Gravitation and Weightlessness - Part IV

4. Weightlessness
Weight of a body is given by W = mg, where m is the mass of the body and g is the acceleration due to gravity.  The acceleration due to gravity is a force that occurs due to “action at a distance”. You can feel your weight because of a second effect called “contact force”. If you are sitting in a chair, your weight is pushing the chair and the chair is pushing a force proportional to your weight back on to you. The contact force comes about due to Newton’s third law of motion.

If now, you and the chair are taken at a height and dropped, both the chair and yourself will fall towards the earth at an acceleration of g. The chair is unable to offer any “contact force” on you, hence you cannot “feel” your weight. Thus while falling, you will feel weightless. This condition is called free fall which means that there is no contact force acting.

When travelling in a lift in an upward direction, sometimes, you may feel a bit uneasy. This is because if
                                                                        
the lift is travelling at an acceleration of   a,    a and   g  are in opposite directions;  your weight will suddenly become W (g-a) instead of Wg. This sudden change in weight makes one uneasy. If you stand on a weighing machine on the lift, you will see the difference. Similarly, if the lift is travelling in a downward direction with an acceleration a, then your weight will increase to W (a+g), as both the
                 
vectors a and   g   are in the same direction.

On the other hand, take a stone and a spring balance. Tie the stone to the spring balance. Now drop the balance. You will notice that while being dropped, the weight of the stone becomes zero!!.
The spring balance and the stone are falling freely under gravitation; hence the spring balance shows its reading to be zero!!.  

If you are travelling in a lift and the lift rope snaps suddenly, you will feel weightless and experience a condition of free fall. The same is experienced by astronauts in a spacecraft. The spacecraft is generally at a height of 300 to 500 km from the surface of the earth. Therefore g is not zero. Despite this the astronauts experience weightlessness because both the spacecraft and the astronauts are in a state of free fall towards the earth. The spacecraft does not offer any contact force and the astronauts therefore feel weightless.

5. Projectiles
We have seen that gravitational acceleration g pulls a body downward towards the center of the earth. Now, what happens to a body that is travelling horizontally? The diagram below shows such a phenomena. A stone is thrown horizontally at a point A. The stone experiences a horizontal force and a vertical force. The vertical force is directed downwards and is due to g. The resultant of the two forces is that the stone takes a parabolic trajectory and not a horizontally straight trajectory.  

Thus instead of reaching point B, the stone will reach the ground at point C. If there were no gravitational pull by the earth, then the stone would continue its motion in the direction AB for ever!

An object that has a horizontal velocity is called a projectile.  Path of the projectile is called the trajectory. Trajectory is a curved path and is parabolic in nature.

Now try and do another experiment. Drop a coin from top of the table vertically and flick a second coin horizontally from the table.  

You will notice that both the coins reach the ground at the same time. This is irrespective of the horizontal velocity imparted to the second coin. Thus we may conclude that the both the coins travel vertical distance in equal time intervals. The horizontal velocity has no effect on the vertical motion of the coins. A coin is a projectile. Thus the vertical motion and horizontal motion of a projectile are independent of each other.

If we flick the coin with increasing speed, we will notice that the coin is hitting the ground at farther distances. This can be seen below.  

If you stand on top a mountain and shoot a projectile at higher and higher speeds, it will reach the ground at farther distances.  

At a certain speed, the projectile will take the path PT and will never reach the earth. In fact the projectile with this trajectory will go round the earth and will become an artificial satellite of the earth. Newton had first thought of this idea. And it took centuries to develop techniques to put a satellite in earth’s orbit.

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