Solar energy can be changed into thermal energy without any work being done. true or false

A 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

Stells [14]

Answer:

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

therefore the center of mass X of the rod is X=61.11 cm

6 0

3 years ago

A wire of cross-sectional area 5.00 106 m2 has a resistance of 1.75 O. What is the resistance of a wire of the same material and

MakcuM [25]

Answer:

the resistance of the second wire is 1 ohm.

Explanation:

Given;

cross sectional area of the first wire, A₁ = 5.00 x 10⁶ m²

resistance of the first wire, R₁ = 1.75 ohms

cross sectional area of the second wire, A₂ = 8.75 x 10⁶ m²

resistance of the second wire, R₂ = ?

The resistance of a wire is given as;

R ∝ $\frac{L}{A}$

Since the length of the two wires is constant

R₁A₁ = R₂A₂

$R_2 = \frac{R_1A_1}{A_2} \\\\R_2 = \frac{1.75\ \times \ 5.00\times 10^6}{8.75\times 10^6} \\\\R_2 = 1 \ ohm$

Therefore, the resistance of the second wire is 1 ohm.

6 0

3 years ago

How would you measure the potential difference across a resistor?

coldgirl [10]

You would need to connect a potential difference across a resistor in parallel

8 0

3 years ago

can someone help me answer this? i dont get it and I need help before the next 30 minutes. ill give a brainiest to whoever helps

Zinaida [17]

Answer:

S=5.83...

Explanation:

s=d/t

Speed=distance/time

s=35/10

s=5.83...

3 0

4 years ago

Which property of sound waves decreases as the square of the distance from the source increases?

Vitek1552 [10]

Answer:

Intensity

Explanation:

The intensity of a sound wave is equal to the ratio between to the power emitted by the source divided by the area of the spherical surface through which the wave propagates:

$I=\frac{P}{4\pi r^2}$

where

P is the power

$4\pi r^2$ is the area of the spherical surface

r is the distance from the source

As we see from the formula, the intensity is inversely proportional to the square of the distance from the source:

$I\propto \frac{1}{r^2}$

so, intensity is the correct answer.

3 0

3 years ago