what happens to co-efficient of friction ,when a body weight is doubled?

the coefficient of friction does not depend upon weight.... as far as I know it is a function only of the materials?

So, coefficient of kinetic / static friction cannot be a negative number?

Correct. No friction is when the coefficient is 0 (zero). 100% friction (no movement) is when the coefficient is 1.

Friction helps us to walk but in water why we cannot walk

We can walk on Land because the number of irregularities present on the surface are very plentiful, and differ from area to area, whereas in water, there are no irregularities and it is actually often used only as a lubricant, which is why the wet floor is extremely difficult to walk on. So, technically the only reason we can walk on land and not on water is actually because the number of irregularities is present in solids and is absent in liquids

I don't understand why when force applied is less than the maximum value of static friction then its value is the same as the value of frictional force. Can someone explain?, thanks.

A good question Imagine you are pushing against a table trying to slide it across the floor. The maximum value of static friciton is 100N. If you reach this force or exceed it, the table will slide. OK?? So you start pushing with a small force; say, 15N. The table does not slide. Why? because the force of friction is opposing your force. how much force is the table pushing back on you with? This force you feel pushing back on you is the force of friciton. Now increase your force to 60N. The table still does not slide. How much force will you feel from the table? again, this the force of friciton. now increased. as you increase your force, the force opposing you (friciton) will also increase according to Newtons third law. Until you exceed the force that friction can push back with.... when you reach or exceed 100N then the table will slide. OK??

how can cars accelerate if its static friction that acts on them. cause the net force would always equal 0 ? plz explain thanks.

why would the net force equal zero? Cars have engines.

Suppose there is an object (block) kept over a smooth surface (friction less surface) , Then can the block move if a force is applied to the block

Yes the object will move since there is no resistive force and if the friction between the object and the surface is zero then the object will move forever according to Newton's first law of motion.

In Example 1 : iii) before the fridge starts moving the person must exert a force of 647 N to overcome the static friction, So, the force just after begining of motion would be 800-647=153 N ! Am I right!

It would seem so but no. The coefficient of friction changes from static to kinetic once the fridge starts moving, and as long as it stays moving it won't change no matter how much you accelerate/decelerate (as long as you don't go back to cero velocity). As you can see in the formula of kinetic friction there is no mention of the force you're aplying, it's only proportional to the kinetic friction coeficient and to the normal force. If you calculate that you get that the force of the kinetic friction is (110kg*9.8m*s^-2)*(0.4)=431.2N. You can then calculate the real magnitude of the force your'e applying using that value: 800N-431.2N=368.8N. At least I believe this is correct :d Be carefull though since the normal force is not allways the same as the weight, in this case it is since there are no other vertical forces.

Does friction force meet the third law of dinamics, the action-reaction principle? If so, what is the reaction force?

Friction arises from two things pushing on each other. However hard thing 1 exerts frictional force on thing 2, that's how hard thing 2 will exert frictional force on thing 1.

can someone please explain how the formulas for static and kinetic frictional forces were derived? is there a way to understand the formula w/o just memorizing it? thanks :)

They're not derived, they're based on observation and on the definition of the coefficient of friction. The harder surfaces press against each other, the bigger the frictional force is. That's all the formula says. The coefficient says that the amount of the force depends on the specific combination of materials that are being pressed together.

so does a small coefficient of friction correspond to a smoother surface? Like 0.2, for example, would represent a smoother surface than 0.9. Also, i saw something saying that 0.6 is the least value for the coefficient of friction possible. is that true?

You can generally use the intuition that low friction corresponds to a smooth surface, but strictly speaking that's not always true, because there can be some very smooth surfaces that are very sticky. You generally won't encounter them in an early physics course, though. you need to understand that friction is actually a very complex phenomenon that is still a very active area of investigation by physicists who specialize in that sort of thing. We use a very simplified version of it to get the basic idea of how it works and how to incorporate it into our understanding of F = ma.

Main content

Course: Physics library > Unit 3

Lesson 5: Inclined planes and friction

What is friction?

Google Classroom

Until now in physics, you've probably been ignoring friction to make things simpler. Now, it's time to include this very real force and see what happens.

What are the forces of static and kinetic friction?

Parking your car on the steep hills of San Francisco is scary, and it would be impossible without the force of static friction.

The force of static friction

F_{s}

is a force between two surfaces that prevents those surfaces from sliding or slipping across each other. This is the same force that allows you to accelerate forward when you run. Your planted foot can grip the ground and push backward, which causes the ground to push forward on your foot. We call this "grippy" type of friction, where the surfaces are prevented from slipping across each other, a static frictional force. If there were absolutely no friction between your feet and the ground, you would be unable to propel yourself forward by running, and would simply end up jogging in place (similar to trying to run on very slippery ice).

Now, if you park on a hill that is too steep, or if you are being pushed backward by a Sumo wrestler you're probably going to start sliding. Even though the two surfaces are sliding past each other, there can still be a frictional force between the surfaces, but this sliding friction we call a kinetic frictional force. This force of kinetic friction

F_{k}

always opposes the sliding motion and tries to reduce the speed at which the surfaces slide across each other. For example, a person sliding into second base during a baseball game is using the force of kinetic friction to slow down. If there were no kinetic friction, the baseball player would just continue sliding (yes, this would make stealing bases in baseball difficult).

Most surfaces (like wood and plastics) seem pretty smooth to the naked eye. But if you were to zoom in, you would see that the surfaces are rough at a microscopic level. For instance, the surfaces of the box and floor as shown below are actually rough and jagged at a microscopic level.

Image Credit: Openstax College Physics

Friction arises in part because of the roughness of the surfaces in contact, as seen in the expanded view. In order for the object to move, it must rise to where the peaks can skip along the bottom surface. Thus a force is required just to set the object in motion. Some of the peaks will be broken off, also requiring a force to maintain motion. Much of the friction is actually due to attractive forces between molecules making up the two objects, so that even perfectly smooth surfaces are not friction-free. Such adhesive forces also depend on the substances the surfaces are made of, explaining, for example, why rubber-soled shoes slip less than those with leather soles. But to be completely honest, we still don't have a complete understanding of the microscopic causes of friction. More recent research in tribology (study of sliding surfaces) suggests that vibration in the surfaces, leading to energy loss through heat, is a main source of friction.

Concept Check: For each of the following cases of a car changing velocity described in the table below, choose whether it is more likely to be the force of static or kinetic friction causing the change in velocity.

	Static frictional force	Kinetic frictional force
A car slows gently to a stop.
A car slams on the brakes and skids to a stop.
A car accelerates gently to a higher speed.
A car "floors it" and peels out of a stop light.
A car takes a turn gently.

If car tires are working the way they should (rolling without slipping) it's the grippy force of static friction that is acting on the tires. The force of static friction between the tires and the ground is what allows cars to speed up, slow down, and turn safely and gently. To speed up, the tires start spinning faster and grip the road using the force of static friction. The tires can then push backward on the street, and the third law dictates that the street has to push forward on the tires. It is the gripping force of static friction

F_{s}

that allows this to happen.

If the tires start spinning too quickly ("flooring it"), or stop spinning too quickly ("slam on the brakes"), there will be skidding (and smoke and skid marks) between tires and the ground. This skidding is an easy way to tell that the force acting is kinetic friction rather than static friction.

People often find it strange to think that a moving car tire can have static friction acting on it. Learners often erroneously think that static friction means the object can't be moving. But static friction just implies that two surfaces aren't slipping/sliding/skidding past each other, not that the objects have no motion. For the case of the car tire, the bottom of the tire that's in contact with the street is momentarily at rest with respect to the street since it isn't slipping. The rest of the tire rotates around the point of contact. The point in contact keeps changing as the tire continues to roll forward.

What is the formula for the kinetic frictional force $F_{k}$ ‍?

If you press your hands into each other hard and rub them together, the force of kinetic friction will be larger than if you were only pressing your hands together lightly. That's because the amount of kinetic frictional force between two surfaces is larger the harder the surfaces are pressed into each other (i.e. larger normal force

F_{n}

Also, changing the types of surfaces sliding across each other will change the amount of kinetic frictional force. The "roughness" of two surfaces sliding across each other is characterized by a quantity called the coefficient of kinetic friction $μ_{k}$ ‍. The parameter

μ_{k}

depends only on the two surfaces in contact and will be a different value for different surfaces (e.g. wood and ice, iron and concrete, etc.). Two surfaces that do not slide easily across each other will have a larger coefficient of kinetic friction

μ_{k}

We can put these ideas into a mathematical form with the following equation.

F_{k} = μ_{k} F_{n}

Note that we can rewrite this equation as

μ_{k} = \frac{F_{k}}{F_{n}}

, which shows that the coefficient of kinetic friction

μ_{k}

is a dimensionless quantity.

Since

μ_{k} = \frac{F_{k}}{F_{n}}

, we know the units of the coefficient of kinetic friction

μ_{k}

are the same as the fraction

\frac{F_{k}}{F_{n}}

. But both

F_{k}

and

F_{n}

have units of newtons, so the ratio of

\frac{F_{k}}{F_{n}}

ends up with no units (the units cancel).

This shows that the coefficient of kinetic friction

μ_{k}

is a number with no units. We call these types of quantities dimensionless quantities since they have no units (i.e. no physical dimensions).

What is the formula for the static frictional force $F_{s}$ ‍?

The static frictional force is a little different from the kinetic frictional force. For one, the static frictional force will change its value based on how much force is being applied to the unbudging object. Imagine, for example, trying to slide a heavy crate across a concrete floor. You may push harder and harder on the crate and not move it at all. This means that the static friction responds to what you do. It increases to be equal to and in the opposite direction of your push. But if you finally push hard enough, the crate seems to slip suddenly and starts to move. Once in motion it is easier to keep it in motion than it was to get it started, indicating that the kinetic frictional force is less than the maximum static frictional force.

If you add mass to the crate, say by placing a box on top of it (increasing the amount of normal force

F_{n}

), you need to push even harder to get it started and also to keep it moving. Furthermore, if you oiled the concrete (reducing the coefficient of static friction

μ_{s}

) you would find it to be easier to get the crate started (as you might expect).

We can put these ideas in a mathematical form by writing the following formula that lets us find the maximum possible static frictional force between two surfaces.

F_{s max} = μ_{s} F_{n}

Be careful, the quantity

F_{s max}

only gives you the maximum possible static frictional force, not the actual static frictional force for a given scenario. For instance, suppose that between a washing machine and a tile floor the maximum possible force of static friction was found to be

F_{s max} = 50 N

. If you were to try and budge the washing machine with

30 N

, the static frictional force will only be

30 N

. If you increase the force you exert to

40 N

, the static frictional force will also increase to

40 N

. This continues until the force you apply is greater than the maximum static frictional force, at which point the washing machine budges and starts sliding. Once the washing machine starts sliding, there is no longer static frictional force but only kinetic frictional force.

What do solved examples involving the force of friction look like?

Example 1: Push the fridge

An initially stationary

110 kg

refrigerator sits on the floor. The coefficient of static friction between the refrigerator and the floor is

0.60

, and the coefficient of kinetic friction between the refrigerator and the floor is

0.40

. The person pushing on the refrigerator tries to budge the fridge with the following forces.

F_{push} = 400 N

ii.

F_{push} = 600 N

iii.

F_{push} = 800 N

For each individual case listed above, determine the magnitude of the frictional force that will exist between the bottom of the refrigerator and the floor.

To start we'll solve for the maximum possible amount of static frictional force.

F_{s max} = μ_{s} F_{n} (start with the formula for the maximum static frictional force)

F_{s max} = (μ_{s}) (m g) (the normal force will be equal to the force of gravity in this case)

F_{s max} = (0.60) (110 kg) (9.8 \frac{m}{s^{2}}) (plug in the coefficient of static friction, mass, and value of g)

F_{s max} = 647 N (calculate)

Now that we know the maximum amount of static frictional force is

647 N

, we know that any force the person exerts below this amount will get matched by the force of static friction. In other words,

i. If the person pushes with $F_{push} = 400 N$ ‍ there will be a matching static frictional force of $F_{s} = 400 N$ ‍ preventing the refrigerator from budging. There will be no kinetic friction since the refrigerator will not slide.

ii. If the person pushes with $F_{push} = 600 N$ ‍ there will be a matching static frictional force of $F_{s} = 600 N$ ‍ preventing the refrigerator from budging. There will be no kinetic friction since the refrigerator does not slide.

For case iii, the force

F_{push} = 800 N

is above the maximum force of static friction, so the fridge will start to slide. Now that the fridge is sliding there will be a kinetic frictional force exerted on it. We can find the force of kinetic friction as follows.

F_{k} = μ_{k} F_{n} (use the formula for kinetic friction)

F_{k} = (0.40) (110 kg) (9.8 \frac{m}{s^{2}}) (plug in the coefficient of kinetic friction and normal force)

F_{k} = 431 N (calculate the kinetic frictional force)

iii. So if the person pushes with $F_{push} = 800 N$ ‍ there will be a kinetic frictional force of $F_{k} = 431 N$ ‍ exerted on the fridge. There will be no static frictional force since the fridge is sliding.

Example 2: Box pulled across a rough table

1.3 kg

box of frozen chocolate chip waffles is pulled at constant velocity across a table by a rope. The rope is at an angle

θ = 60^{o}

and under a tension of

4 N

What is the coefficient of kinetic friction between the table and the box?

Since we don't know the coefficient of kinetic friction we can't use the formula

F_{k} = μ_{k} F_{n}

to directly solve for the frictional force. However, since we know the acceleration in the horizontal direction (it's zero since the box moves at constant velocity) we should start with Newton's second law.

Whenever we use Newton's second law we should draw a force diagram.

a_{x} = \frac{Σ F_{x}}{m} (start with Newton’s second law in the horizontal direction)

0 = \frac{T_{x} - F_{k}}{1.3 kg} (plug in horizontal forces, acceleration, and mass)

0 = \frac{T cos 60^{o} - μ_{k} F_{n}}{1.3 kg} (plug in horizontal component of tension and formula for kinetic friction)

0 = T cos 60^{o} - μ_{k} F_{n} (multiply both sides by mass)

μ_{k} = \frac{T cos 60^{o}}{F_{n}} (algebraically solve for the coefficient of kinetic friction)

At this point you might think we should plug in the normal force as

m g

, but since the rope is also pulling upward on the box, the normal force will be less than

m g

. The normal force will be reduced by the amount we pull up on the box. In this case, the vertical component of the tension is

T_{y} = T sin 60^{o}

. So the normal force in this case will be

F_{n} = m g - T sin 60

Now we can plug this expression for the normal force

F_{n}

into our formula for the coefficient of kinetic friction we found above.

μ_{k} = \frac{T cos 60^{o}}{F_{n}} (use formula we found above for coefficient of kinetic friction)

μ_{k} = \frac{T cos 60^{o}}{m g - T sin 60^{o}} (plug in expression found for normal force)

μ_{k} = \frac{(4 N) cos 60^{o}}{(1.3 kg) (9.8 \frac{m}{s^{2}}) - (4 N) sin 60^{o}} (plug in values for the tension and mass)

μ_{k} = 0.216 (calculate and celebrate)

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Sourav Bal
Posted 8 years ago. Direct link to Sourav Bal's post “what happens to co-effici...”
what happens to co-efficient of friction ,when a body weight is doubled?
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(22 votes)
Answer
- Teacher Mackenzie (UK)
  Posted 8 years ago. Direct link to Teacher Mackenzie (UK)'s post “the coefficient of fricti...”
  the coefficient of friction does not depend upon weight.... as far as I know it is a function only of the materials?
  Comment on Teacher Mackenzie (UK)'s post “the coefficient of fricti...”
  (61 votes)
Maha Amin
Posted 8 years ago. Direct link to Maha Amin's post “So, coefficient of kinet...”
So, coefficient of kinetic / static friction cannot be a negative number?
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(19 votes)
Answer
- Matt B
  Posted 8 years ago. Direct link to Matt B's post “Correct. No friction is w...”
  Correct. No friction is when the coefficient is 0 (zero). 100% friction (no movement) is when the coefficient is 1.
  Comment on Matt B's post “Correct. No friction is w...”
  (21 votes)
ROHAN
Posted 8 years ago. Direct link to ROHAN's post “Friction helps us to walk...”
Friction helps us to walk but in water why we cannot walk
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(11 votes)
Answer
- Aditya Ujwal
  Posted 6 years ago. Direct link to Aditya Ujwal's post “We can walk on Land becau...”
  We can walk on Land because the number of irregularities present on the surface are very plentiful, and differ from area to area, whereas in water, there are no irregularities and it is actually often used only as a lubricant, which is why the wet floor is extremely difficult to walk on. So, technically the only reason we can walk on land and not on water is actually because the number of irregularities is present in solids and is absent in liquids
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  (7 votes)
mercybonny
Posted 7 years ago. Direct link to mercybonny's post “I don't understand why wh...”
I don't understand why when force applied is less than the maximum value of static friction then its value is the same as the value of frictional force. Can someone explain?, thanks.
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(4 votes)
Answer
- Teacher Mackenzie (UK)
  Posted 7 years ago. Direct link to Teacher Mackenzie (UK)'s post “A good question Imagine...”
  A good question
  
  Imagine you are pushing against a table trying to slide it across the floor.
  
  The maximum value of static friciton is 100N. If you reach this force or exceed it, the table will slide.
  
  OK??
  
  So you start pushing with a small force; say, 15N. The table does not slide.
  
  Why? because the force of friction is opposing your force.
  
  how much force is the table pushing back on you with?
  
  This force you feel pushing back on you is the force of friciton.
  
  Now increase your force to 60N. The table still does not slide.
  
  How much force will you feel from the table? again, this the force of friciton. now increased.
  
  as you increase your force, the force opposing you (friciton) will also increase according to Newtons third law. Until you exceed the force that friction can push back with.... when you reach or exceed 100N then the table will slide.
  
  OK??
  Comment on Teacher Mackenzie (UK)'s post “A good question Imagine...”
  (19 votes)
Maha Amin
Posted 8 years ago. Direct link to Maha Amin's post “In Example 1 : iii) befor...”
In Example 1 : iii) before the fridge starts moving the person must exert a force of 647 N to overcome the static friction, So, the force just after begining of motion would be 800-647=153 N !
Am I right!
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(3 votes)
Answer
- Juan Domene
  Posted 8 years ago. Direct link to Juan Domene's post “It would seem so but no. ...”
  It would seem so but no. The coefficient of friction changes from static to kinetic once the fridge starts moving, and as long as it stays moving it won't change no matter how much you accelerate/decelerate (as long as you don't go back to cero velocity). As you can see in the formula of kinetic friction there is no mention of the force you're aplying, it's only proportional to the kinetic friction coeficient and to the normal force. If you calculate that you get that the force of the kinetic friction is (110kg*9.8m*s^-2)*(0.4)=431.2N. You can then calculate the real magnitude of the force your'e applying using that value: 800N-431.2N=368.8N. At least I believe this is correct :d
  Be carefull though since the normal force is not allways the same as the weight, in this case it is since there are no other vertical forces.
  Comment on Juan Domene's post “It would seem so but no. ...”
  (7 votes)
jacobmathewrajesh
Posted 8 years ago. Direct link to jacobmathewrajesh's post “how can cars accelerate i...”
how can cars accelerate if its static friction that acts on them. cause the net force would always equal 0 ? plz explain thanks.
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(4 votes)
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- Andrew M
  Posted 8 years ago. Direct link to Andrew M's post “why would the net force e...”
  why would the net force equal zero? Cars have engines.
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  (5 votes)
Cindy
Posted 8 years ago. Direct link to Cindy's post “can someone please explai...”
can someone please explain how the formulas for static and kinetic frictional forces were derived? is there a way to understand the formula w/o just memorizing it? thanks :)
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(2 votes)
Answer
- Andrew M
  Posted 8 years ago. Direct link to Andrew M's post “They're not derived, they...”
  They're not derived, they're based on observation and on the definition of the coefficient of friction.
  
  The harder surfaces press against each other, the bigger the frictional force is. That's all the formula says. The coefficient says that the amount of the force depends on the specific combination of materials that are being pressed together.
  Comment on Andrew M's post “They're not derived, they...”
  (7 votes)
APP555
Posted 5 years ago. Direct link to APP555's post “Suppose there is an objec...”
Suppose there is an object (block) kept over a smooth surface (friction less surface) , Then can the block move if a force is applied to the block
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(4 votes)
Answer
- Jacob H
  Posted 3 years ago. Direct link to Jacob H's post “Yes the object will move ...”
  Yes the object will move since there is no resistive force and if the friction between the object and the surface is zero then the object will move forever according to Newton's first law of motion.
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  (2 votes)
Jorge Varea
Posted 7 years ago. Direct link to Jorge Varea's post “Does friction force meet ...”
Does friction force meet the third law of dinamics, the action-reaction principle? If so, what is the reaction force?
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(3 votes)
Answer
- Andrew M
  Posted 7 years ago. Direct link to Andrew M's post “Friction arises from two ...”
  Friction arises from two things pushing on each other. However hard thing 1 exerts frictional force on thing 2, that's how hard thing 2 will exert frictional force on thing 1.
  Comment on Andrew M's post “Friction arises from two ...”
  (3 votes)
Marihan Badr
Posted 7 years ago. Direct link to Marihan Badr's post “so does a small coefficie...”
so does a small coefficient of friction correspond to a smoother surface? Like 0.2, for example, would represent a smoother surface than 0.9. Also, i saw something saying that 0.6 is the least value for the coefficient of friction possible. is that true?
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(2 votes)
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- Andrew M
  Posted 7 years ago. Direct link to Andrew M's post “You can generally use the...”
  You can generally use the intuition that low friction corresponds to a smooth surface, but strictly speaking that's not always true, because there can be some very smooth surfaces that are very sticky. You generally won't encounter them in an early physics course, though.
  
  you need to understand that friction is actually a very complex phenomenon that is still a very active area of investigation by physicists who specialize in that sort of thing. We use a very simplified version of it to get the basic idea of how it works and how to incorporate it into our understanding of F = ma.
  Comment on Andrew M's post “You can generally use the...”
  (5 votes)

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