Three identical 4.0-kg cubes are placed on a horizontal frictionless surface in contact with one another. The cubes are lined up from left to right and a force is applied to the left side of the left cube causing all three cubes to accelerate to the right at 4.0 m/s2 . What is the magnitude of the force exerted on the right cube by the middle cube in this case

The amount of force exerted by the middle cube on the right cube will be 16 N.

Explanation:

Newton's second law of motion says that the force acting on some object is directly proportional to the rate of change of momentum of the object and the change occurs in the same direction in which the force is applied. If due to the application of a force (F) an object of mass (m) gains an acceleration (a), mathematically we can write

As according to the problem all the cubes are attached to each other, so the amount of force applied can be written as

This force will be uniformly distributed among the three cubes to generate the acceleration. So if 'f' is the force exerted by the middle cube on the right one then,

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.