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3241004551 [841]

2 years ago

14

Two stars M1 and M2 of equal mass make up a binary star system. They move in a circular orbit that has its center at the midpoin

t of the line that separates them. If M1-M2-6.95 sm (solar mass), and the orbital period of each star is 2.20 days, find their orbital speed. (The mass of the sun is 1.99x 1030 kg.) km/s M2

1 answer:

ozzi2 years ago

3 0

Answer:

V = 365643.04 m/s

Explanation:

mass of the sun = 1.99 x 10^{30} kg

mass of M1 = mass of M2 = 6.95 solar mass = 6.95 x 1.99 x 10^{30} = 13.8305x 10^{30} kg

orbital period of each star (T) = 2.20 days = 2.20 x 24 x 60 x 60 =190,080 s

gravitational constant (G) = 6.67 x 10^{-11} N m2/kg2

orbital speed (V) = $\sqrt{\frac{G(M1+M2)}{r} }$

we need to find the orbital radius (r) before we can apply the formula above and we can get it from Kepler's third law, $T^{2} = r^{3}$ x k

where

T = orbital period

r = orbital radius

k = $\frac{4n^{2} }{G(M1+M2)}$ (take note that π is shown as $n$ )

making r the subject of the formula we now have

$r = (\frac{G(M1+M2).T^{2}}{4n^{2} } )^{\frac{1}{3} }$ (take note that π is shown as $n$ )

$r = (\frac{ 6.67 x 10^{-11} ( 13.8305x 10^{30}+ 13.8305x 10^{30} )x190080^{2}}{4x3.142^{2} } )^{\frac{1}{3} }$

r = 1.38 x 10^{10} m

Now that we have the orbital radius (r) we can substitute all required values into the formula for orbital speed

orbital speed (V) = $\sqrt{\frac{G(M1+M2)}{r} }$

$V = \sqrt{\frac{6.67 x 10^{-11} ( 13.8305x 10^{30}+ 13.8305x 10^{30}}{1.38 x 10^{10} } }\\$

V = 365643.04 m/s

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An asteroid is on a collision course with Earth. An astronaut lands on the rock to bury explosive charges that will blow the ast

forsale [732]

Answer:

The maximum radius the asteroid can have for her to be able to leave it entirely simply by jumping straight up is approximately 1782.45 meters

Explanation:

Whereby the height the astronaut can jump on Earth = 0.500 m, we have the following kinematic equation;

v² = u² - 2·g·h

Where;

v = The final velocity

u = The initial velocity

g = The acceleration due to gravity ≈ 9.8 m/s²

h = The height she jumps

At the maximum height, $h_{max}$ = 0.500 m, she jumps, v = 0, therefore, we have;

0² = u² - 2·g· $h_{max}$

u² = 2 × 9.8 × 0.5 = 9.8

u = √9.8 ≈ 3.13

u = 3.13 m/s

Her initial jumping velocity ≈ 3.13 m/s

Escape velocity, $v_e = \sqrt{\dfrac{2 \cdot G \cdot M}{r} }$

Where;

M = The mass of the asteroid

G = The Universal gravitational constant = 6.67408 × 10⁻¹¹ m³/(kg·s²)

r = The radius of the asteroid

The average density of the Earth = 5515 kg/m³

The mass of the asteroid, M = Density × Volume = 5515 kg/m³× 4/3 × π × r³

The escape velocity, she has, $v_e$ ≈ 3.13 m/s is therefore;

$3.13 = \sqrt{\dfrac{2 \times 6.67408 \times 10^{-11} \times 5515 \times \frac{4}{3} \times \pi \times r^3}{r} } = r \times \sqrt{3.084 \times 10^{-6}}$

$r = \dfrac{3.13}{ \sqrt{3.084 \times 10^{-6}}} \approx 1782.45$

Therefore, the maximum radius of the asteroid can have for her jumping velocity to be equal to the escape velocity for her to be able to leave it entirely simply by jumping straight up = r ≈ 1782.45 meters.

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2 years ago

List the ocean floor features that are formed by the movement of tectonic plates

Andreas93 [3]

Tsunami and under water volcano

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2 years ago

The two speakers at S1 and S2 are adjusted so that the observer at O hears an intensity of 6 W/m² when either S1 or S2 is sounde

Zanzabum

Answer:

The minimum frequency is 702.22 Hz

Explanation:

The two speakers are adjusted as attached in the figure. From the given data we know that

$S_1 S_2$ =3m

$S_1 O$ =4m

By Pythagoras theorem

$S_2O=\sqrt{(S_1S_2)^2+(S_1O)^2}\\S_2O=\sqrt{(3)^2+(4)^2}\\S_2O=\sqrt{9+16}\\S_2O=\sqrt{25}\\S_2O=5m$

Now

The intensity at O when both speakers are on is given by

$I=4I_1 cos^2(\pi \frac{\delta}{\lambda})$

Here

I is the intensity at O when both speakers are on which is given as 6 $W/m^2$

I1 is the intensity of one speaker on which is 6 $W/m^2$

δ is the Path difference which is given as

$\delta=S_2O-S_1O\\\delta=5-4\\\delta=1 m$

λ is wavelength which is given as

$\lambda=\frac{v}{f}$

Here

v is the speed of sound which is 320 m/s.

f is the frequency of the sound which is to be calculated.

$16=4\times 6 \times cos^2(\pi \frac{1 \times f}{320})\\16/24= cos^2(\pi \frac{1f}{320})\\0.667= cos^2(\pi \frac{f}{320})\\cos(\pi \frac{f}{320})=\pm0.8165\\\pi \frac{f}{320}=\frac{7 \pi}{36}+2k\pi \\ \frac{f}{320}=\frac{7 }{36}+2k \\\\ {f}=320 \times (\frac{7 }{36}+2k )$

where k=0,1,2

for minimum frequency $f_1$ , k=1

${f}=320 \times (\frac{7 }{36}+2 \times 1 )\\\\{f}=320 \times (\frac{79 }{36} )\\\\ f=702.22 Hz$

So the minimum frequency is 702.22 Hz

5 0

2 years ago

0.5 kg air hockey puck is initially at rest. What will it’s kinetic energy be after a net force of .8 N acts on it for a distanc

weqwewe [10]

Answer:

1.6 J

Explanation:

Work = change in energy

W = ΔKE

Fd = KE

(0.8 N) (2 m) = KE

KE = 1.6 J

4 0

2 years ago

Energy can be changed from one form to another. Which terms can be used to describe these changes? Select all that apply.

aliya0001 [1]

Energy is the capacity to do work. Energy exists in various forms in the entire universe.

It may be light,sound,electric,magnetic,kinetic,potential,thermal energy etc.

As per the law of conservation of energy, it is neither created not destroyed. It can change from one form to another form.The total energy of the universe is always constant.

The process in which energy will change from one form to another form is called energy conversion.

There is also another terminology for energy conversion called energy transformation.

Energy transference is the process in which energy will be transferred from one body to another body.

Hence the correct answer to this question will be conversion and transformation

5 0

2 years ago

Read 2 more answers