Force and Laws of Motion

What is Force?

Pushing, hitting and pulling if objects are all ways of bringing objects in motion. They move because we make a force act on them. So, force is defined as to change the state of motion by pull, push or any muscular effort.

Balanced and Unbalanced Forces:

If the block is pulled from both the sides with equal forces, the block will not move. Such forces are called as Balanced Forces and do not change the state of rest or of motion of an object.

Now, let us consider another situation in which two opposite forces of different magnitudes pull the block. In this case, the block would begin to move in the direction of the greater force. Thus, the two forces are not balanced and the unbalanced force acts in the direction the block moves.

An object moves with a uniform velocity when the forces acting on the object are balanced and there is no net external force on it. If an unbalanced force is applied on the object, there will be a change either in its speed or in the direction of its motion. Thus, to accelerate the motion of an object, an unbalanced force is required.

Net Force:

When multiple forces acting on an object, they can be resolved into one component known as the net force acting on and object.

Net Force
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First Law Of Motion:

The first law of motion is stated as: An object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied force.

All objects resist a change in their state of motion. The tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called inertia. That is why, the first law of motion is also called as the Law of Inertia.

Newton further studied Galileo’s ideas on force and motion and presented three fundamental laws that govern the motion of the objects.

Galileo observed that when the marble rolls down, its velocity increases under the influence of gravity. On other side, velocity decreases when it climbs up because it opposes the gravity. Galileo argued that when the marble is released fro left it would roll down the slope and go up on the opposite side to the same height from which it is released. If the inclinations of the planes on both sides are equal then the marble will climb the same distance that it covered while rolling down. If the angle of the inclinations of the right-side plane were gradually decreased, then the marble would travel further distances till it reaches the original height. if the right-side plane were ultimately made horizontal, the marble would continue to travel forever trying to reach the same height that it was released from.

Thus, Galileo concluded that: An object will remain in motion or in rest until or unless an external force is applied on it.

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Frictional Force: 

The force that opposes relative motion is called friction. It arises between the surfaces in contact.

For example, When we try to push a car and it does not move because it is balanced by frictional force.

Frictional Force
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Inertia:

Inertia is the natural tendency of an object to resist a change in its state of motion or of rest. The mass of an object is a measure of its inertia. It is directly proportional to the mass of the object. More the mass→ more inertia and vice versa.

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Types of Inertia:

There are three types of inertia:

  1. Inertia of Rest. Tendency of an object to resist any change in the state of motion.
  2. Inertia of Motion. Tendency of an object to resist any change in its state of motion.
  3. Inertia of Direction. Tendency of an object to resist any change in its direction.

Some Examples,

  •  When we are sitting in bus/car which is in rest, suddenly it moves and e fall in backward direction due to inertia of rest.
  •  When the tree’s branch is shaken vigorously, the branch attain to move but the leaves stays at the rest due to inertia of rest.
  •  When a runner finishes a race, he/she will not stop suddenly otherwise he/ she will fall forwards as the feet will come to rest but the upper body is in motion due to inertia of motion.

Momentum:

Impacts produced by the objects depend upon their mass and velocity. the momentum of an object is defined as the product of its mass and velocity. p=m*v( Momentum = mass*velocity) . Vector quantity, has direction and magnitude. SI unit is kg m/s.

Second Law Of Motion:

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

We know that the velocity of an object can be changed by applying an unbalanced force on to it. Similarly, the momentum of an object can change by applying an unbalanced force.

For Example –
A cricketer when catches a ball pulls his hands in the backward direction to give some time to decrease the velocity of the ball. As the acceleration of the ball decreases the force exerted on catching the moving ball also decreases. If the cricketer would try to stop a moving ball suddenly he would have to apply larger force.

Second Law of Motion
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Based on the definition of the second law of motion, we can infer that –

The amount of force that is being exerted on an object. From the formula stated above, we can see that the force is directly proportional to acceleration. So the acceleration of an object can change depending upon the change in force applied.

Mathematical Expression on Second Law of Motion:

                                                        Force ∝ Rate of Change of Momentum

More force↑ , More change in momentum.

Derivation:

Force = m*a

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Force:

It is defined as the product of mass and acceleration.

  • Formula is F = ma.
  • SI unit is kg m/s^2.

In the honor of Issac Newton,

kg m/s^2 = Newton (N)

Force is a vector quantity. So, 1N is the force when an object of 1kg, an acceleration of 1m/s^2 is produced.

F = 1N → Unit Force.

Third Law Of Motion:

When one object a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude bt opposite in direction. These forces act on different objects and never on the same object.

Alternative statement of the third law of motion is that: to every action there is an equal and opposite reaction. However, it is important to note that even though the action and reaction forces are always equal in magnitude, these may not produce accelerations of equal magnitude. This is because each force acts on different object that may have a different masses.

Some Examples-

  • When the bullet is fired, bullet moves in forward direction and hence the gun moves in backward direction.
  • When we jump from a boat, then our body moves in forward direcrtion and the boat moves in backward direction.

Conservation Of Momentum:

Sum of internal momentum of two bodies before collision is equal to final momentum of two bodies after collision.

Conservation Of Momentum
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Derivation:

m1u1+mu2 = m1v1+m2v2

Proof:

By Newton’s Third Law Of Motion,

A=m1(v1u1) (change in momentum of particle A)

B=m2(v2u2) (change in momentum of particle B)

FBA=FAB (from third law of motion)

FBA=m2a2=m2(v2u2)t FAB=m1a1=m1(v1u1)t m2(v2u2)t=m1(v1u1)t m1u1+m2u2=m1v1+m2v2

Final momentum of 2 bodies = Initial momentum of 2 bodies

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