Announcements 22 Sep 2009 1 2 If you have questions on exam 1 a Look over your own exam b Look over the exam solutions see if you can figure out what you got problems wrong c Only then should you come talk to me or Tutorial Lab TAs about things you still don t understand Newton s 2nd Law Problems F ma a Inclined planes b Pulleys c Ropes d Friction e Etc Accelerating Reference Frames from last time Demo Rotating chair Ball on string To be able to ascribe accelerations to real forces you must be observing the motion from a non accelerating constant velocity point of view Physics lingo point of view reference frame Amusement Park Ride Floor drops out What are the forces on you Remember N2 is a blueprint for obtaining a useful equation it s not really the equation itself The F on the left hand side means you have to consider all of the forces from your FBD and include them on the left hand side In accelerating reference frames we tend to invent fictitious forces Do not put any forces on the right hand side Another example Coriolis force Colton Lecture 7 pg 1 Colton Lecture 7 pg 2 Question A car rounds a curve while maintaining a constant speed Is there a net force on the car as it rounds the curve a No because its speed is constant b No because the normal force is balanced by gravity c Yes because it s changing direction d Yes because it s slowing down Clicker quiz A car hits a large icy spot on the road at point P What is the path of the car if there is no friction on the ice P a b c d Colton Lecture 7 pg 3 e Friction kinetic and static Question Same box same magnitude of F which box is easier to get moving F F a left is easier b right is easier c same Friction opposes sliding motion Typically that means it opposes motion period but there are rare exceptions we ll see one later this lecture Colton Lecture 7 pg 4 From warmup Ralph noticed that in the equation for the force of static friction there s a less than or equal to sign but in the equation for kinetic friction there is a plain equals sign He wants to know why they are different What should I tell him Answer from the class Static Friction Demo Friction blocks Demo static vs kinetic friction Book figure Compare with the forces when you break a rope tied to a wall What is the tension in the rope Grows with sideways force to a point At slipping pt Friction force proportional to Normal force Kinetic aka Moving Friction Ff N Tension T mu coefficient of friction Force of pull Colton Lecture 7 pg 5 Colton Lecture 7 pg 6 Friction Summary Static Ff max S N Kinetic Ff K N Worked Problem Mary pulls a box of books with mass 25 kg to the right with a rope Use g 10 m s2 s 0 5 k 0 3 Warning N is sometimes equal to mg but not always a First she pulls horizontally on the box with a force of 40 N The box doesn t move What is the frictional force of the floor on the box b What minimum force will she have to exert to get it moving Clicker quiz If she pulls with force 175 N what will the acceleration be after it starts moving a 1 m s2 c 4 m s2 2 b 2 m s d 6 m s2 e 6 m s2 Answers 40N 125 N Colton Lecture 7 pg 7 Colton Lecture 7 pg 8 Dr Colton s Guide How to solve all Newton s 2nd Law Problems 1 Draw free body diagrams for each object 1b Divide forces into components if necessary 1c Group objects together if it seems convenient 2 Use the Newton s 2nd Law blueprint equation to get a real equation for each object 2b Do this for each direction if necessary Worked Problem If Mary pulls the 25 kg box with force 230 N at an angle of 60 above the horizontal what will the acceleration be k 0 3 FBD N2 for x N2 for y 3 Plug what you know into the equations and look at what results 3b Don t forget to plug in the acceleration if it s known 4 Solve the equations for what you re looking for 4b Sometimes this involves solving simultaneous eqns Plug what you know into equations Solve the equations for what you re looking for Answers N 50 8 N a 3 99 m s2 Colton Lecture 7 pg 9 The tires on a 5000 kg truck have s 0 8 k 0 6 tire to road friction What is the maximum stopping deceleration Colton Lecture 7 pg 10 Friction on slopes Clicker quiz For the same skis and snow as the slope angle increases the ski snow frictional force a increases b decreases c stays the same k What is the maximum stopping deceleration if the wheels are locked Hint Man with mass m what is his frictional force on a slope Use N2 What do anti lock brakes do Answers 0 8g 8 m s2 0 6g 6 m s2 Colton Lecture 7 pg 11 Colton Lecture 7 pg 12 Demo adjustable ramp Warmup questions review You start to push against a refrigerator It initially does not budge but then after you push hard enough it starts sliding along the floor Which is correct a The friction force was smallest just after the refrigerator started to move b The friction force was largest just after the refrigerator started to move c The friction force was largest just before the refrigerator started to move d The friction force was constant the whole time Demo Problem a block on a ramp doesn t slide until the angle is from horizontal What is s A block is sliding down a ramp with constant speed There is friction between the block and the ramp The friction force is a smaller than the component of gravity down the ramp b larger than the component of gravity down the ramp c equal to the component of gravity down the ramp Demo Problem Once the block starts to slide at that angle it takes s to slide down the m of the ramp What is k A small block is riding on top of a large block which is being pulled to the right with a rope Both blocks accelerate at the same rate to the right The force of friction acting on the small block is a to the left b to the right c nonexistent Colton Lecture 7 pg 13 Colton Lecture 7 pg 14 Worked Problem You invent a new Olympic sport called pulley ski jumping If the kinetic coefficient of friction is what is your acceleration m M y direction x direction Could you figure this out How far does the jumper travel Colton Lecture 7 pg 15 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