Lift a car using your muscle power

Yes! you can lift a car by using just you hands! The principle of physics to be applied here is Pascal's Law.

Two cylinders ( vertically placed, different cross-sectional areas ) are constructed with a liquid in the tube ( horizontal ) connecting them. The cylinders have movable pistons with bases, one to place the car and another to push with your hand.

Say, the area of the base on which the car is placed is A₁ and the area of the base you are pushing is A₂.
Let F₁be the force applied to the car as a result of your pushing with the force F₂.

From Pascal's Law,

F₁/A₁ = F₂/A₂

or

F₂ = F₁ * A₂/A₁

So if A₁is much larger than A₂, F₂ is quite small, and so, a very small force is required on your part to lift the whole car.

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First Law of Motion

Newton stated his first law of motion as follows:

Every body continues in its state of rest. or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.

The first law of motion means that if a body is protected from the influence ( forces exerted ) of other bodies, such that no force acts on it, or if balanced forces act on it such that the net force on the body is zero, then there is no change in the state of motion of the body. That is, the body will remain at rest if it is at rest or will move with the same speed with which it moves now if no unbalanced force acts on it.

But, don't we see the stars describing out large circles everyday - they are surely accelerating since they are always changing the direction of their velocity. They are definitely bodies sufficiently far from the influence of other bodies so that no major forces are acting on them. So, what makes them go round in such large circles which surely requires a large amount of force?

To this you may say - "Well, Don't you see that it's actually the earth that is rotating - the stars just "seem" to be revolving in such large circles. They aren't actually doing it." O.K. I agree. But then how do we apply Newton's Laws if things appear to be doing what is not permitted according to Newton's Laws?

The answer to this question is that we need to make observations from a system which itself is not accelerating - no net forces are acting on it. The earth in the above example is rotating, revolving, and thus accelerating, so it is not a permissible place to make observations from.

So, the First Law of Motion, leads to the idea of a special kind of reference frames in which the laws of motion hold true. Thus, in a way, it defines the way in which non-accelerating frames of reference are significant. Therefore, the first law can also be interpreted as a definition of inertial frames of reference, i.e. the frames in which without external unbalanced forces acting on them, bodies continue in their state of motion.

In the special theory of relativity too, inertial frames of reference are significant.

The examples describing the first law of motion can be easily observed in everyday experiences. When objects are set into motion with the application of force, and then the force is removed, they don't stop immediately. This shows that a force is not required to keep the bodies moving. But, we observe that the objects do change their state of motion, their speed decreases and eventually, they stop moving. This is actually because of frictional forces acting between the object and the surface on which it moves. If there were no other such forces, the objects would have never stopped.

A question is - why does the first law hold? Why is it that if observed from inertial frames of reference, bodies continue their state of motion if no net forces act upon them?

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Applications of Classical Mechanics

Classical Mechanics finds a large number of interesting applications in daily life situations. It is used to explain most of the phenomena we encounter in day-to-day activities. In machines and parts of machines, in sports, in simple processes like using simple machines, and not so simple processes like designing a mechanical system, classical mechanics finds a lot of applications.

In fact, in very complex applicaitons like launching rockets and satellites too, the principles of classical mechanics play a very important role. The laws have been cast into various different forms and methods - Newtonian mechanics, Lagrangian Mechanics and Hamiltonian Mechanics these methods are used according to which provides the answer most easily and conveniently.

Listed below are some of the interesting applications that classical mechanics finds.

• Swing a Ball in Air ( Why are Golf balls Dimpled? ) This example shows an application of Bernoulli's theorem to explain the swing of a ball in air.
  
  
• Lift a Car With Your Muscle Power This example describes a simple application of Pascal's law and how one can considerable reduce the force required to lift a car.
  
  
• Helium Balloon in a car - Strange Behavior This example shows the effect of pressure and bouyant force to describe why a helium ballon shows a strange behavior in a moving car.

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Principles of Classical Mechanics

The basic laws of classical mechanics are Newton's Laws of Motion. The laws describe the effect of forces on the state of motion of a body, quantify the effects and relate it to the change in velocity of the body. They also tell us about the nature of a force.

The statements of the laws are :

1. A body continues to be in its state of motion unless an un balanced external force acts on it.
   
   
2. The force acting on a body is equal to the rate of change of its momentum. i.e.
   
   F = dp/dt
   
   
3. To every force, there is another with the same magnitude but acting in the opposite direction. ( To every action there is an equal and oppsite reaction. )

These three laws have a profound meaning and have helped us to analyze different types of motion. They have helped us to determine the orbits of planets, to launch rockets into space, to design complex machine parts and have a lot of other applications.

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ANALYZING NEWTON'S LAWS OF MOTION

• Newton's First Law of Motion
  
  
• Newton's Second Law of Motion
  
  
• Newton's Third Law of Motion
  
  

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Helium Balloon in a Car

A familiar experience in a vehicle is of a forward jerk when the vehicle comes to a stop and a backward jerk when the vehicle starts suddenly. But a helium balloon kept in the vehicle does the opposite. What could be the reason?

The factor that leads to this difference is the density of helium which is less than the density of the air in the vehicle. When the vehicle is set into motion, the air inside it rushes at the back which builds up more pressure at the back than in the front. Helium being less dense than the air moves in the direction of decreasing pressure due to bouyant force. A similar effect is there when the vehicle stops or takes a turn.

This leads to the strange behavior of a Helium Balloon.

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Classical Mechanics Related Technologies

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Swing a Ball in Air

A. The principle of physics at work in this phenomenon is Bernoulli's equation. The ball is released by the bowler in such a manner that it spins in air. The air near the ball is set in motion similar to that of the ball. The speed of air on one side of the ball increases and on the other side, the speed decreases. 

So, in accordance with Bernoulli's equation, the pressure decreases on the side where speed is more and on the other side, it increases. Thus, there is a net force on the ball towards the side of less pressure and it swings in that direction.

If the axis of spinning of the ball is parallel to its linear motion, it deviates sideways depending on the direction of spin. If the axis is horizontal and perpendicular, it deflects upwards or downwards and if the axis is vertical and perpendicular, the ball deflects sideways again.

Golf balls are dimpled to use the same effect to provide them with a lift in air.

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History of Classical Mechanics

Classical mechanics, its laws being very close to everyday experiences and phenomena and hence very perceptible to human beings grew as one of the first sciences and has a long history. There are famous records of ancient greeks having found out many of laws governing the world around them. The law of levers, the Archimedes' principle and Aristotle's works were some developments of physics in that era.

Until about 400 years ago, study af classical mechanics was based upon philophical arguments and quantification of physical quantities and experimentation were not given much importance. At that time, Galileo performed experiments where he attempted to understand and explain phenomena with the help of numbers.

He peformed experiments with inclined planes and motion of bodies on them. He concluded, by dropping two identically shaped balls having different masses from the Leaning Tower of Pisa, that all bodies fall with the same acceleration towards the earth if air resistance is absent.

He also gave the law of inertia that is now famous as the First Law of Motion. He gave a set of mathematical transformations to relate events of different frames of reference. These transformations are classical counterparts of the Lorentz transformations used in the theory of relativity

Then came Issac Newton.

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Introduction to Classical Mechanics

Classical Mechanics is the physics of dealing with motion of matter on a large scale (many orders of magnitude larger than the scale of atoms). The motion may be of a linear type, oscillatory type, rotational, rolling, circular and similar other types of motion encountered in nature. It is an approximation for the laws of nature and gives good results on the macroscopic scale. It was, in fact, considered to be true for matter on every scale till the 19th century. But, in the 20th century, a new set of laws and mechanics (quantum physics) was developed for matter at the atomic scale.

Classical mechanics has ideas of particles, their positions, momentum, energy and motion in space and time. Classical mechanics claims to predict the exact position, velocity, energy, momentum and other such properties of a system at any given point of time if its initial state and the forces acting on it are known. Although, it turns out that all such predictions are not possible in nature for a system to any level of accuracy (Heisenberg's Uncertainity Principle) because of the flaws in the idea of particles inherent to classical mechanics, classical mechanics still gives excellent approximations for most of our analysis of systems where such effects can be neglected.

For example, in dealing with the motion of machine parts in industry, motion of rockets in space, motion of blocks and balls on inclined planes, pullies, motion of planets around the sun and other such macroscopic systems, classical mechanics is quite efficient.

There are different approaches to the study of classical mechanics. Newtonian mechanics, Lagrangian mechanics and Hamiltonian mechanics. They are equivalent in that they lead to the same results, but provide different routes and theorems for analyzing motion.

Classical Mechanics is one of the branches of physics which is rather interesting because of its closeness to our daily experiences. Many of the mechanical phenomena we see around ourselves can be analyzed and understood on the basis of laws of classical mechanics. Easy models and mind pictures can be drawn for solving the problems. Not that the problems are less challenging, but we can relate them to our everyday experience. ( unlike, for example, quantum physics and theory of relativity).