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Static Friction


The Friction force acts everywhere around us and it's quite exaggerating to imagine life without that. In fact it would be impossible to walk on the floor, hold onto a glass, write with a pen or do even the simplest kind of work even for a minute without it.

Friction is of two types - static and kinetic. Static friction is quite opposite to kinetic friction where the motion is resisted. Lets see about this.

What is Static Friction?

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When two surfaces aren't moving but are pressing each other they have a chance to interlock to the microscopic level. This is what static friction is!. To know how much it is in the body the term coefficient of friction is used and is denoted as $\mu_s$. That relies on
  • Nature of material
  • Smoothness of the surfaces and
  • Lubrication between them.

Static Friction Definition

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Static friction is the force that which exists when two objects are not moving. Each object resists the motion of the other due to the interlocking between the surfaces. It is the strongest kind of friction and is experienced often.

Let's take a simple illustration with figure to explain that
Friction in Motion
As the hanging block moves from the highest elevation to its lowest the pulley should have enough load to pull it that should exceed the limiting force acting due to static friction.

Coefficient of Static Friction

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Friction is the force that resists the movement of one body over the other. How much is the friction over a body is decided by the coefficient. It is the ratio of limiting friction to the normal reaction. If F is the limiting friction and N is the normal reaction
$\mu_s$ = $\frac{F}{N}$
Here, $\mu_s$ is a constant known as coefficient of friction which is ratio of two forces and hence is dimensionless.

Static Friction Force

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When a body is in contact with a surface at rest and no external force is applied, the force of friction is zero. When a small force is applied on the body, the force of friction starts acting on the body in a direction opposite to the tendency of motion of the body so far the body remains at rest, the force of friction is equal to the applied force and is called the static friction. Thus, when a body is at rest, the force of friction is called the static friction and is always equal and opposite to the applied force.

Static frictional force adjusts both in magnitude and direction automatically. Its magnitude is always equal to external effective force, tending to cause the relative motion and its direction is always opposite to that of external force.

Static and Kinetic Friction

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Static friction occurs between surfaces at rest relative to each other. Lets see some common illustrations to see how it is greater than kinetic friction:

You often experience static friction when you push something that is at rest. Imagine a box you are unloading onto a ramp starts to slide. To make it stop you can put your foot in its way and after you stop it, the box is more likely to stay put and not start sliding again. It all due to static friction when box at rest that is greater than kinetic friction.

When an increasing force is applied to a book resting on a table, the force of static friction at first increases as well to prevent motion. But to make the book move across the table the force applied to the book should be greater than the starting friction. The kinetic friction that occurs afterward is usually less than the starting friction, so less force is needed to keep the book moving than to start it moving.

Static Friction Vs Sliding Friction

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Lets compare both of them:

Static friction
Sliding friction
Static friction is seen when two body resists each others motion. The interlocking between two rough surfaces illustrates it nicely.Sliding friction happens when two objects slide past each other. Take a brick and push it across the ground. The force that resists it from moving smoothly is what sliding friction is!
2. It is a strong force. It is not as strong force as static friction.

Static Friction Examples

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Lets go through some solved problems on static friction:

Solved Examples

Question 1: A force of 100 N is needed to start a 20 kg car across a road. Calculate the coefficient of friction.
Force F = 100 N, mass m = 20 kg

The coefficient of static friction is given by
$\mu_s$ = $\frac{F}{N}$
   = $\frac{F}{mg}$
   = $\frac{100\ N}{20\ kg\ \times 9.8m/s^2}$
   = 0.51.


Question 2: A wooden block is kept at rest by an adjustable inclined plane that begins to move when angle between the plane and horizontal reaches angle $\theta$ which is the angle of repose. How is the angle related to the coefficient of static friction between block and the plane?
The weight w can be resolved in to the components $F_w$ parallel to the plane and N perpendicular to the plane as shown in figure
Friction Problem

Hence, the magnitudes of $F_w$ and N are
$F_w$ = w sin $\theta$ and N = w cos $\theta$

When the block just begins to move the downward force along the plane $F_w$ must be equal to the maximum force $\mu_s$N of static friction so
$F_w$ = $\mu_s$ N
w sin $\theta$ = $\mu_s$ w cos $\theta$
$\mu_s$ = $\frac{sin \theta}{cos \theta}$ = tan $\theta$

Hence, the coefficient of static friction equals the tangent of the angle of response.