Chapter 8 Friction
Actually, no perfectly frictionless surface exists. For two surfaces in contact, tangential forces, called friction forces, will develop if one attempts to move one relative to the other. Examples: 1. If you send a book sliding down a horizontal surface, the book will finally slow down and stop. 2. If you push a heavy crate and the crate does not move, then the applied force must be counteracted by frictional forces..
. Actually, no perfectly frictionless surface exists. For two surfaces in contact, tangential forces, called friction forces, will develop if one attempts to move one relative to the other. The distinction between frictionless and rough is, therefore, a matter of degree.
Frictional Forces Friction has its basis in surfaces that are not completely smooth:
Frictional Forces The static frictional force keeps an object from starting to move when a force is applied. The static frictional force has a maximum value, but may take on any value from zero to the maximum, depending on what is needed to keep the sum of forces zero.
Frictional Forces where The static frictional force is also independent of the area of contact and the relative speed of the surfaces.
Frictional Forces The kinetic frictional force is also independent of the relative speed of the surfaces, and of their area of contact.
Frictional Forces Kinetic friction: the friction experienced by surfaces sliding against one another The frictional forces (Both static and kinetic) depends on the normal force: The constant kinetic friction. is called the coefficient of
6.2 Frictional Force: motion of a crate with applied forces There is no attempt at sliding. Thus, no friction and no motion. NO FRICTION Force F attempts sliding but is balanced by the frictional force. No motion. STATIC FRICTION Force F is now stronger but is still balanced by the frictional force. No motion. LARGER STATIC FRICTION Force F is now even stronger but is still balanced by the frictional force. No motion. EVEN LARGER STATIC FRICTION f s is the static frictional force f k is the kinetic frictional force Finally, the applied force has overwhelmed the static frictional force. Block slides and accelerates. WEAK KINETIC FRICTION To maintain the speed, weaken force F to match the weak frictional force. SAME WEAK KINETIC FRICTION Static frictional force can only match growing applied force. Kinetic frictional force has only one value (no matching).
6.2 Friction Static frictional force acts when there is no relative motion between the body and the contact surface The magnitude of the static frictional force increases as the applied force to the body is increased Finally when the there is relative motion between the body and the contact surface, kinetic friction starts to act. Usually, the magnitude of the kinetic frictional force, which acts when there is motion, is less than the maximum magnitude of the static frictional force, which acts when there is no motion.
6.2 Frictional Force Often, the sliding motion of one surface over another is jerky because the two surfaces alternately stick together and then slip. Examples: Tires skid on dry pavement Fingernails scratch on a chalkboard A rusty hinge is forced to open A bow is drawn on a violin string
Frictional Forces
Frictional Forces
Summary: friction Property 1. If the body does not move, then the static frictional force and the component of F that is parallel to the surface balance each other. They are equal in magnitude, and is f s directed opposite that component of F. Property 2. The magnitude of has a maximum value f s,max that is given by where m s is the coefficient of static friction and F N is the magnitude of the normal force on the body from the surface. If the magnitude of the component of F that is parallel to the surface exceeds f s,max, then the body begins to slide along the surface. Property 3. If the body begins to slide along the surface, the magnitude of the frictional force rapidly decreases to a value f k given by where m k is the coefficient of kinetic friction. Thereafter, during the sliding, a kinetic frictional force f k opposes the motion.
Summary: friction Maximum static-friction force and kinetic-friction force are: - proportional to normal force - dependent on type and condition of contact surfaces - independent of contact area
W F Equilibrium P F m Motion F k N F P The forces F m and F k are proportional to the normal component N of the reaction of the surface. We have F m = m s N F k = m k N where m s is the coefficient of static friction and m k is the coefficient of kinetic friction. These coefficients depend on the nature and the condition of the surfaces in contact.
P N W F = R sin f N = R cos f f F R It is sometimes convenient to replace the normal force N and the friction force F by their resultant R. As the friction force increases and reaches its maximum value F m =m s N, the angle f that R forms with the normal to the surface increases and reaches a maximum value f s, called the angle of static friction. Angle of Friction
P N F = R sin f N = R cos f W f F R If motion actually takes place, the magnitude of F drops to F k ; similarly the angle f drops to a lower value f k, called the angle of kinetic friction. The coefficient of friction and the angle of friction are related by tan f s = m s tan f k = m k Angle of Friction
W P F required N The magnitude F of the friction force is equal to F m = m s N only if the body is about to slide. If motion is not impending, F and N should be considered as independent unknowns to be determined from the equilibrium equations. The value of F required to maintain equilibrium should be checked to insure that it does not exceed F m.
W P F m = m s N N If motion is known to be impending, F has reached its maximum value F m = m s N, and this expression may be substituted for F in the equilibrium equations.
Sample Problem 8.1 SOLUTION: Determine values of friction force and normal reaction force from plane required to maintain equilibrium. Calculate maximum friction force and compare with friction force required for equilibrium. If it is greater, block will not slide. A 100 lb force acts as shown on a 300 lb block placed on an inclined plane. The coefficients of friction between the block and plane are m s = 0.25 and m k = 0.20. Determine whether the block is in equilibrium and find the value of the friction force. If maximum friction force is less than friction force required for equilibrium, block will slide. Calculate kinetic-friction force.
Sample Problem 8.1 SOLUTION: Determine values of friction force and normal reaction force from plane required to maintain equilibrium. x 3 5 F 0 : 100 lb- 300 lb F 0 y F 80 lb F 0 : N - 4 5 300 lb 0 N 240 lb Calculate maximum friction force and compare with friction force required for equilibrium. If it is greater, block will not slide. F m m N s F m 240 lb 48 lb 0.25 The block will slide down the plane.
Sample Problem 8.1 If maximum friction force is less than friction force required for equilibrium, block will slide. Calculate kinetic-friction force. F actual F k 0.20 m N k 240 lb F actual 48 lb