Physics, 03.08.2019 01:10, robert7248

Amicrowave oven operates with sinusoidal microwaves at a frequency of 2400 mhz. the height of the oven cavity is 25 cm and the base measures 30 cm by 30 cm. assume that microwave energy is generated uniformly on the upper surface of the cavity and propagates directly downward toward the base. the base is lined with a material that completely absorbs microwave energy. the total microwave energy content of the cavity is 0.50 µj. what magnitude force does the microwave beam exert on the base of the oven?

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answered: ggujjnh

$F=2.1\times 10^{-6} N$

Explanation:

From the problem we have

$f=2400MHz\\h=25cm\\A_{base}=(30 \times 30) cm\\E=0.5 \mu J$

Where is frequency, is height, $A_{base}$ and is the microwave energy.

First of all, we need to tranform length units to meters. In the case of the heigh, we just have to divide by 100, because 1 meter equals 100 centimeters:

$h=25cm \frac{1m}{100cm}=0.25m$

Then, the area of the base would be

$A_{base}=(30 \times 30) cm^{2} =900 cm^{2} \frac{1m^{2} }{(100cm)^{2} }=0.09m^{2}$

Now, to find the force exterted on the base of the oven, we first need to find the radiation pressure. But, before that, we need to know the intensity, and to find it, we need to first calculate the power, which is defined as

$P=\frac{E}{t}$ Where is the power, is the energy and is the time.

Replacing all values, we have

$P=\frac{E}{t}=\frac{0.5 \times 10^{-6} }{t}$

As you can see, we need to find the time of the movement of the microwave beam, wich is can be found using constant kinematics

h=ct where is the speed of the light (we are talking about an electromagentic wave), is the height (the distance that the beam will travel), and is the time of the movement.

Also, we know that

$c=3 \times 10^{8} m/s$

Replacing all values, we find the time

$h=ct\\t=\frac{h}{c}=\frac{0.25m}{3\times 10^{8} m/s}=0.08\times 10^{-8}s=8\times 10^{-10}s$

Now, we can find the power

$P=\frac{E}{t}=\frac{0.5 \times 10^{-6} J}{8\times 10^{-10}s }=0.0625\times 10^{5} W=625W$

Then, we calculate the intensity

$I=\frac{P}{A}\\ I=\frac{625W}{0.09m^{2} }=6944.44 W/m^{2}$

Now, the radiation pressure

$P_{r} =\frac{I}{c} =\frac{6944.44W}{3\times 10^{8} m/s} =2314.81\times 10^{-8}=2.31\times 10^{-5}$

Lastly, using this radiation pressure we can find the force that cause it

$P_{r} =\frac{F}{A} \\F=P_{r}A=2.31\times 10^{-5} (0.09m^{2})=0.21\times ^{-5} N=2.1\times 10^{-6} N$

Therefore, the force exterted on the base of the oven is

$F=2.1\times 10^{-6} N$

answered: Guest

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.

answered: Guest

explanation:

earth's surface is mainly heated by the absorption of infrared radiation from the sun.

evaporation occurs because molecules in liquid water are warmed ( usually by the sun) and vibrate quicker, becoming less dense and rise.

condensation occurs because molecules in water vapor are cooled and therefore vibrate more slowly thus becoming more dense and eventually fall to earth.

lines of equal barometric pressure on a weather map are called: isobars : lines of equal temp on a weather map are called: isotherms.

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Amicrowave oven operates with sinusoidal microwaves at a frequency of 2400 mhz. the height of the ov...