What are balanced forces?

:It occurs when the sum of all forces acting on an object equals zero, keeping its motion unchanged.

When does unbalanced force occur?

Unbalanced force occurs when forces acting on an object change its state of rest or motion. For example, when you kick a football, unbalanced forces make it move from one place to another.

Laws of Motion: Newton’s Laws, Momentum, Forces in Mechanics

Term	Description
Weight	The gravitational force with which Earth pulls an object. It is calculated as mg , where g is the acceleration due to gravity.
Normal Reaction	The contact force exerted between two surfaces in contact, acting perpendicular to the surfaces.
Tension	A pulling force exerted on an object by a rope or string. This is a contact force.

Two bodies in contact

$a = \frac{F}{m _{1} + m _{2}}$

or $a = \frac{F _{n e t}}{m _{t o t a l}}$

$N = \frac{m _{2} F}{m _{1} + m _{2}}$

Normal reaction when Two bodies in contact

Three bodies in contact

$a = \frac{F}{m _{1} + m _{2} + m _{3}}$

$N_{2} = \frac{F m _{3}}{m _{1} + m _{2} + m _{3}}$

$N_{1} = \frac{( m _{2} + m _{3} ) F}{m _{1} + m _{2} + m _{3}}$

Normal reaction when Three bodies in contact

Two Connected Bodies

$a = \frac{F}{m _{1} + m _{2}}$

Or $a = \frac{F _{n e t}}{m _{t o t a l}}$

$T = \frac{m _{2} F}{m _{1} + m _{2}}$

Three Connected Bodies

$a = \frac{F}{m _{1} + m _{2} + m _{3}}$

or $a = \frac{F _{n e t}}{m _{t o t a l}}$

$T_{2} = \frac{m _{3} F}{m _{1} + m _{2} + m _{3}}$

$T_{1} = \frac{( m _{2} + m _{3} ) F}{m _{1} + m _{2} + m _{3}}$

Bodies Hanging Vertically

$T_{1} = m_{1} g$

$T_{2} = (m_{1} + m_{2}) g$

$T_{3} = (m_{1} + m_{2} + m_{3}) g$

Bodies Accelerating Vertically Upwards

$T_{1} = m_{1} (g + a)$

$T_{2} = (m_{1} + m_{2}) (g + a)$

$T_{3} = (m_{1} + m_{2} + m_{3}) (g + a)$

Bodies Accelerating Vertically Downwards

$T_{1} = m_{1} (g - a)$

$T_{2} = (m_{1} + m_{2}) (g - a)$

$T_{3} = (m_{1} + m_{2} + m_{3}) (g - a)$

Tension in rod and heavy strings

$T = F (1 - \frac{x}{L})$

1.

$m_{1} = m_{2} = m$

$T = m g$

$a = 0$

Reaction at the point of suspension

$R = 2 T = 2 m g .$

2.

$m_{1} > m_{2}$

$a = \frac{( m _{1} - m _{2} )}{( m _{1} + m _{2} )} g$ and $T = \frac{2 m _{1} m _{2}}{( m _{1} + m _{2} )} g$

and

$g = \frac{W _{1} W _{2}}{W _{1} + W _{2}}$ and

$R = \frac{4 W _{1} W _{2}}{W _{1} + W _{2}}$

3.

$a = \frac{m _{1} g}{( m _{1} + m _{2} )}$ and $T = \frac{m _{1} m _{2}}{( m _{1} + m _{2} )} g$

And $R = 2 T$

4.

$(m_{1} > m_{2})$

$a = \frac{( m _{1} - m _{2} )}{( m _{1} + m _{2} + M )} g$

5.

$a = \frac{( m _{1} - m _{2} s i n θ )}{( m _{1} + m _{2} )} g$

$T = \frac{m _{1} m _{2} ( 1 + s i n θ )}{( m _{1} + m _{2} )} g$

Pulley and block inclined plane free body diagram

6.

$m_{1} sin α > m_{2} sin β$

$a = \frac{( m _{1} s i n α - m _{2} s i n β )}{( m _{1} + m _{2} )} g$

$T = \frac{m _{1} m _{2} ( m _{1} s i n α + m _{2} s i n β )}{( m _{1} + m _{2} )} g$

7.

$a = \frac{( m _{2} + m _{3} - m _{1} )}{m _{1} + m _{2} + m _{3} )} g$

Inertial Frame of Reference	Non Inertial Frame of Reference
The frame for which the law of inertia is applicable is known as the inertial frame of reference.	The frame for which the law of inertia is not applicable is known as the non-inertial frame of reference.
All frames that are either at rest or moving with constant velocity relative to an inertial frame are also considered inertial frames.	All the frames which are accelerating or rotating with respect to an inertial frame will be non-inertial frames.

Case-1

If the lift is at stationary or moving uniformly (a = 0), then

$N = m g$

$W_{a pp} = W_{a c t u a l}$

$W_{a pp} = N$

$W_{a c t u a l} = m g$

Apparent weight of a man in lift when it is stationary

Case-2

If the lift is accelerated upwards,

$N = m (g + a)$

$W_{a pp} > W_{a c t u a l}$

Effective or Apparent weight of a man in lift.If the lift is accelerated upwards

Case-3

If the lift is accelerated downwards,

$N = m (g - a)$

$W_{a pp} < W_{a c t u a l}$

Effective or Apparent weight of a man in lift If the lift is accelerated downwards

Type of Friction	Description	Key Points	Formula
Static Friction	Friction that develops before relative sliding starts, opposing the tendency of motion.	Opposes the tendency of motion Self-adjusting Maximum value is called limiting friction	$f_{s} \leq f_{L}$
Limiting Friction	The peak value of static friction when sliding just begins.	Highest friction value Depends on the nature of contact surfaces	$f_{s} = μ_{s} N$
Kinetic Friction	Friction between surfaces when they are in relative motion.	Constant value Opposes relative motion Slightly less than static friction	$f_{k} \propto N$ $f_{k} = μ_{k} N$

Conservation of Linear Momentum	Laws of Motion	Newton’s First Law of Motion
Newton’s Second Law of Motion	Newton’s Third Law of Motion	Inelastic Collision

Frequently Asked Questions

What are balanced forces?

When does unbalanced force occur?

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Frequently Asked Questions

What are balanced forces?

When does unbalanced force occur?

Join ALLEN!

Laws of Motion

1.0Force and its Effects

2.0Balanced And Unbalanced Forces

3.0Newton’s Laws of Motion

Newton’s First Law of Motion

Linear Momentum

Newton’s Second Law of Motion

Impulse and Average Force

Impulse Momentum Theorem

Conservation of Linear Momentum

Newton's Third Law of Motion

4.0Rocket Propulsion(Variable Mass Problems)

5.0Common Forces in Mechanics

6.0Free Body Diagram

7.0Normal Reaction Force

8.0Tension in String

9.0System of Masses Tied by Strings

10.0Pulley Block Systems

11.0Translational Equilibrium

12.0Spring Force

13.0Frame of Reference and Pseudo Force

14.0Weighing Machine

15.0Effective or Apparent weight of a man in lift

16.0Friction and its Types

17.0Two Block System in Friction

18.0Sample Questions on Laws of Motion

Table of Contents