MAURBHANJ SCHOOL OF ENGINEERING�BARIPADA : 757107 , ODISHA�

Branch : Mechanical Engineering

Semester : 4^th Sem

Subject : THEORY OF MACHINE

Topic : FRICTION

Faculty : Er. Malabika Nayak

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Microscopic bumps and holes crash into each other, causing a frictional force.

FRICTION

Why does friction exist?

Because at the microscopic level, nothing is smooth!

“Kinetic Friction”

• Also called “sliding friction”
• When two flat surfaces are in contact and sliding relative to one another, heat is created, so it slows down the motion (kinetic energy is being converted to thermal energy).

where n is the normal force.

The direction of f_k is opposite the direction of motion.

A wooden block weighs 100 N, and is sliding to the right on a smooth horizontal concrete surface at a speed of 5 m/s. The coefficient of kinetic friction between wood and concrete is 0.1.

A 5 N horizontal force is applied to the block, pushing toward the right. What is the force of kinetic friction of the concrete on the block?

1. 100 N, to the left
2. 10 N, to the left
3. 5 N, to the left
4. 10 N, to the right
5. 5 N, to the right

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• A sled of mass 5.0 kg is pulled at a constant velocity by a rope which makes an angle of 20.0° above the horizontal. The coefficient of kinetic friction between the sled and the snow is 0.030. What is the tension in the rope? (F_pull in the diagram)

Example

“Static Friction”

• When two flat surfaces are in contact but are not moving relative to one another, they tend to resist slipping. They have “locked” together. This creates a force perpendicular to the normal force, called static friction.

There is no general equation for f_s.

The direction of f_s is whatever is required to prevent slipping.

Static Friction

Example: The box is in static equilibrium, so the static friction must exactly balance the pushing force:

This is not a general, “all-purpose” equation. It is found from looking at the free body diagram and applying horizontal equilibrium, since a_x = 0.

Limits to the self-adjusting forces.

• The normal force of a bridge on a truck is what holds up the truck. If the truck’s weight exceeds some maximum value, the bridge will collapse!
• The tension force of a fishing line on a fish is what pulls in the fish. If the fish is too big, the line will break!
• The static friction force is what keeps two surfaces from slipping. If the outside forces are too much, the surfaces will slip!
• In first-year physics, we do not study n_max and T_max. This is the Physics of Fracture.

Maximum Static Friction

  where n is the magnitude of the normal force, and the proportionality constant μ_s is called the “coefficient of static friction”.

There’s a limit to how big f_s can get. If you push hard enough, the object slips and starts to move. In other words, the static friction force has a maximum possible size f_{s max}.

• The two surfaces don’t slip against each other as long as f_s ≤ f_{s max}.
• A static friction force f_s > f_{s max} is not physically   possible. Many experiments have shown the following approximate relation usually holds:

Rolling without slipping

The axle of the wheel moves relative to the ground

Reference frame: the ground

ω

The wheel rotates with angular speed ω.

The tangential speed of a point on the rim is v = ωr, relative to the axle.

In “rolling without slipping”, the axle moves at speed v.

Rolling without slipping

Reference frame: the axle

v_AG = ωr is the speed of the axle relative to the ground.

v = ωr is the tangential speed of any point on the rim.

2

1

4

3

Rolling without slipping

ω

The wheel rotates with angular speed ω.

Since the bottom point is always at rest, it is static friction which acts between the ground and the wheel.

The axle moves with linear speed v = ωr., where r is the radius of the wheel.

Rolling Friction (a type of kinetic friction)

• Due to the fact that the wheel is soft, and so is the surface upon which it is rolling. Plowing effect produces a force which slows down the rolling.
• Transportation engineers call μ_r the tractive resistance.
• Typical values of μ_r are 0.002 for steel wheels on steel rails, and 0.02 for rubber tires on concrete.

Drag force in a fluid, such as air

• Air resistance, or drag, is complex and involves fluid dynamics.
• For objects on Earth, with speeds between 1 and 100 m/s and size between 1 cm and 2 m, there is an approximate equation which predicts the magnitude of air resistance

where A is the cross-sectional area of the object, ρ is the density of the air, C is the drag coefficient, and v is the speed.

• The direction of air resistance, or Drag Force, is opposite to the direction of motion.
• It depends on size and shape, but not mass.

Cross Sectional Area depends on size, shape, and direction of motion.

…Consider the forces on a falling piece of paper, crumpled and not crumpled.

Challenge Question

A box is being pulled to the right at steady speed by a rope that angles upward. In this situation:

1. n > mg.
2. n = mg.
3. n < mg.
4. n = 0.
5. Not enough information to judge the size of the normal force.