Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

NEWTON’S LAWS

Chapter 2

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

To understand Newton’s laws consider the device, linear air track in 1D.

Newton’s Laws

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

A triangular hollow beam of 2 m with holes to emit gentle stream of air

A rider floats on it when air is turned on Air viscosity is 5000 times less than oil The rider behaves like an isolated object It stays at rest and when gently pushed it

moves with constant velocity

If the rider is released from rest it continues

to move slowly and evenly without gaining

or losing speed, contrary to moving bodies

are stopped by friction.

Thus an object moves uniformly in space

when there are no external influences.

Linear Air track

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Motion has meaning only with respect to a particular coordinate system.

In air track experiment the rider moves with respect to the track at rest any coordinate system which is moving w.r.t. the track

with constant velocity, an inertial system

Thus

Newton’s first law

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Consider the rider with a rubber band

If

Its

If the rider is changed, the acceleration is different but remains constant as before.

Thus the acceleration depends on

called mass.

Newton’s second law

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

If m1 and m2 are the mass of the first and second rider respectively, then

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Newton’s third law

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Captain A measured the position of the object with his spaceship as origin as

He concludes

Further

Eg 2.1 – Astronauts in space

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Force is not arbitrary

Newton's laws hold good only in inertial frames

Hence, both A and B set to check their observations.

A released a pencil from rest and found that it floats without acceleration. Hence, he concludes that his spaceship is in inertial frame

Astronauts in space-cont.

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

But what about B? Consider the sketch below

Astronauts in space-cont.

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

So B observed the apparent force,

Or

Thus B found that he

In general, if R is the vector from the origin of an inertial system to the origin of another coordinate system, then

which means that the second coordinate system

is also inertial. Also

Astronauts in space-cont.

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

System of units

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

1. Divide the systems /objects into smaller systems

Applications of Newton’s laws

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Consider the example given below

Applications of Newton’s laws - cont.

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

and

Applications of Newton’s laws - cont.

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Applications of Newton’s laws - cont.

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

For

Applications of Newton’s laws - cont.

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

The vertical acceleration is 0,

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Freight train- cont.

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Consider

With acceleration

Freight train- cont.

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Consider the pulley system shown

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

The

,

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Differentiating twice w.r.to time

From all the above equations

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Acceleration can change instantaneously, but velocity and position cannot.

Hence,

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Also Thus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

The object is to know the forces which are important in everyday mechanics

The force

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Or where g =

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Thus the turtle weight increases as the elevator accelerates up and decreases when moving down.

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

aM is the acceleration of the block

aS is the acceleration of the string

The equations of the motion are

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Hence,

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

The Then equations are

Hence,

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

The forces are as shown.

and the

radial equation of motion is

Since, M should be in vertical equilibrium

and

Or

,

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

or

Consider a solution,

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

An alternate method is

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Thank you