g 16.0 kg sled is pulled on a horizontal frictionless ice rink with a light spring of force constant 220 N/m. If the sled has an acceleration of 2.0 when pulled horizontally, how much does the spring stretch (in meters)

Spring stretches by 0.145m

Explanation:

We are given;

Mass of sled;m = 16 kg

Force constant;k = 220 N/m

Acceleration;a = 2 m/s²

Now, we know that from Newton's second law of motion, Force is given by the expression ; F = ma

Thus,

F = 16 x 2

F = 32 N

Now from Hooke's law, we know that this force is expressed as;

F = -kx

Where x is the distance that the spring stretches.

The minus sign shows that this force is in the opposite direction of the force that’s stretching or compressing the spring. But we'll take the magnitude and therefore ignore the negative sign to get F = Kx

Thus,

32 = 220x

x = 32/220

x = 0.145 m

Explanation:

Information we have:

Mass of the sled:

Spring constant:

acceleration of the sled:

We use the formula for the force on a spring (Hooke's Law)

where k is the spring constant and x the distance the mass moved from the equilibrium

and we also use Newton's second Law of motion:

we combine these two equations:

we solve the last equation for the distance x:

and substitute the values:

the negative number means that the mass was moved in the opposite direction that the force, this because the force in a spring is restorative and points towards the equilibrium point

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.

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