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Friction, force that resists the sliding or rolling of one solid object over another. Frictional forces provide the traction needed to walk without slipping, but they also present a great measure of opposition to motion. Types of friction include kinetic friction, static friction, and rolling friction.
- The Editors of Encyclopaedia Britannica
- Overview
- What are the forces of static and kinetic friction?
- What is the formula for the kinetic frictional force Fk ?
- What is the formula for the static frictional force Fs ?
- Example 1: Push the fridge
- Example 2: Box pulled across a rough table
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 Fs 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 Fk 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).
[Physically, why are there any frictional forces at all?]
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 Fs 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 Fk 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).
[Physically, why are there any frictional forces at all?]
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.
[Wait, what? Explain how a moving car can use the force of static friction?]
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 Fn ).
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 μk . The parameter μk 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 μk .
We can put these ideas into a mathematical form with the following equation.
Fk=μkFn
Note that we can rewrite this equation as μk=FkFn , which shows that the coefficient of kinetic friction μk is a dimensionless quantity.
[What does "dimensionless quantity" mean?]
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 Fn ), 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 μs ) 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.
Fs max=μsFn
[Can we write this equation with an inequality instead?]
Be careful, the quantity Fs 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 Fs 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.
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.
i. Fpush=400 N
ii. Fpush=600 N
iii. Fpush=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.
A 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=60o 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 Fk=μkFn 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.
ax=ΣFxm(start with Newton’s second law in the horizontal direction)
0=Tx−Fk1.3 kg(plug in horizontal forces, acceleration, and mass)
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