Experiment 4 Normal and Frictional Forces Preparation Prepare for this week s quiz by reviewing last week s experiment Read this week s experiment and the section in your textbook dealing with normal forces and friction Principles Whenever two surfaces are in contact there will be two forces between them One is the normal force which is perpendicular to the surfaces The other is the friction force which is parallel to the surfaces The magnitude of the friction force will depend on the magnitude of the normal force The ratio of the friction force to the normal force is called the coefficient of friction The coefficient of friction depends only on the nature of the two surfaces in contact In this experiment you will investigate these two forces as they apply to a block on a flat surface and on an inclined plane The Normal Force Consider what happens when you put your textbook on a table It stays at rest so you know that the net force acting on it equals zero The weight of the book acts downward What keeps the book from falling through the table The answer is that the table exerts an upward force on the book This is the normal force Its magnitude is exactly equal to the weight of the book if you stack another textbook on top of the first the normal force would double A simple way to measure the magnitude of the normal force is to apply a force perpendicular to the surfaces to try and separate them When the surfaces start to separate the applied force is just equal to the normal force Thus if you measure the lift you measure the normal force If you put the same book on a tilted surface the normal force will be less The magnitude of the normal force will equal N W cos where is the angle between the surfaces and the horizontal and W is the weight of the object The direction of N is always perpendicular to the surfaces N is maximum when the two surfaces are horizontal and goes to zero when the two surfaces are vertical In this week s experiment you will actually measure the normal force by lifting a object off an inclined plane Friction Nothing is perfectly smooth under a microscope you could see just how irregular even the smoothest surface is When you put two surfaces together there is actually a lot of space between them and only the jagged parts that stick up are in contact These parts however will bond together and it is necessary to apply a force to separate them If you had to calculate the friction atom by atom you would find the process almost impossible Fortunately we can describe the average behavior of all the atoms of a surface acting together using experimentally determined constants called the coefficients of friction There are two coefficients static s and kinetic k The equations for static and kinetic friction are given by 1 Fs s N Fk kN respectively Static friction Fs is the magnitude of frictional force that a body must overcome before it can begin to move When an object is at rest this force can have any value between zero and s N It equals zero when no force is acting on the object and increases as increasing force is applied to the body Its direction is always opposite that of the applied force When the applied force is greater than s N the object will start to move Once the body actually begins to move it experiences sliding friction which acts to retard its motion For two given surfaces sliding or kinetic friction Fk is smaller than static friction and its direction is always opposite the direction of the object s motion Consider what happens when you put a friction box on a level surface and try to pull or push it The box will not move at first because the static friction force between the bottom of the box and the plane is greater than the force you are applying Up to a point the force will increase as you pull harder If you attach a scale to the box and watch carefully you will see that the reading on the scale which is the value of the force you are applying will increase until suddenly the box breaks free and starts to slide It will take less force to keep the box sliding once it starts to move The force necessary to get the box moving will is Fs max sN Its direction is opposite the direction the force you apply If you then pull the box so that it moves at constant velocity the value you see on the scale will be the force necessary to overcome the kinetic friction and it will be less than the static friction force This force will be Fk kN Now consider what happens if you put the box on a plane and start raising the plane The magnitude of the component of the box s weight acting parallel to the plane will be F W sin The magnitude of the static friction force acting in the opposite direction equals F Fs sN sW cos As long as the net force is zero the box will not move As you increase the angle W sin will increase and the normal force will decrease The static friction force will increase until it reaches its maximum When W sin is just a tiny bit larger than Fs max the box will start to slide Once 2 it starts to move it will actually accelerate down the plane because there is now a net force acting on it If you set the net force equal to zero at this point you can solve for s Fnet 0 sW cos s W sin s You can rearrange this to see that s sin s cos s tan s You can use this same technique to find the coefficient of kinetic friction Adjust the plane until you find the angle where the box slides down at constant velocity after you give it a push to overcome the force of static friction This time k tan k Now consider what happens if you pull the box up the plane at constant velocity The sum of the forces acting on it must be zero since it is not accelerating Three forces are now acting on the box the force you apply the frictional force and the component of the box s weight acting parallel to the plane Their sum equals zero W sin kN Fapplied 0 If we take the direction up the plane to be positive Fapplied is positive and W sin and kN are negative The net force acting on the box should be close to zero You can test this for yourself with your equipment Equipment 1 wood friction box 1 5 N spring balance 1 plane 1 threaded rod 1 table clamp 1 90 clamp 1 plain rod 1 protractor 2 90 cm pieces of string 250 300 grams of extra mass Procedure Be sure you remember the correct way …