Newton

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Newton's second law of motion states that rate of change of momentum is directly proportional to applied force and takes place in the same direction as the applied force.

Explanation

Momentum is the force possessed by a body at any particular instant during its course of motion. Mathematically momentum is the product of mass and velocity.

Consider a body of mass m, having an initial velocity u. Let the body be acted upon by some force F for time t, such that its final velocity is v.

\Initial momentum = mu

Final momentum = mv

\Change in momentum in time t = m(v - u)

Change in momentum in unit time =

But (acceleration)

\ Change in momentum in unit time = ma

or

Rate of change of momentum = ma

According to Newton's second law

Rate of change of momentum a F

\ F a m.a

F = Km.a (K is the constant of proportionality)

If a body has unit mass and unit acceleration, such that force possessed by it is also one unit then

1 = K 11

or K = 1

\ F = ma

Force = mass acceleration

Unit of Force

Recall that F = ma

We know that SI unit of mass is kg and acceleration is m/s².

SI unit of force is kgm/s². But 1kgm/s² is defined as 1 Newton in honour of Sir Issac Newton.

1 N = 1 kgm/s²

One Newton force is that force which produces an acceleration of 1 m/s

² on an object of mass 1 kg.

To show that 1 kg m/s = 1 N s

By definition 1N = 1kg m/s²

Multiply equation (1) by second

To show that Newton's first law of motion is a consequence of Newton's Second law of motion

The mathematical representation of Newton's second law of motion is

If F = 0

i.e., in the absence of an external force the acceleration of the object will be zero, which means that the object will either move with uniform velocity or is at rest. This is Newton's first law of motion. Thus, we can conclude that Newton's first law of motion is a consequence of Newton's second law of motion.

Force is a vector quantity

Newton's second law of motion gives a quantitative definition of force.

Impulse

Mathematical representation of Newton's second law of motion is

or

When the time of application of force is short then Ft is defined as impulse. Impulse is a large force acting for a short duration.

SI unit of impulse = N s or kg m/s.

Example for an impulsive force

When we kick a football, the kick lasts only for a fraction of a second. The force, which we apply on a football, is an example for impulsive force.

Solved Examples

1)

A force of 625 N acts on a body of mass 25 kg. Find the acceleration of the body.

Solution:

Force (F) = 625 N

Mass (m) = 25 kg

Acceleration (a) = ?F = ma

Acceleration = 25 m/s²

2)

What force will produce an acceleration of 7m/s² in a body of 10 kg.

Solution:

Mass (m) = 10 kg

Acceleration (a) = 7m/s²

Force = 70 kgm/s²

Force = 70 N

3)

Calculate the mass of a body when a force of 225 N produces an acceleration of 2.5 m/s²?

Solution:

Force (F) = 225 N

Acceleration (a) = 2.5 m/s²

Force (F) = ma

Mass of the body = 90 kg