.80 m/s 2 / f=29.1 N, a=4.8 m/s 2
Example 4.8 Given m 1 = 10 kg and m 2 = 5 kg: a) What value of µ s would stop the block from sliding? b) If the box is sliding and µ k = 0.2, what is the acceleration? c) What is the tension of the rope? a) µ s = 0.5 b) a=1.96 m/s 2 c) 39.25 N
Example 4.9 What is the minimum µ s required to prevent a sled from slipping down a hill of slope 30 degrees? µ 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 W = r F!( r x f " r x i ) = F#x cos$ Scalar quantity Independent of time
Units of Work and Energy W = F! x SI unit = Joule 1 J = 1 N m = 1 kg m 2 /s 2
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 Δx by constant force F. N f k F mg Work of F > 0 Work of N = 0 Work of mg = 0 Work of f k < 0 Work of (kinetic) frictional force is always < 0. -> It removes mechanical energy from system.
Kinetic Energy KE = 1 2 mv2 Same units as work Remember the Eq. of motion v f 2 2! v i 2 = a"x Multiply both sides by m, 2 1 mv 2 2 f " 1 mv 2 2 i = ma#x KE f " KE i = F net #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 = PE i + KE i!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 has the fastest speed when it hits the ground? A) Ball 1 B) Ball 2 C) Ball 3 D) All have the same speed.
Example 5.5 Two blocks, A and B (m A =50 kg and m B =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