Ablock of mass 1.6 kg is attached to a horizontal spring that has a spring constant of 1,000 latex: \frac{n}{m}n m. the spring is compressed 2 cm and is then released from rest. calculate the speed of the block as it passes through the equilibrium position if a constant friction force of 4 n acts on the block from the moment it is released.

3.52 m/s

Explanation:

work done by the compressing the spring = 1/2 K e² where K is the force constant = 1000 N/m, e is the compression = 2cm = (2 / 100) to convert it to m we divide by 100  = 0.02 m

work done by compressing the spring = elastic potential energy stored in the spring = 0.5 × 1000 × 0.02 = 10 J

work done by force of friction to hinder the motion = F × d = 4 × 0.02 m = 0.08 J

Kinetic energy of the body = work done by compressing the spring - work done by force of friction against the motion = 10 - 0.08 = 9.92

9.92 = 1/2 m v² where  m is the mass of the body which = 1.6 kg and v is the speed as it passes through the equilibrium point

9.92 = 1/2 × 1.6 × v²

9.92 × 2 / 1.6 = v²

v² = 19.84 / 1.6 = 12.4

v = √12.4 = 3.52 m/s

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.