Learning Objectives

Discuss the general characteristics of friction.Describe the various species of friction.Calculate the magnitude of static and kinetic friction.

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Friction is a force that is around us all the moment that opposes relative motion in between surfaces in contact yet also enables us to relocate (which girlfriend have discovered if girlfriend have ever before tried come walk on ice). If a typical force, the actions of friction is in reality very complicated and is still not completely understood. We need to rely greatly on observations for whatever understandings we deserve to gain. However, we deserve to still resolve its an ext elementary basic characteristics and also understand the circumstances in which that behaves.

One the the simpler characteristics of friction is the it is parallel come the contact surface in between surfaces and always in a direction that opposes movement or attempted movement of the systems family member to every other. If two surfaces are in contact and also moving loved one to one another, climate the friction in between them is dubbed kinetic friction. For example, friction slowly a hockey puck slide on ice. Yet when objects space stationary, revolution friction can act between them; the revolution friction is usually better than the kinetic friction between the surfaces.

If 2 surfaces are in contact and also moving family member to one another, then the friction in between them is called kinetic friction.

Imagine, for example, do the efforts to on slide a hefty crate throughout a concrete floor—you might push harder and also harder ~ above the crate and also not move it in ~ all. This way that the revolution friction responds to what girlfriend do—it increases to be same to and also in the opposite direction of her push. Yet if you finally push hard enough, the crate seems to slip suddenly and starts to move. As soon as in activity it is easier to keep it in motion than it to be to gain it started, indicating the the kinetic friction force is much less than the static friction force. If you include mass come the crate, say by place a crate on optimal of it, you need to push also harder to get it began and likewise to store it moving. Furthermore, if you oiled the concrete girlfriend would uncover it to be simpler to acquire the crate started and keep it going (as you could expect).

(Figure)is a crude photographic representation of just how friction occurs at the interface in between two objects. Close-up investigate of this surfaces reflects them to be rough. So as soon as you press to get an object moving (in this case, a crate), you should raise the object till it deserve to skip along with just the tips of the surface ar hitting, break off the points, or carry out both. A substantial force can be stood up to by friction through no apparent motion. The harder the surfaces are propelled together (such together if one more box is inserted on the crate), the more force is required to move them. Component of the friction is because of adhesive forces between the surface ar molecules the the two objects, which define the dependency of friction top top the nature that the substances. Adhesion varies through substances in contact and is a complex aspect of surface physics. Once things is moving, there space fewer points of contact (fewer molecules adhering), so less pressure is compelled to keep the thing moving. At small but nonzero speeds, friction is almost independent the speed.

Frictional forces, such as


where is the coefficient of revolution friction and also is the size of the normal force (the force perpendicular come the surface).

Magnitude of revolution Friction

Magnitude of static friction is


where is the coefficient of static friction and also is the size of the typical force.

The prize

way less 보다 or same to, implying that static friction deserve to have a minimum and a maximum value of
. Revolution friction is a responsive force that rises to it is in equal and also opposite to every little thing force is exerted, approximately its best limit. As soon as the applied force exceeds
, the object will certainly move. Thus


Once an item is moving, the size of kinetic friction

is provided by

where is the coefficient that kinetic friction. A device in i beg your pardon

is described as a device in i m sorry friction behaves simply.

Magnitude the Kinetic Friction

The magnitude of kinetic friction is offered by

where is the coefficient of kinetic friction.

As checked out in (Figure), the coefficients that kinetic friction are less than their static counterparts. That values of

in (Figure) are declared to only one or, at most, 2 digits is one indication that the approximate description of friction given by the over two equations.

Coefficients the Static and also Kinetic FrictionSystemStatic frictionKinetic friction
Rubber on dry concrete1.00.7
Rubber ~ above wet concrete0.70.5
Wood on wood0.50.3
Waxed timber on wet snow0.140.1
Metal on wood0.50.3
Steel on steel (dry)0.60.3
Steel on stole (oiled)0.050.03
Teflon top top steel0.040.04
Bone lubricated by synovial fluid0.0160.015
Shoes on wood0.90.7
Shoes on ice0.10.05
Ice on ice0.10.03
Steel ~ above ice0.040.02

The equations given previously include the dependence of friction ~ above materials and the regular force. The direction of friction is constantly opposite the of motion, parallel come the surface between objects, and also perpendicular come the normal force. Because that example, if the crate you shot to press (with a force parallel to the floor) has actually a massive of 100 kg, then the normal pressure would be equal to that is weight,

, perpendicular come the floor. If the coefficient of revolution friction is 0.45, girlfriend would have to exert a force parallel come the floor greater than
to relocate the crate. As soon as there is motion, friction is less and also the coefficient that kinetic friction could be 0.30, so that a force of only 290 N (
) would save it relocating at a consistent speed. If the floor is lubricated, both coefficients are substantially less than they would be there is no lubrication. Coefficient the friction is a unit less quantity with a size usually between 0 and 1.0. The coefficient the the friction relies on the two surfaces that room in contact.

Find a small plastic thing (such as a food container) and also slide the on a kitchen table by providing it a gentle tap. Currently spray water top top the table, simulating a irradiate shower of rain. What happens now when you offer the object the same-sized tap? Now include a couple of drops that (vegetable or olive) oil top top the surface of the water and give the same tap. What happens now? This latter case is specifically important for vehicle drivers to note, particularly after a light rain shower. Why?

Many human being have proficient the slipperiness of wade on ice. However, numerous parts the the body, particularly the joints, have much smaller coefficients that friction—often 3 or 4 times much less than ice. A share is developed by the ends of two bones, which are linked by special tissues. The knee joint is created by the lower leg bone (the tibia) and also the thighbone (the femur). The hip is a sphere (at the end of the femur) and socket (part of the pelvis) joint. The end of the skeleton in the joint space covered by cartilage, which offers a smooth, nearly glassy surface. The joints likewise produce a fluid (synovial fluid) the reduces friction and also wear. A damaged or arthritic joint have the right to be changed by an artificial joint ((Figure)). These replacements can be make of metals (stainless steel or titanium) or plastic (polyethylene), likewise with very small coefficients that friction.

Artificial knee replacement is a procedure that has been perform for an ext than 20 years. In this figure, we check out the post-op X-rays that the right knee share replacement. (credit: Mike Baird, Flickr)
Other organic lubricants include saliva produced in our mouths to aid in the swallowing process, and the slippery mucus found between organs in the body, permitting them to move openly past every other throughout heartbeats, throughout breathing, and when a human moves. Synthetic lubricants are additionally common in hospitals and doctor’s clinics. Because that example, when ultrasonic imaging is carried out, the gelatin that couples the transducer come the skin likewise serves to to lubricate the surface between the transducer and the skin—thereby reducing the coefficient the friction in between the 2 surfaces. This enables the transducer to move freely over the skin.

A skier through a mass of 62 kg is sliding under a snowy slope. Find the coefficient the kinetic friction because that the skier if friction is recognized to be 45.0 N.


The size of kinetic friction was given in to be 45.0 N. Kinetic friction is pertained to the normal force as ; thus, the coefficient the kinetic friction can be found if we can uncover the normal force of the skier ~ above a slope. The normal force is constantly perpendicular to the surface, and since over there is no activity perpendicular come the surface, the normal force should same the ingredient of the skier’s weight perpendicular come the slope. (See the skier and also free-body diagram in (Figure).)

The motion of the skier and also friction space parallel to the slope and so it is many convenient to job all forces onto a coordinate device where one axis is parallel come the slope and the other is perpendicular (axes presented to left of skier).
(the regular force) is perpendicular to the slope, and also
(the friction) is parallel come the slope, however
(the skier’s weight) has components along both axes, namely
and also
is same in magnitude to
, so there is no movement perpendicular to the slope. However,
is less than
in magnitude, so there is acceleration down the slope (along the x-axis).


This result is a little smaller 보다 the coefficient noted in (Figure) because that waxed lumber on snow, however it is still reasonable due to the fact that values the the coefficients the friction deserve to vary greatly. In instances like this, where an object of fixed

slides under a slope that makes an angle through the horizontal, friction is given by
. Every objects will slide down a slope with consistent acceleration under this circumstances. Proof of this is left because that this chapter’s Problems and Exercises.

An object will certainly slide down an inclined airplane at a constant velocity if the net force on the thing is zero. We deserve to use this reality to measure up the coefficient of kinetic friction between two objects. As shown in (Figure), the kinetic friction on a slope

. The component of the weight down the slope is equal to
(see the free-body chart in (Figure)). These pressures act in the contrary directions, so as soon as they have actually equal magnitude, the acceleration is zero. Writing these out:

Put a coin top top a book and tilt it until the coin slides in ~ a continuous velocity under the book. You can need come tap the book lightly to get the coin to move. Measure up the edge of tilt relative to the horizontal and find . Note that the coin will not begin to slide at all till an angle better than is attained, due to the fact that the coefficient of revolution friction is larger than the coefficient the kinetic friction. Talk about how this may affect the value for and also its uncertainty.

We have debated that when things rests on a horizontal surface, over there is a normal force supporting it equal in magnitude to that is weight. Furthermore, basic friction is constantly proportional to the normal force.

The simpler elements of friction encountered so much are the macroscopic (large-scale) characteristics. Great strides have actually been do in the atomic-scale explanation that friction throughout the previous several decades. Researchers room finding the the atomic nature the friction appears to have several basic characteristics. These features not only define some that the simpler aspects of friction—they likewise hold the potential because that the development of virtually friction-free settings that might save numerous billions the dollars in power which is currently being converted (unnecessarily) to heat.

(Figure) illustrates one macroscopic properties of friction the is defined by microscopic (small-scale) research. Us have noted that friction is proportional to the common force, but not come the area in contact, a somewhat counterintuitive notion. As soon as two turbulent surfaces space in contact, the actual contact area is a tiny portion of the full area since only high spots touch. When a higher normal force is exerted, the actual contact area increases, and also it is uncovered that the friction is proportional come this area.

Two stormy surfaces in call have a lot smaller area that actual contact than their complete area. Once there is a greater normal pressure as a an outcome of a greater applied force, the area the actual call increases together does friction.
But the atomic-scale view assures to explain far more than the much easier features of friction. The device for how warmth is produced is currently being determined. In various other words, why do surfaces get warmer once rubbed? Essentially, atoms are linked with one an additional to kind lattices. Once surfaces rub, the surface atoms adhere and cause atom lattices come vibrate—essentially producing sound waves that penetrate the material. The sound tide diminish with distance and their energy is converted right into heat. Chemistry reactions the are pertained to frictional stay can also occur in between atoms and also molecules ~ above the surfaces. (Figure) shows how the guideline of a probe drawn throughout another material is deformed through atomic-scale friction. The pressure needed to traction the tip can be measured and is discovered to be regarded shear stress, which will be debated later in this chapter. The variation in shear anxiety is impressive (more 보다 a element of
) and daunting to suspect theoretically, however shear tension is yielding a fundamental understanding of a large phenomenon known since old times—friction.

The reminder of a probe is deformed party by frictional pressure as the probe is dragged across a surface. Dimensions of exactly how the pressure varies for various materials room yielding an essential insights right into the atomic nature that friction.
Explore the pressures at work when you try to push a filing cabinet. Create an applied force and see the result friction force and also total pressure acting on the cabinet. Charts present the forces, position, velocity, and acceleration vs. Time. Draw a free-body diagram of every the pressures (including gravitational and also normal forces). Click to open up media in new browser.

Section Summary

Friction is a call force in between systems that opposes the activity or test motion between them. Straightforward friction is proportional come the normal force pushing the solution together. (A normal pressure is always perpendicular to the contact surface between systems.) Friction depends on both of the products involved. The size of revolution friction between systems stationary relative to one one more is given by

wherein is the coefficient of revolution friction, which relies on both that the materials.The kinetic friction force between systems moving relative to one one more is given by
where is the coefficient of kinetic friction, which additionally depends ~ above both materials.

Conceptual Questions

Define normal force. What is its relationship to friction as soon as friction behaves simply?

The glue on a item of tape deserve to exert forces. Deserve to these forces be a type of simple friction? Explain, considering specifically that tape deserve to stick to vertical walls and even come ceilings.

When you discover to drive, you discover that you have to let up slightly on the brake pedal together you pertained to a avoid or the auto will stop with a jerk. Describe this in terms of the relationship between static and also kinetic friction.

When you push a piece of chalk across a chalkboard, it periodically screeches because it swiftly alternates between slipping and sticking to the board. Explain this procedure in more detail, in details explaining just how it is regarded the fact that kinetic friction is less than static friction. (The same slip-grab procedure occurs as soon as tires screech on pavement.)

A physics major is cooking breakfast once he notices the the friction force between his steel spatula and his Teflon frying pan is only 0.200 N. Understanding the coefficient of kinetic friction in between the 2 materials, he quickly calculates the normal force. What is it?

(a) as soon as rebuilding she car’s engine, a physics major must exert 300 N of force to insert a dry steel piston into a steel cylinder. What is the size of the common force between the piston and cylinder? (b) What is the size of the force would she have to exert if the steel components were oiled?

(a) What is the best frictional force in the knee share of a person who supports 66.0 kg of her mass on the knee? (b) during strenuous practice it is possible to exert forces to the joints the are quickly ten times better than the load being supported. What is the maximum pressure of friction under together conditions? The frictional pressures in joints are reasonably small in all circumstances except when the joints deteriorate, such as from injury or arthritis. Enhanced frictional forces can cause further damage and pain.

Suppose you have a 120-kg wooden crate relaxing on a wood floor. (a) What maximum pressure can friend exert horizontally ~ above the crate without relocating it? (b) If you continue to exert this pressure once the crate starts to slip, what will the magnitude of that acceleration then be?

(a) If half of the weight of a little

utility van is supported by its two drive wheels, what is the magnitude of the best acceleration it can accomplish on dry concrete? (b) will a metal cabinet lying on the wooden bed the the truck slip if it speeds up at this rate? (c) resolve both problems assuming the truck has four-wheel drive.

A team the eight dog pulls a sled through waxed wood runners ~ above wet snow (mush!). The dogs have average masses that 19.0 kg, and also the invited sled v its rider has a massive of 210 kg. (a) calculation the magnitude of the acceleration starting from rest if each dog exerts one average force of 185 N behind on the snow. (b) What is the magnitude of the acceleration once the sled starts to move? (c) for both situations, calculation the magnitude of the pressure in the coupling in between the dogs and also the sled.

Consider the 65.0-kg ice skater being moved by two others displayed in (Figure). (a) uncover the direction and also magnitude of , the complete force exerted on her by the others, offered that the magnitudes

are 26.4 N and also 18.6 N, respectively. (b) What is her initial acceleration if she is initially stationary and also wearing steel-bladed skates that point in the direction of ? (c) What is she acceleration assuming she is currently moving in the direction the ? (Remember the friction always acts in the direction opposite that of activity or attempted motion in between surfaces in contact.)

Show the the acceleration of any object down a frictionless incline that provides an edge through the horizontal is

. (Note that this acceleration is live independence of mass.)

Show the the acceleration of any object under an incline where friction behaves just (that is, whereby ) is

note that the acceleration is live independence of mass and reduces to the expression found in the previous problem when friction becomes negligibly tiny

Calculate the deceleration the a snow boarder going increase a

, steep assuming the coefficient of friction for waxed lumber on wet snow. The result of (Figure) might be useful, however be cautious to take into consideration the reality that the eye boarder is going uphill. Explicitly display how you monitor the steps in Problem-Solving Strategies.

(a) calculate the acceleration that a skier heading under a

slope, suspect the coefficient that friction for waxed hardwood on wet snow. (b) discover the angle of the slope under which this skier could coast at a consistent velocity. You deserve to neglect air resistance in both parts, and you will find the an outcome of (Figure) to be useful. Explicitly display how you follow the steps in the Problem-Solving Strategies.

If an object is to rest on one incline without slipping, then friction have to equal the component of the load of the thing parallel come the incline. This needs greater and greater friction for steeper slopes. Present that the maximum angle of one incline over the horizontal because that which things will no slide down is

. You may use the an outcome of the previous problem. Assume the
and also that static friction has actually reached its maximum value.

Calculate the maximum deceleration that a auto that is heading down a slope (one that provides an edge of through the horizontal) under the adhering to road conditions. You may assume the the weight of the vehicle is evenly spread on all four tires and that the coefficient of static friction is involved—that is, the tires room not permitted to slip during the deceleration. (Ignore rolling.) calculation for a car: (a) On dried concrete. (b) top top wet concrete. (c) ~ above ice, assuming that

, the exact same as because that shoes top top ice.

Calculate the maximum acceleration of a auto that is heading up a slope (one that provides an angle of through the horizontal) under the complying with road conditions. Assume that only fifty percent the weight of the automobile is supported by the two drive wheels and that the coefficient of revolution friction is involved—that is, the tires are not enabled to slip throughout the acceleration. (Ignore rolling.) (a) On dried concrete. (b) on wet concrete. (c) top top ice, assuming the

, the same as because that shoes on ice.

A freight train consists of two

engines and 45 car with mean masses that
. (a) What pressure must each engine exert behind on the monitor to advice the train in ~ a price of
if the force of friction is
, assuming the engines exert the same forces? This is no a large frictional pressure for such a substantial system. Rolling friction for trains is small, and consequently trains are really energy-efficient transportation systems. (b) What is the magnitude of the pressure in the coupling in between the 37th and 38th cars (this is the pressure each exerts on the other), assuming all cars have actually the same mass and also that friction is evenly dispersed among every one of the cars and also engines?

Consider the 52.0-kg mountain climber in (Figure). (a) discover the tension in the rope and the pressure that the hill climber have to exert through her feet top top the vertical rock challenge to continue to be stationary. Assume the the force is exerted parallel to she legs. Also, i think negligible pressure exerted by her arms. (b) What is the minimum coefficient that friction between her shoes and also the cliff?

Part of the climber’s weight is sustained by she rope and component by friction in between her feet and also the rock face.

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A contestant in a winter sporting event pushes a 45.0-kg block that ice across a frozen lake as displayed in (Figure)(a). (a) calculate the minimum force
he have to exert to acquire the block moving. (b) What is the magnitude of the acceleration once it starts come move, if that pressure is maintained?

Repeat (Figure) v the contestant pulling the block that ice through a rope end his shoulder at the exact same angle above the horizontal as shown in (Figure)(b).

Which technique of sliding a block of ice cream requires less force—(a) advertise or (b) pulling in ~ the exact same angle over the horizontal?


frictiona force that opposes relative movement or attempts at motion between systems in contactkinetic frictiona pressure that opposes the movement of two equipment that space in contact and moving loved one to one anotherstatic frictiona pressure that opposes the motion of two solution that are in contact and are not relocating relative to one anothermagnitude of static friction
, where
is the coefficient of static friction and is the size of the typical forcemagnitude of kinetic friction
, where
is the coefficient of kinetic friction