A factory worker pushes a 31.0 kg crate a distance of 4.20 m along a level floor by pushing downward at an angle of 32.0 ∘ below the horizontal. The coefficient of kinetic friction between the crate and floor is 0.260.

Now assume that, instead of the previous situation, the worker pushes harder (without changing the direction of his push), so that the crate moves with increasing speed. Assume the crate is pushed over the same displacement as before.

How much work is done on the crate by the force of friction during the displacement of 4.20 m when the pushing force is 118.00 N?

Explanation:

The kinetic force of friction is:

Before calculating work, it is require to determine if force exerted on the crate is enough to move it at least. The equation of equilibrium for the crate is:

The acceleration experimented by the crate is:

This positive result indicates that motion is physically reasonable. Hence, the work done by the force of friction is:

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.