# Force And Law’s of Motion

When we want to open the door and close the door, pick up any objects in his hand, pull the branch to move it from its position, push the basket on the wall side. In all situations, we either pull or push the body to move it from its earlier position. These are some examples, but in our everyday life, all objects move by this pull and push functions. *A push and pull on a body is called Force*. Our everyday life, all objects move by this pull and push functions, So we can say this all objects move by the apply of Force on it. Force is used in our everyday actions like *pushing, pulling, lifting, stretching, twisting, pressing*. We know, to move any object we used force on it. So, Force has some characteristics that move any stationary objects. Let’s discuss these effects of force.

**Effects Of Force**

Force can

any stationary body.moveForce can

the moving body.stopForce can

of the moving body.change the speedForce can

of the moving body.change the directionForce can

of the body.change the shapeForce can

of the body.change the size

The direction in which such body pulled or pushed is called the direction of the force.

All force be not always equal. Some force (that act on a body) very greater ( *overcome the force of friction*) that moves the body. But, Some time force is not so greater and *not overcome the force of friction*, So this force does not move the body. We see some time force small or sometimes large and sometimes it moves the body, but sometimes not. Let’s discuss, Why this happened.

Force are two types: Balanced And Unbalanced Force

## Balanced Forces

*If the result of all the force acting on the body is zero ( net force be zero), force is called balanced force.*

In this picture, Four different types of forces applied to the body. These forces are the *force of Our push, force of Friction* (that oppose the force of our push), the *force of Gravity, *and* force exerted by the earth on the body*. These forces are balanced force because the force of friction balances the force of our push and force exerted by the ground balance the force of gravity. So, all force has canceled and *Net Force* has been *Zero*. Due to this reason, the box cannot move from its position ( *balance force apply on the box or Net force is 0 *).

## Unbalanced Forces

*If the result of all the force acting on the body is not zero ( net force be not zero), force is called an unbalanced force.*

In this picture, again four different types of forces applied to the car. Again, Force exerted by the earth balances the force of gravity (*weight of the car on the earth*). But that time, the force of our push greater than the force of friction (*that applies in the opposite direction of our push or oppose our force*). So, Force of friction cannot balance the force of our push. Now all the forces acting on the car are not Zero (*net force not equal to zero*). Due to this reason, the car may move in the direction of greater force(* force of our push*), and the direction of our push in the forward direction. So, the car move in the forward direction.

Conclusion of the above discussion, Due to unbalanced force all the bodies move in our surrounding if no unbalanced force exist than movement is not possible.

# Newton’s Law Of Motion

In the seventeenth century a “natural philosopher” name Sir Isacc Newton. He was given three laws of motion. He has described these laws in the “Principia Mathematica” a book written by Newton own. Newton did not give these laws directly, first, he studies the law of Galileo Galilee.

**Galileo’s Law Of Motion**

The object moves in constant motion (or uniform motion ) when no force act on them.

Galileo’s law also called *Galileo’s law of inertia*. Newtons’ 1st law and Galileo’s law some similar. But why Newtons’ 1st law so famous and Galileo’s law not. Let’s studies about Newton, 1st law. And try to find the answer to it.

## Newton’s First Law Of Motion

A rest object will remain at the state of rest and object moving in the uniform motion will continue to move in the straight line with uniform motion, unless

compelled by an external force to changes it’s the state of rest or uniform motion.

Newton said first, a body that stands in the rest state will always stand in the rest position. Unless an unbalanced external for applied on them. When an unbalanced external for act on them then the leave his rest state and move in the direction of external force.

Second, a body that travels with uniform motion always travels in the straight-line direction with the same uniform motion (constant motion). Unless an unbalanced external for applied on them. When an external force act on them *then according to the effects of force the body can change its speed, direction, shape(or size)*.

Galileo said the only “the second statement of Newton’s 1st law.” But newton also said this, a body stand-in rest remain in the rest unless an unbalanced external for applied on them.

We study the present in which position will continue in that always when no unbalanced external force act on them. That means something is present that made the body continue in there last position. What is this? This is called ** Inertia**.

*The tendency of the body to remain at rest, and or in moving continues in the moving in the straight line is called inertia.Mass measures the inertia of the body. Inertia is proportional to the Mass (*

*Inertia*∝*mass**)*

Inertia is proportional to the mass of the body. So, If the mass of the body higher (leather ball) then inertia is large, and if the mass is low (plastic ball) then inertia is small.

## Newton’s Second Law Of Motion

The rate of change of momentum of an body is directly proportional to the applied unbalanced external force on them in the direction of the force.

Now one question is arises from the above statement. And this is a very important term to understand this law and force.

What is **Momentum**? Momentum is a term which has given by *Sir Isacc Newton*.

Momentum is the

product of the mass and the velocityof the body.

The formla of momentum is:p=mv

The symbol of momentum is ** P**. The SI ( standard identity) unit of momentum is

*Kilogram meter per second ( Kg m/s )**.*Momentum is a

*vector Quantity because momentum has magnitude as well as direction .*Force is proportional to the rate of change of momentum **F∝(mv-mu)/t**. And force is the product of two terms Mass and Acceleration.

If force will increase than the acceleration of the body will also increase, and if force decrease than the acceleration of the body will decrease. And if the mass of an object is higher then we need to apply more force on them for made them move, and if the mass is low then we need to apply low force to move them. So,

Force is directly proportional to the acceleration of the body (

force ∝ acceleration), and

Force is also directly proportional to the mass of the body (force ∝ mass).c

Suppose an object of mass (** m**) is moving along a straight line with an initial velocity (

**). It is uniformly accelerated to velocity (**

*u***) in time (**

*v***) by the application of a constant force (**

*t***) throughout the time(**

*F***). The initial and final momentum of the object will be**

*t***p1 =**and

*mu***p2 =**respectively.

*mv*The change in momentum ∝ p2 — p1

The change in momentum ∝ mv — mu

The change in momentum ∝ m × (v — u).And the rate of change of momentum ∝ m × (v-u)/t

Force is proportional to the rate of change of momentum. So

Force ∝ the rate of change of momentum

Force ∝ m × (v-u)/t

Force = m × (v-u)/t

Acceleration is equal to (initial velocity — final velocity)/time taken *(v-u)/t.* so

F = m × a

F = m a

The symbol of the Force is **F**.** **And the SI unit of Force is **Newton (N), Kilogram meter per second square (Kg m/s²)**. Force is the

*Vector Quantity because it has magnitude as well as direction*.

One other term’s name ** impulse** comes from the rate of change of momentum. By it, we also find the change in the momentum in the given interval of time.

Impulse is the change of the momentum of the body (

mv-mu)when some force (F) acts on it for some interval of time (t).

F = m a

Replace the ** a** to the full expression of acceleration:

F = m ×(v-u)/t

F = (mv-mu)/t

Ft= mv-muJ (Imp) = Ft

The symbol of impulse is** J, Imp. **The SI unit of it is

**.**

*Newton Second (Kg m/s)*When we are not applying any external force on the body (F= 0 N) for any interval of time (t).

Then the change in momentum = 0 N × t = 0. So, the change in momentum is 0 means initial momentum (mu) = final momentum (mv). So, if the body travel in uniform motion will continue in the uniform motion and if the body in rest state will remain in the rest position.

## Newton’s Third Law Of Motion

when one body exerts a force on another body, the second body instantaneously (immediately) exerts an equal and opposite force back on the body.

*The force exerted by the first body on the second body is called the **action force**, The force exerted by the second body on the first body in the opposite direction is called the *

*reaction force**. The action and reaction force always acts on the two different bodies in opposite directions.*

The action and reaction are the same in the magnitude. But mostly, they not produced an equal magnitude of acceleration in both bodies, Because mostly condition the mass of the two bodies is different from each other. But if the mass of both has the same then the magnitude of the acceleration is the same.

When one body exerts some force on the other body like when we walk on the road then we exert force on the road in the backward direction (*action force*), then the road exerts an equal and opposite force (in the forward direction) on us (*reaction force*), that means the second body immediately exert an equal and opposite on the first one. By this process, we walk in the forward direction.

The swimmer pushes the water in backward (*action force*), the water pushes the swimmer in the forward (*reaction force*) and pushes her forward.

See all the above example images and try to understand the Action and Reaction force of how to work.

## Conservation Of Momentum

Suppose two ball *A* and *B* of masses *mA* and *mB* are traveling in the same direction along a straight line at different initial velocities *uA* and *uB*, respectively. And no other external unbalanced forces are acting on them. Let *uA* > *uB* and the two balls collide with each other. During collision which lasts for a time t, the ball *A* exerts a force *F_ab* on ball *B* and ball *B* exerts a force F_ba on ball *A*. Suppose *vA* and *vB* are the final velocities of the two balls A and B after the collision, respectively.

*The change of momentum of the object A = **mA × vA — mA× uA*

And the rate of change of momentum( F_ab action)= *mA (vA- uA)/t*

Similarly,

*The change of momentum of the object B= **mB × vB — mB× uB*

And the rate of change of momentum( F_ba reaction)= m*B ( vB — uB)/t*

According to the Newton Third Law Of Motion, *to every action, there is an equal and *** opposite reaction. **So,

F_ab =-( F_ba)

mA (vA- uA)/t = -( mB ( vB — uB)/t )

Multiply ** t** to both side:

mA (vA- uA) = — mB ( vB — uB)

mA×vA-mA×uA =-mB×vB + mB×uB

-mA×uA -mB×uB = -mA×vA -mB×vB

-(mA×uA + mB×uB) = -(mA×vA + mB×vB)

Canceling (-) to both side:

mA×uA + mB×uB = mA×vA + mB×vB

As a result of this ideal collision experiment, we say that ** the sum of the total momenta of the two objects before the collision is equal to the sum of total momenta after the collision** provided there is no external unbalanced force acting on them. This is known as the

**.**

*law of conservation of momentum*