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Prof S. Karthiyayini, BITS Pilani, Dubai Campus NEWTON’S LAWS Chapter 2

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Page 1: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

NEWTON’S LAWS

Chapter 2

Page 2: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

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

Newton’s Laws

Page 3: Newtons Laws & Apps

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

Page 4: Newtons Laws & Apps

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

Page 5: Newtons Laws & Apps

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

Page 6: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

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

Page 7: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

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Prof S. Karthiyayini, BITS Pilani, Dubai Campus

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Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Newton’s third law

Page 10: Newtons Laws & Apps

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

Page 11: Newtons Laws & Apps

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.

Page 12: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

But what about B? Consider the sketch below

Astronauts in space-cont.

Page 13: Newtons Laws & Apps

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.

Page 14: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

System of units

Page 15: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

1. Divide the systems /objects into smaller systems

Applications of Newton’s laws

Page 16: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Consider the example given below

Applications of Newton’s laws - cont.

Page 17: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

and

Applications of Newton’s laws - cont.

Page 18: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Applications of Newton’s laws - cont.

Page 19: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

For

Applications of Newton’s laws - cont.

Page 20: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

The vertical acceleration is 0,

Page 21: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Freight train- cont.

Page 22: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Consider

With acceleration

Freight train- cont.

Page 23: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

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Prof S. Karthiyayini, BITS Pilani, Dubai Campus

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Prof S. Karthiyayini, BITS Pilani, Dubai Campus

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Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Page 27: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Consider the pulley system shown

Page 28: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

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Prof S. Karthiyayini, BITS Pilani, Dubai Campus

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Prof S. Karthiyayini, BITS Pilani, Dubai Campus

The

,

Page 31: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Page 32: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Differentiating twice w.r.to time

From all the above equations

Page 33: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Acceleration can change instantaneously, but velocity and position cannot.

Hence,

Page 34: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Page 35: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Page 36: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Also Thus

Page 37: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

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

The force

Page 38: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Page 39: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Or where g =

Page 40: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Page 41: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

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

Page 42: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

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Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Page 44: Newtons Laws & Apps

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

Page 45: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Hence,

Page 46: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

The Then equations are

Hence,

Page 47: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Page 48: Newtons Laws & Apps

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

,

Page 49: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

or

Consider a solution,

Page 50: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

An alternate method is

Page 51: Newtons Laws & Apps

Prof S. Karthiyayini, BITS Pilani, Dubai Campus

Thank you