Why?

(1) Why do stars twinkle? 

(2) Why is the earth's sky blue?

(3) Why does the sky during the sunshine and sunset appear red?

(4) Why do diamonds sparkle? 

(5) Why is the moon's sky black?

Newton's Law of Gravitation

Every object in the Universe attracts other object with a force F which is (i) directly proportional to the product of their masses, and (ii) inversely proportional to the square of the distance between them. If the masses of the two objects be M and m respectively and they are separated by a distance r,  then the gravitational force, F between them is,  F = (GMm/r^2) in magnitude and is directed towards the attracting mass. This is called the Newton's Universal Law of Gravitation.  The quantity G is called the Universal Gravitational constant and G = 6.67 * 10^-11 Nm^2/kg^2.

The value of G was experimentally determined by the British Physicist Henry Cavendish about a century later, by doing a simple experiment with a torsion pendulum as described in here. 

Test Yourself 


(1)  Calculate the magnitude of the force between two 1 kg point masses separated by a distance of 1m.

Work

The Merriam-Webster online dictionary defines work as 'an activity in which one exerts strength or faculties to do or perform something'. For example, a standing gate man exerts strength and does his duty. Similarly, a person carrying a load on his head and walking on a horizontal platform is also doing some work. But, in physics, work is defined in a slightly different way: work is the product of the magnitude of the applied force, F and the magnitude of the displacement, s of the force in its direction. It is given by the formula: W = F s cos(theta), where theta is the angle between the direction of the force and its displacement. Therefore, the work done depends upon (i) the magnitude of a force, (ii) the displacement of the force, and (iii) the cosine of the angle between the direction of the force and that of the displacement. The work done by a force in making some displacement is maximum, if the applied force and its displacement are in the same direction and the work done by a force is 0 if the two quantities are directed at right angle. 

Therefore, a workman carrying a load on his head on a horizontal platform does zero work in carrying the load, but he still does work against friction between his feet and the ground. 

Test Yourself:

(1) Compute the work done by a force of 200N if it makes a displacement of 2 meters (i) in its own direction, (ii) at an angle of 30 degrees with its direction, and (iii) at right angle to its direction. 

Momentum

Momentum of an object is the product of its mass m and the velocity v. Momentum being the product of  a scalar (mass) and a vector (velocity), it is a vector quantity. The direction of momentum is that of the velocity. 

The momentum of a system remains constant in the absence of an external force. This is called the principle of conservation of (linear) momentum, and is a very powerful law to solve physical problems.  

Consider an object of mass m moving with velocity v collides with an object of mass M moving with velocity V. Assume that the objects do not  lose their masses during collision but their velocities after collision become  v' and V' respectively. If the force in the system is only due to collision and there is no external force, then, the principle of  conservation of momentum can be written as : 

                                                             mv + MV = mv' + MV'

Test Yourself

(1) An object of mass 2 kg moving on a smooth surface with velocity of 20m/s towards east collides with a stationary object of mass 1kg on its path. If they coalesce and move together, predict their common velocity after collision.

Energy conservation

The total energy of a system is always constant. This means that energy can neither be created nor destroyed; it can simply be transformed from one form into the other. This is called the energy conservation principle. 

One simple example is the conservation of mechanical energy of a freely falling object. Imagine that an object of mass m is dropped from the top of a tower of height h. If we consider the bottom of the tower to be at zero level of potential energy, the object has a potential energy of mgh at the top of the tower. Here g is the acceleration due to gravity and its average value is 9.81 meters per second per second on the surface of the earth. The initial kinetic energy,  (1/2) m v^2,  of the object is zero because it is at rest  (v =0)  at that instant. Therefore, the total mechanical energy of the object is  mgh. Once it starts falling, its height from the bottom of the tower goes on decreasing and hence the potential energy of the object goes on decreasing. On the other hand, since the object is accelerating downwards, its velocity v goes on increasing, and hence its kinetic energy goes on increasing. At the bottom of the tower, the potential energy of the object is zero and the total energy of the object is its kinetic energy at this instant. By simple kinematics, we can show that the total energy is equal to  mgh at each point of the trajectory of the object. 

Test yourself

(1) A block of mass 5 kg is dropped from the top of a 10 meter tall tower. Calculate its potential energy at the top of the tower. Predict its velocity at the bottom of the tower using the formulas of kinematics. Then calculate the kinetic energy of the block at the bottom of the tower. Check whether the kinetic energy at the bottom of the tower is equal to the potential energy at the top of the tower. 

Vectors

A car starts from a garage, goes towards South through a distance of 3km and then turns towards West,  moves further through a distance of 4 km, and finally comes straight to the garage and stops. What is the displacement made by the car in this journey? What's about the distance traveled by the car? The answer to the first question is zero and the answer to the second question is 12km. This simple example gives an idea of two kinds of physical quantities - vectors and scalars. 

A vector quantity is the quantity which requires magnitude and direction both to specify it completely. On the other hand, a scalar quantity has only a magnitude, but no direction. In the example of the opening paragraph, therefore, displacement is a vector quantity but distance is a scalar quantity. Similarly, speed is a scalar where as velocity is a vector. Mass, time, electric potential, etc., are some other examples of scalars. Force or weight, acceleration, electric field, etc., are some examples of vectors. 

A vector is represented by a letter with an arrow on top of it or a bold-faced letter in print. A scalar, on the other hand,  is represented by an ordinary letter (no bold-faced) without arrow on it. Scalars follow algebraic rules in addition and multiplication but some specific rules should be followed while adding and multiplying two vectors.

Test yourself 

(1) Your friend started to walk from the campus center, moved towards South through 6 steps and then towards East through 8 steps. What is her displacement in this motion? What's about the distance covered by her?

Interesting Facts

The following are some facts in nature. Think of the physical reasons for them:

(1) The center of the geometric shadow of a coin placed in front of a narrow source of light contains a bright   spot. This is called the Poisson Spot or Arago Spot or Fresnel Bright Spot.
(2) The moon's sky is black.
(3) The surface of mars is red.
(4) The pitch of the sound from the siren of an approaching ambulance is higher than that of a receding one. This is due to the phenomenon called Doppler effect.
(5)  Black-topped roads are seen covered with water on a hot summer day. This phenomenon is called mirage.
(6) A metal bar feels colder than a wooden one although they are in the same environment.
(7) A plastic ball keeps on floating if it is placed on the top a water fountain or on an air-jet. This can be explained by Bernoulli's Principle.
(8) A nitrogen cooled magnet floats on top of a superconductor. This is related to the phenomenon called the Meissner effect.
(9) A postcard placed on top of a glass filled with water will remain there if you gently turn it upside down holding up the postcard, and then remove your had carefully from the postcard.
(10) Sometimes you can see colorful lights at night time in the northern sky. This light is also called Aurora Borealis.