(a) during an ice skating performance, an initially motionless 80.0-kg clown throws a fake barbell away. the clown’s ice skates allow her to recoil frictionlessly. if the clown recoils with a velocity of 0.500 m/s and the barbell is thrown with a velocity of 10.0 m/s, what is the mass of the barbell? (b) how much kinetic energy is gained by this maneuver? (c) where does the kinetic energy come from?

a) Barbell mass = .2kg

b) Energy gained = 10 Joules

c)Newton's Third Law of Motion; explained more below

Explanation:

I'm always weary of Physics problems so I apologize ahead of time if this comes out wrong.

a) We know that in a system, the initial energy input must equal the final energy that is output. I'm going to assume part b) is regarding the energy of the clown's movement; meaning the clown is our "system". And since the system disregards friction we have a system where the initial side has the energy of the clown and the barbell, while the final side just has the final energy of the clown. This gives us:

(1/2)(Clown mass)(Initial clown velocity)² + (1/2)(Barbell mass)(Initial barbell velocity)² = (1/2)(Clown mass)(Final Clown Velocity)²

The clown is initially standing still on the ice, so the initial clown velocity is 0; which wipes out that part of the equation. Plugging in our knowns, we end up with:

(1/2)(Barbell mass)(10m/s)² = (1/2)(80kg)(.500m/s)²

Isolating the barbell mass and doing some calculating leaves us with .2kg.

b) Again, assuming the clown is our main focus, the energy gained by the throw simply equals (1/2)(Clown mass)(Final clown velocity)².

(1/2)(80)(.500)² = 10 Joules

c) The energy gained, as well as the movement of the clown, is explained by Newton's Third Law of Motion. "For every action there is an equal and opposite reaction" might sound familiar. In this case, the clown acted on the barbell and the barbell reacted on her. Had she not been on ice, the friction of the ground would've kept her in place; but then you couldn't get a Physics problem out of it eh?

diagram is missing, but i will try to explain your doubt.

answer:

amplitude is the maximum displacement or distance moved on a point of a vibrating body or wave measured from its equilibrium position.it is equal to half the length of vibration path.

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.