IEMDaily - Video Lecture Notes

Example

Finding coefficient of friction

Example. A car begins to move at time

t = 0

and then accelerates along a straight track with a speed given by

V (t) = 2 t^{2} m s^{-} 1

for

0 \leq t \leq 2

. After the end of acceleration, the car continues to move at constant speed. A small block initially at rest on the floor of the car begins to slip at

t = 1 s e c

. and stops slipping at

t = 3 s e c

. Find the coefficient of static and kinetic friction between the block and the floor.
Solution:

a (t) = \frac{d v (t)}{d t} = 4 t

t = 1

a = 4

When the block is just starting to slip we have,

μ_{s} N = m a

\Rightarrow μ_{s} m g = 4 m

\Rightarrow μ_{s} = 0.4

Now, it goes on slipping till 3 seconds, therefore in 2 seconds the block's
velocity changes from

2 t o 2 \times (2)^{2} = 8 m / s e c

Hence, acceleration from

t = 1

t = 3

secs is:

a_{a v g} = \frac{8 - 2}{2} = 3 m / s^{2}

Applying equation of motion

μ_{k} \times m \times g = m \times a_{a v g} = 3 m

\Rightarrow μ_{k} = 0.3

Definition

Self-adjusting nature of friction

When a moving body is suddenly stopped, then frictional force arises when there is a relative motion between two surfaces. When body is stopped means there is no relative motion and no resultant force is there hence frictional force acting becomes zero.

Definition

Limiting Friction

The maximum static friction that a body can exert on the other body in contact with it is called limiting friction. This limiting friction is proportional to the normal contact force between the two bodies, It is given by:

(f_{s})_{m a x} = μ_{s} N

Diagram

Graph of total external force Vs frictional force

Definition

Angle of Friction

It is the angle (

α

), measured between the normal force (N) and resultant force (R).

A body rests on a rough horizontal plane. A force is applied to the body directed towards the plane at an angle

α

with the vertical.
The body can be moved along the plane:
Consider a block placed on a rough horizontal plane. Now, the reaction force

\vec{R}

is because it is equal and opposite to the
weight

\vec{W}

. If the force

\vec{F}

is applied to the block towards the plane at an angle

α

, the resolved forces will act along vertical and horizontal direction.
The horizontal component of force

F \sin α

have to overcome the frictional force so that the block just begins to slide. Frictional force is equal to limiting friction

F_{l i m i t i n g}

, when this condition is satisfied the angle of applied force

α

will be greater than angle of friction

α

and block can move along the plane.

t a n α = μ

Example

Laws of friction and example

Laws of Friction are:

When an object is moving, the friction is proportional and perpendicular to the normal force (N)
Friction is independent of the area of contact as long as there is an area of contact.
The coefficient of static friction is slightly greater than the coefficient of kinetic friction.
Within rather large limits, kinetic friction is independent of velocity.
Friction depends upon the nature of the surfaces in contact.

Example: A body of mass

M

is placed on a rough inclined plane of inclination

θ

and coefficient friction

μ_{k}

. A force of (

m g s i n θ + μ_{k} m g c o s θ

) is applied in the upward direction, the acceleration of the body is:
Equating forces along X and Y axes,

N = m g c o s θ

Also,

- m g s i n θ - μ_{k} m g c o s θ - m a + m g s i n θ + μ_{k} m g c o s θ = 0

∴ m a = 0

Example

Kinetic Friction: Explained

Frictional force that opposes relative motion between surfaces in contact is called kinetic or sliding friction and is denoted by

f_{k}

. It is given by:

f_{k} = μ_{k} N

where

μ_{k}

is the coefficient of kinetic friction, which depends only on the surfaces in contact and

N

is the normal force.
Example: When a wooden block is sliding on the floor the friction acting between the wood surface and the floor will be kinetic friction.

Formula

relation between normal reaction and friction force

When two bodies are kept in contact, electromagnetic forces act between the charged particles at the surfaces of the bodies. Thus, each body exerts a contact force of the other. The magnitudes of the contact forces acting on the two bodies are equal but their directions are opposite and therefore the contact forces obey Newton's third law.

The direction of the contact forces acting on a body is not necessarily perpendicular to the contact surface. The resolution of contact forces in two components i.e. perpendicular to contact surface and along surface.
Perpendicular component is normal force and parallel component is friction.

∴

R =

\sqrt{(} f^{2} + N^{2})

R - Contact force

Definition

Normal Reaction

When any two surfaces are in contact, a contact force is exerted between the surfaces. Normal reaction is the component of the contact force normal to the contact surface.
For example, for a block placed on ground, the ground exerts an upward normal reaction force on the block.

Example

Normal reaction forces in real life

Some examples of normal reaction forces in real life are:
1. When standing on the ground, we feel a normal reaction equal to the weight due to the ground. This principle is used to measure the weight of a body.
2. A boy pushing a wall feels a normal reaction force due to the wall equal to the force applied on the wall.