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