Laws of Mechanics

Laws of Mechanics

• Newton’s laws of motion

• Newton’s law of gravitation

• The parallelogram law

• Principle of transmissibility of force

 Newton’s laws of motion

First Law: -

A body remains at rest or continues to move with uniform velocity (in a straight line with a constant speed) if there is no external force acting on it.

Example

If a ball is rolling on a plane surface (neglecting the effect of air resistance, friction resistance etc.), if we want to stop or reduce the speed of ball, we have to applied some resistance against the motion of the ball to stop or reduce the speed of the ball.

Q    A bus running at a speed of 60 km/hr on a straight road. Air resistance and friction force between tyre and road surface are experience by a bus during running. What amount of force driver is to apply on accelerator pedal to maintain the speed of bus at 60 km/hr?

(A)Equal to Air resistance                                                          (B)Equal to Friction force

(C)Sum of Air resistance and friction force                                  (D) Can’t say

Q   A block having mass m is rest on a rough surface, the coefficient of friction between the surface and block is u. what amount of force is to be applied on block to move it over the rough surface.

Give the answer in comment box

Second Law: -

The rate of change in linear momentum of a body is proportional to the impressed force and takes place in the direction of the applied force.

The product of mass (m) and velocity (v) is called momentum.

F = Applied force (units)                     m = mass of body (units)                     v = linear velocity (units)

We very well know that mass of the body is constant but velocity depends on distance and time.

Rate of change of velocity = final velocity – initial velocity

Final velocity (v2) = velocity of a particle after t interval of time

Initial velocity (v1) = velocity of particle at t becomes zero.

The rate of change of linear momentum          = mass * (final velocity – initial velocity)

                                                                  = m*(v2 – v1) units

And

The applied force F = m*(v2 – v1) = m*a (units)                                [a= linear Acceleration]

The above equation use

To find force needed to brake the momentum

To find acceleration of a body etc.

Third Law:-

To every action, there is an equal and opposite reaction.

The force of action and reaction between interacting bodies are equal in magnitude, opposite in direction, and collinear.

Question

Give the real life examples of Second law and third law in comment.

Newton’s law of gravitation

Two particles are mutual attracted along their connecting line with a force whose magnitude is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Body 1 having mass m

F= GMm/r2       G= 6.67*10^-11 m^2 /kg s^2

g = GM/r2 = gravitational constant

F = gm  

g = [(6.67*10^-11)* (5.972*10^24)]/ 6371000 = 9.81 unit

                                           Figure - Gravitational law of force

Principle of Transmissibility of force

The point of application of a force applied to a rigid body may be transmitted anywhere along its line of action without changing its resultant effects external to the rigid body.

                                        Figure - Principle of Transmissibility of forces

Composition and Resolution of Forces

Resultant Force

A resultant force is the force which can replace two or more forces and produce the same effect on the body as the forces.

Principle of  resolved parts

The sum of resolved parts of two forces acting at a point in any given direction is equal to the resolved parts of their resultant in that direction. 

Composition of Forces 

It is a process to replaces number of forces acting on a body by a single force, without changing net effect acting on a body.

Example - Resultant force  

Laws of Forces

the various laws are used for the composition of forces are as follows

1. Parallelogram law of forces. 
2. Triangle law of Forces.
3. Polygon law of forces

Parallelogram law of forces-

    

      "If two forces acting simultaneously on a particle, be represented in magnitude and direction by the two adjacent sides of a parallelogram then their resultant may be the diagonal of the parallelogram which passes through their point of intersection." 

FIGURE 1 

Two Concurrent force P and Q are acting along the two sides of Parallelogram, R is the resultant of the parallelogram.

Equation 1 and equation 2 shows a relation to find the value of resultant and direction of resultant respectively.

Triangle law of forces-

    "If the forces acting simultaneously on a body are represented in magnitude and direction by the two sides of triangle taken in order then their resultant  may be represented in magnitude and direction by third side taken in opposite order."

Polygon law of forces

      "If a number of coplanar concurrent forces, acting simultaneously on a body are represented in magnitude and direction by the sides of polygon taken in order then their resultant  may be represented in magnitude and direction by closing side of a polygon, taken in opposite order."

     

Introduction to Mechanics

INTRODUCTION

Mechanics is defined as “A science which deals with the laws and principle of mechanics.” Engineering Mechanics is the application of laws of mechanics to engineering problems.

                                      CLASSIFICATION OF ENGINEERING MECHANICS

• Particle is a point mass. If the dimension of body can be ignored while studying its equilibrium or motion, it may be treated as a particle

• Rigid body: - A body said to be rigid if it does not change its shape and size under the influence of forces acting over it. In rigid body the distance between to particle remains same before and after loading.

• Force: - Force is the external agent which changes or tends to change the state of rest or of motion of a body in a straight line. Force is the vector quantity.

• Effects of force

1. It may change the motion of body. The motion may be accelerated or retarded.
2. It may bring body in equilibrium under unbalance forces are already acting over it.
3. It may change the shape and size of the body.

• Characteristics of force

1. Magnitude
2. Direction
3. Sense of nature
4. Point of application

• System of forces: -

1. Co-planar forces : -The forces, whose line of action lie on the same plane.
2. Co-linear forces: -The forces, whose line of action lie on the same line.
3. Concurrent forces: -The forces, meet at one point. 
4. Co-planar concurrent forces: -The forces, whose line of action lie on a plane and meet at one point on the same plane.
5. Co-planar non-concurrent forces: -The forces, whose line of action lie on a plane and do not meet at one point on the same plane.
6. Non-coplanar non-concurrent forces: -The forces, which do not meet at one point and their line of action of do not lies on the same plane.

Engineering Mechanics Question

Engineering Mechanics is the branch of  applied science, which deals with laws and principles of Mechanics, along with their applications. The knowledge of Engineering Mechanics is very essential for an engineer in planning, designing and construction of various types of structures and machines.