What is Friction?

Friction, a Speed killer:

Friction is the force resisting the relative motion of two surfaces (mostly solid or fluid) sliding against each other. There are several types of friction like:
1) Dry friction
2) Lubricated friction
3) Skin friction etc.

So basically friction is something that opposes the motion of  an object.

The thing we are interested in is studying the motion of objects when there is no friction at all (we dis-regard air resistance).

Therefore, the key question we are going to answer is: "How is the motion of objects when there is no friction?"

What is Motion without Friction?

Motion without friction is a phenomenon in which an object is in motion whilst its surface is not in contact with other surfaces. An example of such motion is that of a hovercraft.

As you can see in the image, the hovercrafts's bottom surface and the ground do not actually make contact, it is thanks to the continuous movement of air which pushes the hovercraft with enough force to keep it off the ground.

Back in Time

How did Newton get the idea of finding this Law whose discovery eventually made him find the other Laws?

The Apple Incident:

One fine evening, Newton happened to be dozing off in a garden under an apple tree when an apple fell on his head, This small event gave birth to one of the greatest discoveries mankind has ever made: Gravitation.After the  apple fell on his head, Newton wondered why it had done so. This was when the notion of gravitation came to his mind.
"Why should the apple constantly fall perpendicularly to the ground? Why should it not go sideways or upwards? but constantly towards the earth's center?", he asked himself.
It is said that Newton spent the whole night trying to uncover the mysterious force which made the apple fall in that particular manner. After a few days he came up with an outstanding theory:
"The Earth draws the apple towards its center, that would mean the sum of the drawing power in the matter of the Earth must be in its center and not in any other side. If matter thus draws matter therefore the apple draws the earth and vice-versa, When the apple falls in the ground, the reason it stays immobile is because the drawing power of the apple and the Earth are compensated."

This is how Issac Newton solved the mystery.
The shocking news is that Newton was the first one to discover gravitation but not the first one to discover the First Law of Motion.

The First Law was actually stated by Galileo Galilei who stated that a force is necessary to change the velocity of an object (acceleration) but not to maintain it. Galileo named the tendency of objects to resist: inertia. Newton's first law is a restatement of Galileo's and Newton honestly gave all the credit to Galileo.

The First Law apparently occurred to many natural philosophers, like Aristotle and Thomas Hobbes. The 17th century philosopher Rene Descartes is said to have perfected the law but was unable to perform any experiment to confirm it.

Newton's Laws of motion

First Law of motion:

If the net force ( the vector sum of all the forces) is a null vector, the object maintains a uniform rectilinear motion i.e. the velocity of the object is constant.
If the velocity is constant, then the speed and direction are constant since the vector velocity characterizes both the magnitude (speed) and direction.
The first law can thus be mathematically stated as:

We can deduce from the law that:
- If the object is at rest (Net Force = null vector) , it will stay at rest until and unless an external force acts upon it.
- If the motion, it will maintain its movement (uniform rectilinear motion) i.e. with constant velocity until and   unless an external force acts upon it.

Second Law of motion:

The Second Law of motion states that the net force (sum of all the forces acting on the object) is equal to the differentiation of its linear momentum by that of time.

Momentum= mass * velocity






The Second Law can also be stated in terms of acceleration . Since the law works only for constant mass systems, we take the mass out of the differentiation operator.

Using this law, we can say that a body at rest tends to stay at rest until and unless an external force acts on it.

We can also say that an object in motion will maintain a uniform rectillinear motion unless and until an external force acts on it.

 We thus proved that the First Law is actually part of the Second Law.

After finding the first Law, Newton took 2 more years to come up with the Second Law (according to some physicists.) what took him so long?

Newton had to invent an essential mathematical tool to make progress in his work: Infinitesimal Calculus. It is said that Issac Newton teamed up with a German Mathematician : Gottreid Leibniz and it is said that these two developed it independently.
  

The Hovering Device Experiment

Things needed for the experiment:
1) A web camera.
2) A glass platform
3) A hovering device.
4) A program that can take chrono-photographs through the webcam.

The Procedure:
1) Place the hovering device in such a way that it stays at rest  i.e. with a net force equal to null vector.
2) Push the device and take a chonophotograph.

In the chronophotograph, the gap between each consecutive photo was 0.1 sec. Here's a diagram of how the chonophotograph looked.

Observation:
As we see in the chronophotograph, the gap between every two points is the same. In other words, the distance traveled by the hovering device is the same for every 0.1 sec.
The hovering device's motion was thus a motion with constant velocity.

First of all, how is the motion of a hovering device friction-less?

The hovering device has a motor that pushes it away from the surface thus compensates for the weight of the object.

There is thus no friction between the hovercraft and the surface and its motion is frictionless.

We know that the net force on the hovering device is Zero, According to Newtons's First Law , if the net force acting on an object is zero, the object will maintain its state of motion (at constant velocity). The chronophotograph proved the fast that the velocity was constant:

Conclusion of the first experiment:
The motion of a hovering device which is a friction-less motion is with a constant velocity (i.e. a uniform rectilinear motion).


An alternative to the hovering device experiment is a balloon hovercraft:

Things we need to make a balloon hovercraft:
-A CD
-Some blue tag or a sealing tag
-A balloon
-A bottle cap

Procedure:
Take the CD and fix the bottle cap at its center with the blue tag. Attach the balloon to the cap and inflate it. Thats it! Its a perfect substitute for a hovering Device

"Mass Misconception"

Here's an interesting question: "Why do two balls of different masses when dropped from a certain height drop at the same time?"

People in the ancient times had a general misconception about free-falling objects. Aristotle thought that an object of more mass would fall faster than an object with lesser mass. Since Aristotle was a renowned philosopher, people agreed blindly with his proposition without asking for any proof. Centuries passed and science progressed...
On one fine day, Galileo Galilei, a brilliant young scientist determined to understand the functioning of the universe and the objects in it went up the Leaning Tower of Pisa and threw two balls down (one made of iron and the other made of wood) from an equal height. To the awe of the audience, both the balls touched the ground at the same time, Galileo hence said, disproving Aristotle's hypothesis that:
"The Acceleration of falling objects is same. Thus, the time taken for any object to hit the ground does not depend upon its mass."

Going back to our topic :How is the motion of a free-falling object frictionless?
A free-falling object is not in contact with any surface. We neglect air friction. This motion can thus be called frictionless.

Since the epic experiment that Galileo conducted was at the Leaning Tower Pisa, we named our experiment: "The Pisa Balls"

The Pisa Balls Experiment

                                                            Material required:
 1) Two balls of different masses.
2) Thermacol sheet with two holes of the same diameter as the balls
3) A cardboard sheet of the same dimensions as the thermacol sheet.
4) A sound analyzing software (Audacity)

                                                                    

Procedure:
1) Take the cardboard sheet in your hands put the thermacol sheet on top of it.
2) Then place both the balls in the holes
3) Then pull the cardboard sheet swiftly so that both the balls fall at the same time.

4) Place an audio receptor between the falling position of both the balls and connect it to a computer and save the sound wave we obtain when the balls hit the ground.

The sound wave in Audacity clearly showed that both the balls hit the ground at the same time. In the sound wave below, the first spike is when both the balls hit the ground.

The proof with calculation:

First of all, we know that the only force pulling the objects down (acting on the objects) is their weight ( W representing the vector weight of the object).

We know that a force is represented as:

In this case, weight is a force with the vector gravity as acceleration.

the only force acting on free-falling objects is W.
Thus:

From this, we could say that the time taken for the objects to hit the ground is the same since they have the same acceleration.

Mathematical Demonstration of the fact that the time of descent of a free-falling object does not depend on its mass:

By integrating acceleration, we get the velocity of the object:

We are interested in knowing when the ball hits the ground i.e. when the Y coordinate of the position vector OM is equal to zero.
To find t, we do :

By this, we conclude by saying that the time of descent of a free-falling object depends on the initial height and the gravity but not on its mass.