Newton’s Laws of motion
Newton’s first law of motion states that "everything in the universe continues its state of rest or uniform motion in a straight line unless an external force acts on it".
From the above definition, we can say that an external agent is required to change the state of the body. That external agent is force, hence, the first law gives the definition of force. This statement also concludes that everything in the universe possesses a property due to which it remains or tends to remain in its own state on rest or uniform motion in a straight line. Therefore, Newton’s first law of motion also gives the definition of Inertia.
Inertia is generally of three types:
(i) Inertia of rest: The opposition of a body to change its state of rest (i.e. the property of a body by virtue of which it remains or tends to remain in its own state of rest unless or even external force is applied) is called Inertia of rest. E.g.
- When a bus suddenly moves from rest, passengers standing in a bus fall backwards. It is because the lower part of the passenger’s body which is in the contact of the bus come to motion with the bus whereas the upper body still ted to remain it its own state of rest due to inertia of rest.
- When we shake a tree, fruits fall down. It is so because initially tree is in rest and also the fruits. When we shake the tree, it comes into motion but the fruits attached to it still tend to be in its initial state or rest. Hence, fruits are detached from the tree and they fall down.
(ii) Inertia of motion: The opposition of a body to change its state of motion (i.e. the property of a body by virtue of which it remains or tends to remain in its own state of uniform motion unless or even external force is applied) is called Inertia of rest. For example; When a moving bus suddenly stops, passengers fall forward. It is because when bus suddenly stops the lower part of passenger’s body come to rest with the bus but the upper part still tends to be in its own state of motion in forward direction.
(iii) Inertia of direction: This is out of the scope of this book.
Linear Momentum
Momentum is the motion contained in a body and is the product of mass and velocity of a moving body.
p = m. v
It is a vector quantity and its SI unit is kg. m/s. Its dimensional formula is [MLT-1].
Newton’s second law of motion states, "the acceleration produced in a body is directly proportional to the external force applied to the body and inversely proportional to the mass of the body". Or
The rate of change of momentum of a body with respect to time is directly proportional to a net external force applied on it and change takes place in the direction of force.
If F is applied on a body for time t and its momentum is p, then from the second law of motion,
F α dp/dt
Or F = K. dp/dt,
where k is proportionality constant, whose value depends upon the choice of unit of force. If the system of units so chosen the k = 1, then
F = dp/dt,
If ‘m’ is the mass of the body and ‘v’ is the velocity of the moving object then,
Linear momentum (p) = m. v and
F = d (mv) / dt
or, F = m dv / dt
Therefore,
F = m. a
Units of force,
In SI unit
F = 1kg * 1ms-2
= 1kgms-2
= 1 newton = 1N
IN C.G.S unit
F = 1000g * 100 cms-2 [ 1kg --> 1000g and 1m --> 100cm]
= 105 gcms-2
= 105 dynes
Newton’s third law of motion state that, "for every action there is equal and opposite reaction".
Example of Newton’s third law of motion,
- A block resting on a table: Due to the weight W of the block, it presses on the table by its weight which is taken as action. The table also exerts a force on the block equal in magnitude but opposite in direction to that of the weight of the block called the reaction R. So, the reaction acts on two different bodies and W = -R.
- Pushing a block: When A man pushes a block on a smooth horizontal surface with negligible friction, he exerts force F1 on the block and the block also exerts a force F2 on the man. To move the block forward, the man must push back against the ground and the man gets reaction force which is applied on the block. So, the motion of the block is possible. If there had been no friction, then it is not possible to move the block.
- Flying of a rocket: The burnt fuel comes out of the rocket in the form of hot and highly compressed gases in the backward direction, whereas the escaping gases push the rocket in the forward direction.
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