A bowling ball weighing 71.2 N is attached to the ceiling by a 3.70 m rope. The ball is pulled to one side and released; it then swings back and forth like a pendulum. As the rope swings through its lowest point, the speed of the bowling ball is measured at 4.20 m/s. At this instant, what are (a) the acceleration of the bowling ball, in magnitude and direction, and (b) the tension in the rope?

a, 7.26kg

b, 36.59N

Explanation:

The question says it swings like a pendulum, as such, we would use the formula for circular acceleration.

a = v²/r

a = 4.2²/3.7

a = 17.64/3.7

a = 4.77m/s²

The acceleration of the ball is directed towards the centre because circular acceleration is usually directed towards the centre

To find tension, recall, F = ma

m = F/a

m = 71.2/9.81

m = 7.26kg

In solving for tension then, we use our acceleration to be (9.81 - 4.77) = 5.04m/s²

Tension = ma

Tension = 7.26 * 5.04

Tension = 36.5904

Hence the tension in the rope is 36.59N

33: i think it’s b

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.