Description of Force and their Types

Force:

Force is a push or pull by which the state of the object changes or tends to change.

Types of forces:

There are two types of forces-

1.) Contact Force
2.) Non-Contact Force

1.) Contact force:

When there is physical contact between the two objects by push or pull then it is known as contact force.

For Example:

i.) When a coiled spring is stretched (pulled), the two ends of the spring must be in actual contact with the person's hands.
ii.) Kicking a football, and pulling a cart are also contact forces.

Types of Contact Force:

I.) Applied Force
II.) Frictional Force
III.) Normal Force
IV.) Tension Force
V.) Air Resistance (Drag Force)
VI.) Elastic or Restoring force

I.) Applied Force:

When a force is exerted by a person or an object to another person or object then this force is known as applied force.

$F=ma$

Example: Pushing a shopping cart, pulling a door open.

II.) Frictional Force:

When two surfaces are in motion relative to each other and in contact then a force acting in the opposite direction of the motion of one surface over the other is called the force of friction. The frictional force is also called the force of friction or simply friction.

$F=\mu R$

A smooth surface exerts a lesser force of friction than a rough surface. The rolling frictional froce is always less than the sliding frictional force.

Types of Friction Force:

i.) Static Friction:

When the frictional force is applied on the object due state of the rest of the object then frictional force is known as static friction.

ii.) Kinetic Friction:

When the frictional force is applied to the object due motion of the object then frictional force is known as dynamic friction.

iii.) Limiting Friction:

The maximum value of static frictional force is known as limiting friction.

Example: Rubbing hands together, a car’s brakes stopping a vehicle

III.) Normal Reaction Force:

When an object is placed on a surface (or another object), the object exerts a force on the surface (or another object) vertically downwards. However, the object does not move in the direction of the force. This is because the surface (or another object) exerts an equal and opposite force on the object vertically upwards. then this force is called normal reaction force.

$Normal \: reaction \: force (N) = Weight \: of \: the \: object (mg) $

Example: A book resting on a table, a person standing on the ground.

IV.) Tension force:

The force on the string, rope, or cable due to pulled tight is known as Tension. Force is transmitted through a s when pulled tight.

Example: A person pulling a rope in a tug-of-war, a hanging lightbulb.

V.) Air Resistance (Drag Force):

It is a type of friction force that acts against objects moving through the air.

Example: A parachute slowing down a skydiver, wind resistance on a car.

VI.) Spring Force (Elastic Force Or Restoring force):

A force that always acts in the opposite direction of the object's displacement is known as elastic or restoring force.

Example: A compressed spring in a toy, a rubber band being stretched.

2. Non-Contact Forces (Act at a distance)

I.) Gravitational Force (F)

The force of attraction between two heavy objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

$F=G \frac{m_{1}m_{2}}{r^{2}}$

This force is most effective between very heavy objects like satellites, Planets Su,n and Stars.

Example: Objects falling to the ground, Earth’s gravity keeping the Moon in orbit.

II.) Electromagnetic Force:

When electric force and magnetic force are applied perpendicular to each other on charged particles then a force acts perpendicular to both this force is known as electromagnetic force.

The force between charged objects include both electric force and magnetic forces.

Example: Lightning (electric force), magnets attracting iron nails.

i.) Magnetic Force:

The force between magnetic materials, either attracting or repelling is known as magnetic force. The magnitude of magnetic force due to moving charge is described by Lorentz's law ($F=qvB sin \theta$)and direction is described by Fleming's left-hand rule. Similarly, the magnetic force due to the conductor is described by the formula $F=iBl sin\theta$ that is deduced by Lorentz's law, and the direction of force in a conductor is also described by Fleming's left-hand rule.

Example: A compass needle pointing north, fridge magnets sticking to a fridge.

ii.) Electric Force:

The attraction and repulsion force between the charges is known as the electric force. The magnitude of this force is described by Coulomb's law and the direction is described by the vector form of Coulomb's Law.

$F=\frac{1}{4\pi \epsilon_{\circ} K} \frac{q_{1}q_{2}}{r^{2}}$

IV.) Nuclear Forces: The force between the nucleons (i.e. proton and neutron) is known as nuclear force. Nuclear forces are two types.

i.) Strong Nuclear Force:

It is the very strongest and short-distance force that holds protons and neutrons together in an atomic nucleus.

ii.) Weak Nuclear Force:

When the nucleus is involved in radioactive $\beta$ decay then the force between the particles is known as weak nuclear force. The force is involved in the reaction of nuclear fission and fusion.

Example: The energy released in nuclear reactions, like in the Sun or nuclear power plants.

Finding Significant Figures in a Measurement

What is significant Figure?

The total number of digits (i.e. doubtful digit and confirm digits) in any measurement is known as significant figure.

Or

The digits that reflect the precision of the measurement are called significant figures.

Counting of Significant Figures in any Measurement:

Knowing the significant figures in a measure is based on the following rules-

(1) All non-zero numbers are significant figures.

For example, $46.3598$ has $6$ significant figures.

(2) All zero numbers between two non-zero numbers are significant figures.

For example, $600.8049$ has $7$ significant figures.

(3) If there is no non-zero number before the decimal point, then all the digits in the number except the zero numbers immediately after the decimal point are significant figures.

For example, $0.002809$ has $4$ significant figures.

(4) The zero after any non-zero digit to the right of the decimal point is a significant figure.

For example, $0.46920$ has $0$ significant figures.

(5) If a number is multiplied by a power of $10$, it does not affect the number of significant figures.

For example, $6.75\times 10^{3}$ has $3$ significant figures.

(6) Choosing different units does not change the number of significant figures.

For example, if a measurement is $2346 km$, then in different units, this measurement will be $23460 m$, $2346000 cm$ or $23460000 mm$. Here, the number of significant figures in each measurement is $4$.

Limitations of Dimensional Analysis

Limitations of Dimensional Analysis:

(1) It is not possible to find the numerical value of constants $k$ (dimensionless) present in the formulas by this method. It can be obtained by experiment or other method.

(2) If any physical quantity depends on more than three quantities, then the mutual relation between these quantities cannot be established by this method. However, the dimensional correctness of any given equation of this type can be checked.

(3) If any physical quantity depends on only three physical quantities, but the dimensions of two of the three quantities are the same, then also the mutual relation between these quantities cannot be established by the dimensional method, but the dimensional correctness can be checked.

(4) If an equation has more than one term on one side, like $v=u+at$ (Here two terms on the right side), then this equation cannot be derived by dimensional method. That is, such relations cannot be derived in which there is a positive $(+)$ or negative $(-)$ sign anywhere. But whether the equation is dimensionally correct or not, can be checked.

(5) Deduction of equations containing trigonometric ratios ($ sin \theta$, $cos \theta$, $tan \theta$, etc.), variable exponential ($e^{x}$) and logarithmic ($log\:x$) terms is not possible by dimensional analysis method, but their dimensional truth can be checked.

(6) Whether a physical quantity is vector or scalar cannot be determined by the dimensional analysis method.

(7) If the constant in an equation is not dimensionless, then the dimensional analysis method cannot be used for the deduction of that equation.

(8) For a physical relation represented by an equation to be true, it is a necessary condition for this equation to be in dimensional balance, but only dimensional balance is not sufficient for the physical relation to be true. That is,

"Even if the equation is true physically and mathematically, it may not be true dimensionally."

Difference between Forced Vibrations and Resonant Vibrations

Forced Vibrations:

1. The vibrations of a body under an external periodic force of frequency different from the natural frequency of the body, are called forced vibrations.

2. The amplitude of vibration is small.

3. The vibrations of the body are not in phase with the external periodic force.

4. These vibrations last for a very short time after the periodic force has ceased to act.

Resonant Vibrations:

1. The vibrations of a body under an external periodic force of frequency exactly equal to the natural frequency of the body, are called resonant vibrations.

2. The amplitude of vibration is very large.

3. The vibrations of the body are in phase with the external periodic force.

4. These vibrations last for a long time after the periodic force has ceased to act.

Difference between Natural Vibrations and Damped Vibrations

Natural Vibrations:

1. The amplitude of natural vibrations or free vibrations remains constant and the vibrations continue forever.

2. Natural vibrations never lose energy during vibrations.

3. There are no external forces acting on the vibrating body. The vibrations are only under the restoring force.

4. The frequency of vibrations depends on the size and shape of the body and it remains constant.

Damped Vibrations:

1. The amplitude of damped vibrations gradually decreases or reduces with time and ultimately the vibrations cease.

2. In each vibration, there is some energy loss in the form of heat.

3. Besides the restoring force, a frictional or damping force acts on the body to oppose its motion.

4. The frequency of damped vibrations is less than the natural frequency. The decrease in frequency of vibrations depends on the damping force.

Difference between Natural (Free) Vibrations and Forced Vibrations

Natural (Free) Vibrations:

1.) The vibrations of a body in absence of any resistive or external force are called natural vibrations.

2.) The frequency of vibration depends on the shape and size of the body.

3.) The frequency of vibration remains Constant.

4.) The amplitude of vibration remains constant with time (in absence of surrounding medium).

Forced Vibrations:

1.) The vibrations of a body in a medium in presence of an external periodic force are called forced vibrations.

2.) The frequency of vibration is equal to the frequency of the applied force.

3.) The frequency of vibration changes with change in the frequency of the applied force.

4.) The amplitude of vibration depends on the frequency of the applied force.

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