A crate is being pushed across a rough floor surface. If no force is applied on the crate, the crate will slow down and come to a stop. If the crate of mass 50 kg moving at speed 8 m/s comes to rest in 10 seconds, what is the rate at which the frictional force on the crate takes energy away from the crate

Energy is being taken away at a rate of 160 J per second from the crate.

Explanation:

The only energy the crate has when it moves is kinetic energy. Friction takes this away at a specific rate. The total kinetic energy at the start is as follows:

Kinetic energy = 0.5 * m * V^2

Here m = 50 kg

V = 8 m/s

Kinetic energy = 0.5 * 50 * 8^2

Kinetic energy = 1600 J

This is also the total energy taken away by friction. We may divide this by the time to find out the rate of change of energy of the crate:

Rate of change of energy = 1600 / 10 = 160 J

Thus, energy is being taken away at a rate of 160 J per second from the crate.

the total distance traveled by the car is

30km + 49km = 79 km .

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.