# Friction

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## Friction

Friction is the force that resists the motion of one surface relative to another with which it is in contact. It is parallel to the contact surfaces and opposite to the direction of motion or impeding motion.

• SI unit of friction is newton (N). It is a vector quantity.
• Viscous force is the equivalence of friction in fluids that resists the relative motion of a body through the fluid.

## Body In Motion

Friction between a moving object and its environment plays a crucial role by acting to diminish the object’s velocity. When a consistent braking force is exerted on a car, it induces a uniform deceleration, causing the car to gradually slow down and eventually stop. The distance covered by the car during braking is contingent upon the magnitude of the resultant force, determined by the force applied by the brakes and the level of friction.

When a body is in motion, friction will tend to slow it down.

• Example: Pushing a box along the table. The box will eventually come to rest.
• The friction comes from the microscopic surface irregularities of the two surfaces (of the box and the table). The surface irregularities catch onto each other and resist motion.

## Body In Motion (With Pushing Force)

When the magnitude of the pushing force is equal to the magnitude of frictional force on the object, the object will travel at a constant speed.

In the case of a falling object, gravity propels it to accelerate (gravity is the pushing force), but the drag force stemming from air resistance hinders this acceleration. If the drag force increases to the point where it balances the object’s weight, resulting in a zero resultant force, the object will maintain a constant speed.

## Body At Rest

When a body is at rest, friction will have to be overcome before the body can start to move.

• Why? For a body to embark on a state of motion, there needs to be acceleration. From Newton’s 2nd law of motion ($F = ma$), we will require a non-zero resultant force to be acting on the body. Hence, the pushing force (or driving force) must be greater than the frictional force.

In the picture above, the pushing force of 4N is not enough to overcome the frictional force. Hence the body is at rest.

If the pushing force is further increased, the block eventually initiates motion, at which point the frictional force reaches its maximum value known as starting or static friction ($f_s$). Once the block is in motion at a constant speed, the equilibrium reading is slightly lower than that for starting friction, indicating that sliding or dynamic friction ($f_k$) is less than static friction.

If you plot the above in a graph, the graph will look like the following:

The graph shows that:

• Static friction $f_s$ increases as the magnitude of the applied force increases, keeping the object in place.
• When it is on the verge of moving, $f_s$ is at maximum.
• When the applied force exceeds $\left(f_s \right)_{max}$, the force overcomes the static friction. Now the object is only experiencing dynamic friction. Since the applied force is more than the dynamic friction, by Newton’s Second Law of Motion, the object accelerates .
• Once the object is in motion, the retarding frictional force becomes less than $\left(f_s \right)_{max}$.

Introducing additional mass onto the block amplifies the force pressing the surfaces together, subsequently increasing friction. When work is done against friction, the temperatures of the contacting bodies rise, converting kinetic energy into thermal energy through mechanical work, as evidenced by the warming sensation when rubbing hands together.

Solid friction is characterized as the force between two surfaces that can impede motion and generate heat. Friction, often referred to as drag, manifests when an object like a vehicle or falling leaf moves through a gas (encountering air resistance), hindering the object’s motion. Similarly, friction (drag) comes into play when an object moves through a liquid. Drag intensifies with the object’s speed, functioning to decrease acceleration and decelerate the object.

## Methods To Reduce Friction

• To reduce friction, applying lubrication to the surfaces in contact can minimize resistance and facilitate smoother motion.
• Smoothening the surfaces through techniques like polishing is an effective method to decrease friction, promoting more seamless interaction between them.
• Introducing ball bearings or rollers between surfaces helps in reducing friction by allowing smooth rotation, minimizing direct surface-to-surface contact.
• Employing an air cushion between surfaces, as seen in technologies like hovercrafts, creates a layer of air that significantly reduces friction, enabling smoother movement over surfaces.

## Maximizing The Beneficial Impacts Of Friction

Utilizing Treads: Friction plays a crucial role in the movement of vehicles. In the absence of friction, a vehicle would be unable to progress, as its tires would simply spin in place. Friction facilitates the tires in gripping the road surface, allowing them to roll without slipping. Particularly on rainy days, a moving vehicle might skid on wet roads. To counter this, tires are designed with treads—grooves that efficiently channel water away from beneath the tires. This design enhances tire grip on wet roads, preventing skidding.

Using a Parachute: Air resistance, a form of friction in the air, influences the speed of a skydiver in midair. To accelerate, the skydiver minimizes air resistance by reducing the surface area in contact with the air, adopting a head-first position. Conversely, to decelerate, the skydiver increases air resistance by expanding the surface area in contact with the air, assuming a spread-eagle position. For a safe landing, the skydiver significantly boosts air resistance by employing the much larger surface area of an open parachute.

Using Chalk: Rock climbers rely on a secure grip on the rock surface with their hands and feet. To enhance their grip, climbers commonly use chalk powder on their hands to absorb perspiration. This application of chalk helps to improve their grip and maintain a firm hold on the rock surface.

## [Optional] Additional Notes On Friction

• The major cause of friction between solids appears to be the forces of attraction, known as adhesion (electromagnetic forces), between the contact regions of the surfaces, which are always microscopically irregular. Friction arises from shearing these “welded” junctions and from the actions of the irregularities of the harder surface plowing across the softer surface.
• Sliding friction arises because of relative motion between surfaces. There are two kinds of sliding friction: static and kinetic. Static sliding friction refers to the amount of force that needs to be overcome to start motion. On the other hand, kinetic sliding friction is the force that needs to be overcome in order to maintain relative motion between the surfaces.
• The force required to start motion, or to overcome static friction, is always greater than the force required to continue the motion, or to overcome kinetic friction.
• From experiments, sliding friction is found to be proportional to the load or weight of the body in contact with a surface and is nearly independent of the area of contact.
• Rolling friction occurs when a wheel, ball, or cylinder rolls freely over a surface. (Not possible to roll without friction!)
• Sliding friction is generally 100 to 1,000 times greater than rolling friction. Thus, a body on a sledge is harder to pull than the same body on wheels.

### [Uni Physics] Empirical Laws Of Friction

The direction of the force of static friction between any two surfaces in contact is opposite the direction of any applied force.

$$f_{s} \leq \mu_{s} n$$

,where
μs is coefficient of static friction

The direction of the force of kinetic friction acting on an object is opposite the direction of its motion and is given by:

$$f_{k} = \mu_{k} n$$

, where
μk is coefficient of kinetic friction

### [Uni Physics] Coefficients Of Friction

The values of μs and μk depend on the nature of the surfaces (0.05-1.5), but μk is generally < μs.

The coefficients of friction are nearly independent of the area of contact between the surfaces.

Although μk varies with v, we normally neglect this (cf. stick-and slip motion at low v).

### [Uni Physics] Experimental Determination Of $\mu_{s}$ And $\mu_{k}$

Suppose a block is placed on a rough surface inclined relative to the horizontal. The incline angle is increased until the block starts to move. By measuring the critical angle, $\theta_{c}$ at which this slippage just occurs, we can obtain $\mu_{s}$.

Once the block starts to move, it accelerates down the incline. However, if $\theta$ is reduced to a value less than $\theta_{c}$, it may be possible to find an angle $\theta_{c}^{\prime}$ such that the block moves down the incline with constant speed. We can then obtain $\mu_{k}$

Let’s work out the details:

The horizontal forces acting on the block:

\begin{aligned} \sum F_{x} &= 0 \\ mg \sin{\theta}-f_{s} &= 0 \end{aligned}

The above equation will give the static frictional force on the block:

$$f_{s} = mg \sin{\theta}$$

The vertical forces acting on the block:

\begin{aligned} \sum F_{y} &= 0 \\ n-mg \cos{\theta} &= 0 \end{aligned}

The above equation will give the normal force on the block by the ramp:

$$n = mg \cos{\theta}$$

Hence, we have:

$$f_{s} = n \tan{\theta}$$

Since $f_{s} \leq \mu_{s} n$, at max angle $\theta_{c}$, we can calculate $\mu_{s}$:

$$\mu_{s} = \tan{\theta_{c}}$$

If moving at constant $\vec{v}$, from $f_{k} = \mu_{k} n$, we have:

$$\mu_{k} = \tan{\theta_{c}^{\prime}}$$

## Worked Examples

### Example 1

A man pushes a trolley forward with a force of 10 N. The floor exerts a frictional force of 7 N on the trolley. Find the acceleration of the trolley, given that the mass is 10 kg. If there is no friction, what would be the new acceleration?

\begin{aligned} \text{Net resultant force: } F_{\text{res}} &= F_{\text{man}} \, – F_{\text{fric}} \\ &= 10-7 \\ &= 3 \text{ N} \end{aligned}

Net resultant acceleration is given by Newton’s 2nd law of motion,

\begin{aligned} a &= \frac{F_{\text{res}}}{m} \\ &= \frac{3}{10} \\ &= 0.3 \text{ ms}^{-2} \end{aligned}

If there is no friction,

Net resultant force $F_{\text{new res}} = F_{\text{man}}$

Net resultant acceleration,

\begin{aligned} a &= \frac{F_{\text{new res}}}{m} \\ &= \frac{10}{10} \\ &= 1.0 \text{ ms}^{-2} \end{aligned}

### Example 2

Can you lean against a wall if frictional forces are absent?

No! You will slide down the wall.

When you are leaning against a wall, frictional forces help to “neutralise” part of the gravitational forces that are acting on your body.

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