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LenaWriter [7]
3 years ago
13

Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This

statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is |v with arrow| = 230 km/s and the orbital period of each is 15.5 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 1030 kg.)
Physics
1 answer:
vova2212 [387]3 years ago
6 0

Answer:

1.554\times 10^{32}\ \text{kg}

Explanation:

M = Mass of each star

T = Time period = 15.5 days

v = Orbital velocity = 230 km/s

G = Gravitational constant = 6.674\times 10^{-11}\ \text{Nm}^2/\text{kg}^2

Radius of orbit is given by

R=\dfrac{vT}{2\pi}

We have the relation

\dfrac{Mv^2}{R}=\dfrac{GM^2}{(2R)^2}\\\Rightarrow M=\dfrac{4Rv^2}{G}\\\Rightarrow M=\dfrac{4\dfrac{vT}{2\pi}v^2}{G}\\\Rightarrow M=\dfrac{2v^3T}{\pi G}\\\Rightarrow M=\dfrac{2\times 230000^3\times 15.5\times 24\times 60\times 60}{\pi\times 6.674\times 10^{-11}}\\\Rightarrow M=1.554\times 10^{32}\ \text{kg}

The mass of each star is 1.554\times 10^{32}\ \text{kg}

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Answer:

magnitude = 304.14 km/h

direction: 9.46^o West of North

Explanation:

The final plane's vector velocity will be the result of the vector addition of one pointing North of length 300 km/h, another one pointing West of length 50 km/h.

To find the magnitude of the final velocity vector (speed) we need to apply the Pythagorean theorem in a right angle triangle with sides: 300 and 50, and find its hypotenuse:

|v|=\sqrt{300^2+50^2}=\sqrt{92500}  = 304.14 km/h

The actual direction of the plane is calculated using trigonometry, in particular with the arctan function, since the tangent of the angle can be written as:

tan(\theta)=\frac{50}{300} = \frac{1}{6} \\\theta = arctan(\frac{1}{6} ) = 9.46^o

So the resultant velocity vector of the plane has magnitude = 304.14 km/h,

and it points 9.46^o West of the North direction.

3 0
3 years ago
Nina and Jon are practicing an ice skating routine. Nina is standing still. Jon, who is twice as heavy as Nina, skates toward he
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Answer:

A

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• Nina experiences a force equal to f.

5 0
3 years ago
Suppose the U.S. national debt is about $14 trillion. If payments were made at the rate of $3,500 per second, how many years wou
andreyandreev [35.5K]

Answer:

It will take 126.84 years to pay off the debt

Explanation:

Total debt = $14,000,000,000,000.00

Paid $3,500 per second

Number of seconds to pay off the debt will be:

14 ×10^12 /3500

Number of seconds = 4× 10^9 seconds

Converting seconds to year:

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Therefore, number of years it will take to pay off $14 Trillion =( 4 ×10^9 ) × ( 3.171 × 10^-8)

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3 years ago
A hydrogen atom that has an electron in the n = 2 state absorbs a photon. What wavelength must the photon possess to send the el
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Answer:

486nm

Explanation:

in order for an electron to transit from one level to another, the wavelength emitted is given by Rydberg Equation which states that

\frac{1}{wavelength}=R.[\frac{1}{n_{f}^{2} } -\frac{1}{n_{i}^{2} }] \\n_{f}=2\\n_{i}=4\\R=Rydberg constant =1.097*10^{7}m^{-1}\\subtitiute \\\frac{1}{wavelength}=1.097*10^{7}[\frac{1}{2^{2} } -\frac{1}{4^{2}}]\\\frac{1}{wavelength}= 1.097*10^{7}*0.1875\\\frac{1}{wavelength}= 2.06*10^{6}\\wavelength=4.86*10{-7}m\\wavelength= 486nm\\

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4 0
3 years ago
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Drupady [299]

Answer:

The magnitude of the average induced emf is 90V

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E = -NAB/t

E = -(15 x 0.4 x 0.75) / 0.05

E = -90 V

|E| = 90 V

Therefore, the magnitude of the average induced emf is 90V

6 0
3 years ago
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