**Branch :**First Year-Engineering Syllabus

**Subject :**Elements of Mechanical Engineering

## Kinetics of a Particle: Direct application of Newton's second law

**Direct application of Newton's second law:**** **The acceleration of a particle is proportional to resultant force acting on it and is in the direction of this force.

F = *m*a

where F is the resultant force and a is the acceleration.

This relation can be verified only experimentally.

Assume the existance of a fixed primary inertial system. Newton's second law is valid in this system as well as with respect to any nonrotating reference system that translates with respect to the primary system with a constant velocity. Such a system is called an inertial system.

We can also say that"inertial" system is a system in which F = ma is valid.

To understand the concept of inertial system, consider a cart from the roof of which a bob is suspended by a thread.

Whenever the cart accelerates or decelerates, the bob deflects. An observer sitting in the cart will think that bob is accelerating/decelerating without applying any force. Thus, for him the Newton's second law does not hold good. However, the fallacy is that he is applying the Newton's law in non-inertial system. One has to be careful in applying Newton's law to only an inertial frame of reference.

An application of Newton's law will be illustated by solving the dynamics of the following system:

It is desired to find out the acceleration of 30 kg mass , when the chord is being pulled by (20×9.81) N force.

**Sol:**

We neglect friction and the mass of the pulley and make the free body diagram of 30 kg mass as well as the pulley attached with it. In that case, the tension everywhere in the chord is equal to the pull of (20×9.81) N.

Upward force =

Downward force due to gravity =

Net force (in upward direction)