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GREYUIT [131]
3 years ago
5

What is the intensity in W/m2 of a laser beam used to burn away cancerous tissue that, when 85.0% absorbed, puts 470 J of energy

into a circular spot 2.60 mm in diameter in 4.00 s?
Physics
1 answer:
Advocard [28]3 years ago
8 0

Answer:

26036485.6433 W/m²

Explanation:

E= Energy = 470 J

t = Time = 4 seconds

d = Diameter = 2.6 mm

Power is given by

P=\dfrac{E}{t}

Intensity is given by

I=\dfrac{P}{\pi r^2}\\\Rightarrow 0.85I=\dfrac{E}{t\dfrac{\pi}{4} d^2}\\\Rightarrow I=\dfrac{470}{0.85\times 4\times \dfrac{\pi}{4}\times (2.6\times 10^{-3})^2}\\\Rightarrow I=26036485.6433\ W/m^2

The intensity of the laser beam is 26036485.6433 W/m²

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At a rock concert, the sound intensity 1.0 m in front of the bank of loudspeakers is 0.10 W/m². A fan is 30 m from the loudspeak
Klio2033 [76]

To solve this problem we will apply the concepts related to the Area, the power and the proportionality relationships between intensity and distance.

The expression for sound power is,

P = AI

Here,

A = Area

I = Intensity

P = Power

At the same time the area can be written as,

A = \frac{\pi d^2}{4}

Now the intensity is inversely proportional to the square of the distance from the source, then

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

The expression for the intensity at different distance is

\frac{I_1}{I_2}= \frac{r^2_2}{r_1^2}

Here,

I_1 = Intensity at distance 1

I_2 = Intensity at distance 2

r_1 = Distance 1 from light source

r_2 = Distance 2 from the light source

If we rearrange the expression to find the intensity at second position we have,

I_2 = I_1 (\frac{r_1^2}{r_2^2})

If we replace with our values at this equation we have,

I_2 = (0.10W/m^2)(\frac{1.0m^2}{30.0m^2})

I_2 = 1.11*10^{-4} W/m^2

Now using the equation to find the area we have that

A = \frac{\pi (8.4*10^{-3}m)^2}{4}

A = 5.5*10^{-5}m^2

Finally with the intensity and the area we can find the sound power, which is

P = AI

P = (5.5*10^{-5}m^2)(1.11*10^{-4}W/m^2)

P = 6.1*10^{-9}J/s

Power is defined as the quantity of Energy per second, then

E = 6.1*10^{-9}J

8 0
3 years ago
Mass Center Determine the coordinates (x, y) of the center of mass of the area in blue in the figure below. Answers: x=(3)/(8)a
Naya [18.7K]

Explanation:

The x and y coordinates of the center of mass are:

xcm = ∫ x dm / m = ∫ x ρ dA / ∫ ρ dA

ycm = ∫ y dm / m = ∫ y ρ dA / ∫ ρ dA

Assuming uniform density, the center of mass is also the center of area.

xcm = ∫ x dA / ∫ dA = ∫ x y dx / A

ycm = ∫ y dA / ∫ dA = ∫ ½ y² dx / A

First, let's find the area:

A = ∫ y dx

A = ∫₀ᵃ (-h/a² x² + h) dx

A = -⅓ h/a² x³ + hx |₀ᵃ

A = -⅓ h/a² (a)³ + h(a)

A = ⅔ ha

Now, let's find the x coordinate of the center of mass:

xcm = ∫ x y dx / A

xcm = ∫₀ᵃ x (-h/a² x² + h) dx / (⅔ ha)

xcm = ∫₀ᵃ (-h/a² x³ + hx) dx / (⅔ ha)

xcm = (-¼ h/a² x⁴ + ½ hx²) |₀ᵃ / (⅔ ha)

xcm = (-¼ h/a² (a)⁴ + ½ h(a)²) / (⅔ ha)

xcm = (¼ ha²) / (⅔ ha)

xcm = ⅜ a

Next, we find the y coordinate of the center of mass:

ycm = ∫ y² dx / A

ycm = ∫₀ᵃ ½ (-h/a² x² + h)² dx / (⅔ ha)

ycm = ∫₀ᵃ ½ (h²/a⁴ x⁴ − 2h²/a² x² + h²) dx / (⅔ ha)

ycm = ½ (⅕ h²/a⁴ x⁵ − ⅔ h²/a² x³ + h² x) |₀ᵃ / (⅔ ha)

ycm = ½ (⅕ h²/a⁴ (a)⁵ − ⅔ h²/a² (a)³ + h² (a)) / (⅔ ha)

ycm = ½ (⁸/₁₅ h²a) / (⅔ ha)

ycm = ⅖ h

6 0
3 years ago
A cycle track is 500 metres long. Amy completes 10 laps. She travelled at an average speed of 12.5 metres per second. She puts o
yanalaym [24]
The fast lap is irrelevant to the question, because it didn't happen
until after the 9 laps that you're interested in.

To be perfectly technical about it, we don't actually have enough
information to answer the question.  You told us her average speed
for 10 laps, but we don't know anything about how her speed may
have changed during the whole 10 laps.  For all we know, maybe
she took a nap first, and then got up and drove 10 laps at the speed
of 125 metres per second.  That would produce the average speed
of 12.5 metres per second and we would never know it  Why not ?
That's only 280 miles per hour.  Bikes can do that, can't they ?

IF we can assume that Amy maintained a totally steady pace through
the entire 10 laps, then we could say that her average for 9 laps was
also 12.5 metres per second.
5 0
3 years ago
What part of a standing sound wave does a musician seek in playing a musical note of a specific pitch?
marusya05 [52]
The correct answer to the question above is that the magician is seeking the wavelength of the standing wave. The part of a standing sound wave, which is its wavelength, the magician is seeking when playing a musical note of a specific pitch. 
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3 years ago
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Lady_Fox [76]
I think it's a solar power might seem strange or futuristic but it's already quite common place you might have a solar powered quartz watch on your wrist or solar powered pocket calculator
3 0
3 years ago
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