Sulfur :) is a chemical element with the symbol S and atomic number 16. It is abundant, multivalent, and nonmetallic. Under normal conditions, sulfur atoms form cyclic octatomic molecules with a chemical formula S8. Elemental sulfur is a bright yellow, crystalline solid at room temperature.

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An air-core solenoid consists of 200 turns of wire wound on a form that is 71 cm long and has a inner diameter of 6 cm. A curren

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**Explanation:**

To calculate this, you need to use the correct expression which is the following:

L = Uo * N² * I * A / l

Where:

Uo = permeability of free space

N: number of turns

I: current

A: Cross sectional area of wire

l: length

The cross sectional area is calculated with the expression:

A = πr²

Replacing:

A = π*(3)² = 28.3 cm² or 2.83x10^-3 m²

Therefore the self inductance is:

L = 4πx10^-7 * 2.83x10^-3 * 200² / 0.71

L = 2x10^-4

Explain why the Newton’s Cradle device eventually comes to rest. Justify your mmsanotherstage2019.com with your Knowledge of Energy (pls mark Bra

The balls in a Newton"s cradle hit each other in a series of elastic collisions, transferring the energy of Ball One through the line on to Ball Five, losing no energy along the way.

Friction takes away the system of energy, slowly bringing the balls to a standstill as the friction becomes greater and greater.

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A meter stick A hurtles through space at a speed v = 0.25c relative to you, with its length aligned with the direction of motion

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**Explanation:**

Given:

relativistic length of stick A, relativistic velocity of stick A with respect to observer,*Since the object is moving with a velocity comparable to the velocity of light with respect to the observer therefore the length will appear shorter according to the theory of relativity.*

Mathematical expression of the theory of relativity for length contraction:

where:

L = relativistic length

original length at rest Lorentz factorA 1.00-m–long straight rod is manufactured to have a smoothly increasing linear mass density, so that at one end, it is 20.0 g/c

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a) ρL(x)= 20+4/5*x

b) the total mass of the rod is M=6000gr = 6 Kg

c) the center of mass of the rod is X= 61.11 cm

**Explanation:**

The linear mass density ρL is defined as

ρL(x)= dm(x)/dx , where m(x) is the mass of the rod at x (d represents the derivative operator)

a) since the linear density is a linear function:

ρL(x)= a+b*x

at x= 0 → ρL(x)=a =20 g/cm

at x=1 m=100 cm → ρL(x)=ρL(x)= 20 g/cm +b* (100 cm) = 100 g/cm → b= (100 g/cm - 20 g/cm)/100 cm = 4/5 g/cm²

ρL(x)= 20+4/5*x

b) considering that ρL(x)= dm(x)/dx → dm(x) = ρL(x) dx → m(x) = ∫ρL(x) dx + C

m(x) = ∫ρL(x) dx + C = ∫ (20+4/5*x) dx + C = 20x +4/5 (x²/2) + C = 2/5 x² + 20 x + C

now

m(0) = 0 → m(0) = 2/5 (0) + 20 (0) + C = C = 0

therefore

m(x) = 2/5 x² + 20 x

since the rod has 1m=100 cm long

M = m(100 cm) = 2/5 gr/cm² (100cm)² + 20 gr/cm (100cm) = 6000 gr = 6 Kg

c) the center of mass of the rod X is

X = (∫x dm) /M (evaluated between integration limits 0 and 100 cm of length)

but dm(x) = ρL(x) dx

X = (∫x ρL(x) dx ) /M = (1/M)*(∫ x*(20+4/5*x) dx ) = (1/M)*(∫ (20*x+4/5*x²) dx ) =

(1/M) ( 20(x²/2)+ 4/5*(x³/3) ) = (1/6000) ( 20*(100²/2) )+ 4/5*(100³/3) - 0 ) = 61.11 cm