Dynamics:Dynamics:

*“It is the branch of Physics which deals with causes of motion and their effects”*

__Law Of Motion:__

Newton formulated three laws of motion in his book.

__Newton First Law Of Motion:__

Newton’s first law of motion is also known as the Law of Inertia.

__Statement:__**“Every body continues its state of rest or uniform motion in a straight path until it is acted upon by an external, or unbalance force to change its state of rest or uniform motion”.**

__Explanation:__**This law consists of a two parts**

(a) When body is at rest

(b) When body is moving with uniform velocity

__(a). When Body is At Rest:__**Newton’s Law states that when a body is at rest, it continues its rest unless we apply a force on it. When we apply a force, it changes its state of rest and starts moving along a straight line.**

__(b) When body is moving with uniform velocity:__**Newton’s Law states that when a body is moving, it moves in a straight line with uniform velocity, but when we apply an opposite force, it changes its state of motion and come to rest.**

__Examples____A body riding a push-bike along a leveled road does not come to rest immediately when we apply a force, it changes its state of rest and starts moving along a straight line.__

If a bus suddenly starts moving, the passengers standing in the bus will fall in the backward direction. It is due to the reason that the lower part of the passengers which is in contract with the floor of the bus is carried forward by the motion of the bus, but the upper part of the body remains at rest due to inertia and so the passengers fall in backward direction.

__Second Law Of Motions:__

__Statement:__**“When a force acts on an object it produces an acceleration which is directly proportion to the amount of the force and inversely proportional to the product of mass”**

__Explanation:__**It is well known fact that if we push a body with greater force then its velocity increases and change of velocity takes place in the direction of the force. If we apply a certain force F on a mass m, then it moves with certain velocity in the direction of the force. If the force becomes twice then its velocity will also increase two times. In this way if we go on increasing the fore there will be increase in velocity, which will increase the acceleration.**

__Derivation:__**According to the Newton`s Second law of motion when a force acts on an object it produces an acceleration which is directly proportion to the amount of the force.**

a α F and inversely proportional to the product of mass

a α 1/m

Combining all:.

a α F/m

a = K F/m

If the Value of K is 1

so,

a = F/m or

F = ma

*Force is an agent which produces motion in a body but some time force may not be succeeded to produce motion in a body so we can say that the force is an agent which produces or tends to produce motion in a body.*

__1. Force:__We can further say that:

Force is an agent which stops or tends to stop the motion of a body. In simple word we can also say that force is an agent which changes or tends to change the sate of an object.

*The quantity of matter contained in a body is called mass.*

__2. Mass:__

__Formula:__**F = ma**

m = F/a

*The unit of mass in M.K.S system is Kilograme (kg)*

__Unit:__*It is a force with which earth attracts towards its centre is called weight.*

__3. Weight:__

__Formula:__**W = mg**

*The unit of weight in M.K.S system is Newton (N).*

__Unit:__

__Third Law Of Motion:__

” To every action there is always an equal and opposite reaction ”

__Explanation:__**According to Newton’s Law of Motion, we have:**

F(action) = – F(reaction

The negative (-) sign indicates that the two forces are parallel but in the opposite direction. If we consider one of the interacting objects as A and the other as B, then according to the third law of motion:

F(AB) = – F(BA)

F(AB) represents the force exerted on A and F(BA) is the force exerted on B.

__Examples:__**We we walk on the ground, we push the ground backward and as a reaction the ground pushes us forward. Due to this reason we are able to move on the ground.**

If a book is placed on the table, it exerts some force on the table, which is equal to the weight of the book. The table as a reaction pushes the book upward. This is the reason thta the book is stationary on the table and it does not fall down.

__Inertia:__

__Definition__

*“Inertia is the tendency of a body to resist a change in its state.”*

__Examples:__**Cover a glass with a post card and place a coin on it. Now strike the post card swiftly with the nail of your finger. If the stroke has been made correctly, the postcard will be thrown away and the coin will drop in the glass.**

If a moving bus stops suddenly, the passenger standing in it feels a jerk in the forward direction. As a result he may fall. It is due to the fact that the lower part of the standing passengers comes to rest as the bus stops. But the upper portion remains in motion due to inertia.

__Difference Between Mass And Weight:__

__Mass:__**1. The quantity of matter present in a body is called mass.**

2. The mass of a body remains constant everywhere and does not change by change in altitude.

3. Mass of a body possesses no direction. So it is a scalar quantity.

4. Mass can be determined by a physical balance.

__Weight:__**1. The force with which the earth attracts a body towards its centre is called the weight of the body.**

2. The weight of a body is not constant. It is changed by altitude.

3. Weight of a body has a direction towards the centre of the earth. So it is a vector quantity.

4. Weight can be determined by only a spring balance.

__Momentum:__

*“The quantity or quality of motion is called momentum and it is denoted by P”*

__Mathematical Definition:__**“It is the product of mass and velocity.”**

__Mathematical Representation:__**P = mV**

where:

p is the momentum

m is the mass

v the velocity

__Law Of Conservation Of Momentum:__

The law of conservation of momentum is a fundamental law of nature, and it states that the total momentum of a isolated system of objects (which has no interactions with external agents) is constant. One of the consequences of this is that the centre of mass of any system of objects will always continue with the same velocity unless acted on by a force outside the system

*:*

__Example__Consider two bodies A and B of mass m1 and m2 moving in the same direction with velocity U1 and U2 respectively such that U1 is greater than U2. Suppose the ball acquire velocity V1 and V2 respectively after collision

Momentum of the system before collision = m1U1 + m2U2

Momentum of the system after collision = m1V1 + m2V2

According to the law of conservation of momentum:

Total momentum of the system before collision = Total momentum of the system after collision =

m1U1 + m2U2 = m1V1 + m2V2

__FRICTION__**Definition**

*“When a body moves over the surface of another body then the opposing force is produce and this opposing force is called force of friction”*

__Explanation__Suppose a wooden block is placed on a table and a spring balance is attached on it. If we apply a very small force of magnitude F by pulling the spring gradually and increase it, we observe that the block does not move until the applied force has reached a critical value. If F is less then critical value, the block does not move. According to Newton’s Third Law of motion an opposite force balance the force. This opposing force is known as the force of friction or friction.

**Causes of Friction**If we see the surface of material bodies through microscope, we observe that they are not smooth. Even the most polished surfaces are uneven. When one surface is placed over another, the elevations of one get interlocked with the depression of the other. Thus they oppose relative motion. The opposition is known as friction.

**Factors on which Friction Depends**The force of friction depends upon the following factors:

__1. Normal Reaction (R)__Force of friction is directly proportional to normal reaction (R), which act upon the body in upward direction against the weight of the body sliding on the surface.

__2. Nature of Surfaces__Force of friction also depends upon the nature of the two surfaces. It is denoted as u and has constant values for every surface. It is different for the two surfaces in contact.

__Coefficient Of Friction:____The coefficient of friction is a number which represents the friction between two surfaces. Between two equal surfaces, the coefficient of friction will be the same. The symbol usually used for the coefficient of friction is U, where 0 ≤ U ≤ 1 .__

The maximum frictional force (when a body is sliding or is in limiting equilibrium) is equal to the coefficient of friction × the normal reaction force.

F = UR

Where m is the coefficient of friction and R is the normal reaction force.

This frictional force, F, will act parallel to the surfaces in contact and in a direction to oppose the motion that is taking/ trying to take place.

__Advantages Of Friction:____1, We could not walk without the friction between our shoes and the ground. As we try to step forward, we push your foot backward. Friction holds our shoe to the ground, allowing you to walk.__

2, Writing with a pencil requires friction. we could not hold a pencil in our hand without friction.

3, A nail stays in wood due to frction

4, Nut and bold cal hold due to friction

__Disadvantages Of Friction:____1, In any type of vehicle–such as a car, boat or airplane–excess friction means that extra fuel must be used to power the vehicle. In other words, fuel or energy is being wasted because of the friction.__

2, The Law of Conservation of Energy states that the amount of energy remains constant. Thus, the energy that is “lost” to friction in trying to move an object is really turned to heat energy. The friction of parts rubbing together creates heat.

3, Due to the friction a machine has less frequency 100%

4, Due to friction machine catch fire.

__Methods Of Reducing Friction:____Friction can be reduced by the following methods:__

1. The various parts of the machines that are moving over one another are properly lubricated.

2. In machines, the sliding of various parts is usually replaced by rolling. This id done by using ball bearings.

3. Where sliding is unavoidable, a thick layer of greasing material is used between the sliding surfaces.

4. The front of the fast moving objects, e.g. cars, aeroplanes are made oblong to decrease air friction.

__Law Of Friction:__

__Statement:__**The value of limiting friction increases proportionally with the increase in normal reaction. Hence, liming friction F(s) is directly proportional to the normal reaction.**

F(s) α R (Here α represents the sign of proportionality dont’ write it in the examination paper.)

=> Fs = uR ……….. (i)

u = F(s)/R

u is the constant of proportionality, which depends upon the nature of the surfaces of the two surfaces in contact. It is known as the coefficient of friction. It is only a number without any unit. We know that the normal reaction is directly proportional to the weight of the block, therefore,

R = W = mg

Substituting the value of R in equation (i)

=> Fs = umg

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