A flat (unbanked) curve on a highway has a radius of 260 mm . A car successfully rounds the curve at a speed of 32 m/sm/s but is on the verge of skidding out. Required:
a. If the coefficient of static friction between the car’s tires and the road surface were reduced by a factor of 2, with what maximum speed could the car round the curve?
b. Suppose the coefficient of friction were increased by a factor of 2; what would be the maximum speed?

I suppose you meant to say the radius of the curve is 260 m, not mm?

There are 3 forces acting on the car as it makes the turn,

• its weight mg pulling it downward;

• the normal force exerted by the road pointing upward, also with magnitude mg since the car is in equilibrium in the vertical direction; and

• static friction keeping the car from skidding with magnitude µmg (since it's proportional to the normal force), pointing horizontally toward the center of the curve.

By Newton's second law, the net force on the car acting in the horizontal direction is

F = ma   =>   µmg = ma   =>   a = µg

where a is the car's radial acceleration given by

a = v ^2 / R

with v = the car's tangential speed and R = radius of the curve. At the start, the car's radial acceleration is

a = (32 m/s)^2 / (260 m) ≈ 3.94 m/s^2

(a) If µ were reduced by a factor of 2, then the radial acceleration would also be halved:

1/2 a = 1/2 µg

Then the car can have a maximum speed v of

1/2 a = v ^2 / R   =>   v = √(aR/2) = √((3.94 m/s^2) (260 m) / 2) ≈ 22.6 m/s

(b) If µ were increased by a factor of 2, then the acceleration would also get doubled. Then the maximum speed v would be

2a = v ^2 / R   =>   v = √(2aR) = √(2 (3.94 m/s^2) (260 m)) ≈ 45.3 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.