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ddd [48]
3 years ago
13

The value of the gravitational acceleration g decreases with elevation from 9.807 m/s2 at the sea level to 9.767 m/s2 at an alti

tude of 13000 m, where large passenger planes cruise. Determine the percentage reduction in the weight of an airplane cruising at 13000 m relative to its weight at sea level.
Physics
1 answer:
alexira [117]3 years ago
6 0

Answer: 0.41%

Explanation:

If we want to calculate the percentage decrease (the reduction) in weight of an airplane, we can use the given values of gravity, because the weight is directly proportional to the gravity acceleration.

Now the formula for the percentage decrease for ths case is:

\% weightdecrease=\frac{g_{sea}-g_{13000m}}{g_{sea}}(100)

Where:

g_{sea}=9.807 m/s^{2} is the gravity at sea level

g_{13000m}=9.767 m/s^{2} is the gravity at 13000 m

\% weightdecrease=\frac{9.807 m/s^{2} - 9.767 m/s^{2}}{9.807 m/s^{2}}(100)

\% weightdecrease=0.00407 (100)

\% weightdecrease=0.407 \% \approx 0.41 \% This is the percentage reduction in the weight of an airplane

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Convert 1 mm to meters using scientific notation. Include units in your answer.
miskamm [114]

Answer:

1.0 x 10^-3 m

Explanation:

1mm = (1/1000) m = 0.001m = 1.0 x 10^-3m (because to get 1.0, you have to  movi the decimal point in the "0.001" three spots over to the right)

3 0
3 years ago
To teach you how to find the parameters characterizing an object in a circular orbit around a much heavier body like the earth.
Karolina [17]

Answer:

a)  T² = (\frac{4\pi ^2}{GM})  r³

b) veloicity the dependency is the inverse of the root of the distance

kinetic energy  depends on the inverse of the distance

potential energy dependency is the inverse of distance

angular momentum depends directly on the root of the distance

Explanation:

1) for this exercise we will use Newton's second law

            F = ma

in this case the acceleration is centripetal

            a = v² / r

the linear and angular variable are related

           v = w r

we substitute

           a = w² r

force is the universal force of attraction

           F = G \frac{m M}{r^2}

we substitute

         G \frac{m M}{r^2} = m w^2 r

         w² = \frac{GM}{r^3}

angular velocity is related to frequency and period

         w = 2π f = 2π / T

we substitute

            ( \frac{2\pi }{T} ) = \frac{GM}{r^3}

the final equation is

             T² = ()  r³

b) the speed of the orbit can be found

           v = w r

            v = \sqrt{\frac{GM}{r^3} } \ r

            v = \sqrt{\frac{GM}{r} }

in this case the dependency is the inverse of the root of the distance

Kinetic energy

           K = ½ M v²

           K = ½ M GM / r

           K = ½ GM² 1 / r

the kinetic energy depends on the inverse of the distance

Potential energy

          U =

          U = -G mM / r

dependency is the inverse of distance

Angular momentum

          L = r x p

for a circular orbit

           L = r p = r Mv

           L =

         L =

The angular momentum depends directly on the root of the distance

8 0
3 years ago
Suppose that an asteroid traveling straight toward the center of the earth were to collide with our planet at the equator and bu
vlada-n [284]

Answer:

\frac{1}{10}M

Explanation:

To apply the concept of <u>angular momentum conservation</u>, there should be no external torque before and after

As the <u>asteroid is travelling directly towards the center of the Earth</u>, after impact ,it <u>does not impose any torque on earth's rotation,</u> So angular momentum of earth is conserved

⇒I_{1} \times W_{1} =I_{2} \times W_{2}

  • I_{1} is the moment of interia of earth before impact
  • W_{1} is the angular velocity of earth about an axis passing through the center of earth before impact
  • I_{2} is moment of interia of earth and asteroid system
  • W_{2} is the angular velocity of earth and asteroid system about the same axis

let  W_{1}=W

since \text{Time period of rotation}∝\frac{1}{\text{Angular velocity}}

⇒ if time period is to increase by 25%, which is \frac{5}{4} times, the angular velocity decreases 25% which is \frac{4}{5}  times

therefore W_{1} = \frac{4}{5} \times W_{1}

I_{1}=\frac{2}{5} \times M\times R^{2}(moment of inertia of solid sphere)

where M is mass of earth

           R is radius of earth

I_{2}=\frac{2}{5} \times M\times R^{2}+M_{1}\times R^{2}

(As given asteroid is very small compared to earth, we assume it be a particle compared to earth, therefore by parallel axis theorem we find its moment of inertia with respect to axis)

where M_{1} is mass of asteroid

⇒ \frac{2}{5} \times M\times R^{2} \times W_{1}=}(\frac{2}{5} \times M\times R^{2}+ M_{1}\times R^{2})\times(\frac{4}{5} \times W_{1})

\frac{1}{2} \times M\times R^{2}= (\frac{2}{5} \times M\times R^{2}+ M_{1}\times R^{2})

M_{1}\times R^{2}= \frac{1}{10} \times M\times R^{2}

⇒M_{1}=}\frac{1}{10} \times M

3 0
3 years ago
You are trying to overhear a juicy conversation, but from your distance of 20.0 m , it sounds like only an average whisper of 30
12345 [234]

Answer:

r₂ = 0.2 m

Explanation:

given,

distance = 20 m

sound of average whisper = 30 dB

distance moved closer = ?

new frequency = 80 dB

using formula

\beta = 10 log(\dfrac{I_1}{I_0})

   I₀ = 10⁻¹² W/m²

now,

30 = 10 log(\dfrac{I_1}{10^{-12}})

\dfrac{I_1}{10^{-12}}= 10^3

I_1= 10^{-8}\ W/m^2

to hear the whisper sound = 80 dB

80 = 10 log(\dfrac{I_2}{10^{-12}})

\dfrac{I_2}{10^{-12}}= 10^8

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

we know intensity of sound is inversely proportional to square of distances

\dfrac{I_1}{I_2}=\dfrac{r_2^2}{r_1^2}

\dfrac{10^{-8}}{10^{-4}}=\dfrac{r_2^2}{20^2}

10^{-4}=\dfrac{r_2^2}{20^2}

  r₂ = 0.2 m

6 0
3 years ago
Describe a vector and how it is used​
Ilia_Sergeevich [38]

Answer:

Vectors are used in science to describe anything that has both a direction and a magnitude. They are usually drawn as pointed arrows, the length of which represents the vector's magnitude.

Explanation:

They are usually drawn as pointed arrows, the length of which represents

8 0
4 years ago
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