Force & Laws of Motion Notes | SSC CGL, CHSL | Railways | IB

# Force (F)

A force is any interaction that, when unopposed, will change the motion of an object.

`   F = m x a`
• A force can cause an object with mass to change its velocity, i.e., to accelerate.
• Force can also be described intuitively as a push or a pull.
• Vector quantity
• SI unit: N
• CGS Unit: dyne
• 1N = 1 Kg m s-2
• 1N = 105 dyne
• Balanced and Unbalanced Forces: Balanced forces do not cause a change in motion whereas Unbalanced Forces does.

## Fundamental Forces (In order of Increasing Strength)

### 1. Gravitational Force (Gravity)

It is a natural phenomenon by which all things with mass or energy, including planets, stars, galaxies, and even light are brought toward one another.

• Very long range

### 2. Weak Nuclear Force

These forces were discovered during the study of the phenomenon of β-decay, in radioactivity.

• The WNF is 1025 times stronger than Gravitational Force.
• Very short range

### 3. Electromagnetic Force

Force which acts between charged particles and is the combination of all electrical and magnetic forces.

• Can be attractive or repulsive
• Electrostatic forces: When the charges are at rest.
• These forces are governed by coulomb’s law.
• Long range

### 4. Strong Nuclear Force

The forces that bind the neutrons and protons together in a nucleus.

• Very short range

Gravitational Forces are the weakest and strong nuclear forces are the strongest forces among the four fundamental forces.

## Inertia

The natural tendency of objects to resist a change in their state of rest or uniform motion is called inertia.

• Inertia of Rest
• Inertia of Motion
• Inertia of Direction

## Sir Isaac Newton (4 January 1643 – 31 March 1727)

• Philosophiæ Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”) – a book by Newton, first published in 1687, laid the foundations of classical mechanics.

## Newton’s First Law of Motion (AKA Law of Inertia)

An object continues to be in a state of rest or of uniform motion along a straight line unless acted upon by an unbalanced force.

```   Ft = mv - mu
(when F = 0, v = u
i.e., initial velocity = final velocity)
```

Applications around Us

• Only the carom coin at the bottom of a pile is removed when a fast moving carom coin (or striker) hits it.
• When the playing card is flicked with the finger, the coin placed over it falls in the tumbler.
• Tree leaves and fruits gets detached from the three, if we vigorously shake its branch.
• Passengers fall in forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest.

## Momentum (p)

A property of a moving body that the body has by virtue of its mass and motion.

```   p = m x v
```
• Has the same direction as that of the velocity.
• Vector quantity
• SI Unit: kg m s-1

## Newton’s Second Law of Motion

The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force.

```   F ∝ (p2 - p1) / t
∝ (mv - mu) / t
∝ [m x (v - u)] / t
∝ ma                (∵ (v - u) / t = a)
F = kma
F = ma                (∵ for 1 unit of force, k =  1)
```

## Newton’s Third Law of Motion (AKA Law of Action and Reaction)

To every action, there is an equal and opposite reaction and they act on two different bodies.

```FAB = - FBA
```

Applications around Us

• A forward force on the bullet and recoil of the gun.
• As the sailor jumps in forward direction, the boat moves backwards.

## Law of Conservation of Momentum

In an isolated system, the total momentum remains conserved.

```   Fa + Fb + Fc + . . . + Fz = 0
```

## Impulse

If a large force is acting on a body for a very short time, then the product of this large force and time is known as impulsive force.

```   Impulse = change in momentum
Impulse = f x t
```
• Vector Quantity
• SI Unit: N s

Examples

• Hitting a ball with bat, firing a gun

Application:

• A cricket player lowers has hands while catching the ball : by doing so the time of impact increases and hence the effect of force decreases.
• When a person falls from a certain height on floor, he receives more injuries as compared to falling on a heap of sand. It is because the Cemented floor does not yield whereas the sand yield there by increasing the time of impact hence decreasing the impact of force.
• The shock absorbers provided in the vehicle helps to travel smoothly on an uneven road. It is because the shockers increases the time of impulse which reduces the force.

## Apparent weight of a person in a lift

lift at rest

`apparent weight = actual weight`

moving uniformly in upward or downward direction

`apparent weight = actual weight`

accelerating upwards

`apparent weight > actual weight`

accelerating downwards

`apparent weight < actual weight`

lift is under free fall

`apparent weight = 0 (feel of weightlessness)`

## Friction

When a body slides or rolls over another body or on a surface, then a force opposing the motion acts between those surfaces of the body which are in contact. This force is called as force of friction.

• Types of friction: Rolling Friction, Fluid Friction, Sliding Friction, etc.

Friction can be reduced by

• Changing sliding friction into rolling friction
• By using lubricants such as oil, water, or grease

• It is becomes difficult to walk on a slippery road due to low friction. When we move on ice, it becomes difficult to walk due to low friction of ice.
• We can not fix nail in the wood or wall if there is no friction. It is friction which holds the nail.
• A horse can not pull a cart unless friction furnishes him a secure Foothold.
• We can write on a paper or on a board.
• Friction helps in applying the brakes.

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