A 76.7 g mass is attached to a horizontal spring with a spring constant of 3.34 N/m and released from rest with an amplitude of 38 cm. What is the speed of the mass when it is halfway to the equilibrium position if the surface is frictionless? Answer in units of m/s.

0.687 m/s

Explanation:

Given

Mass of object, m = 76.7 g = 0.767 kg

Force constant of the spring, k = 3.34 N/m

Amplitude of the spring, x = 38 cm = 0.38 m

EPE(i) = KE(f) + EPE(f)

1/2kx(i)² = 1/2mv² + 1/2kx(f)²

1/2 * 3.34 * 0.38² = (1/2 * 0.767 * v²) + [1/2 * 3.34 * (0.38/2)²]

1/2 * 3.34 * 0.1444 = (1/2 * 0.767v²) + 1/2 * 3.34 * 0.0361

1/2 * 0.482 = 1/2 * 0.767v² + 1/2 * 0.121

0.241 = 1/2 * 0.767v² + 0.06

1/2 * 0.767v² = 0.181

0.767v² = 0.181 * 2

0.767v² = 0.362

v² = 0.362 / 0.767

v² = 0.472

v = √0.472

v = 0.687 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.

dec 23, 2016 - a load of bricks weighing 680 n a distance of 10 m across a parking lot. if if the worker pushes the cart with a constant force of 209 n, what work= force x distance = 220 n x 10 m = 2200 n.m = 2200 j i don't know where the person got it from, but the initial part, work= force x distance me.