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
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