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OLEGan [10]
3 years ago
14

Astronomers have recently observed stars orbiting at very high speeds around an unknown object near the center of our galaxy. Fo

r stars orbiting at distances of about 1014 m from the object, the orbital velocities are about 106 m/s. Assume the orbits are circular, and estimate the mass of the object, in units of the mass of the sun (MSun = 2x1030 kg). If the object was a tightly packed cluster of normal stars, it should be a very bright source of light. Since no visible light is detected coming from it, it is instead believed to be a supermassive black hole.
Physics
1 answer:
nataly862011 [7]3 years ago
6 0

Answer:

<em>The mass of the object is 745000 units of the sun</em>

Explanation:

We know that the centripetal force with which the stars orbit the object is represented as

F_{c} = \frac{mv^{2} }{r}

and this centripetal force is also proportional to

F_{c} = \frac{kMm}{r^{2} }

where

m is the mass of the stars

M is the mass of the object

v is the velocity of the stars = 10^6 m/s

r is the distance between the stars and the object = 10^14 m

k is the gravitational constant = 6.67 × 10^-11 m^3 kg^-1 s^-2

We can equate the two centripetal force equations to give

\frac{mv^{2} }{r} = \frac{kMm}{r^{2} }

which reduces to

v^{2} = \frac{kM}{r}

and then finally

M = \frac{rv^{2} }{k}

substituting values, we have

M = \frac{10^{14}*(10^{6})^{2}  }{6.67*10^{-11} } = 1.49 x 10^36 kg

If the mass of the sun is 2 x 10^30 kg

then, the mass of the the object in units of the mass of the sun is

==> (1.49 x 10^36)/(2 x 10^30) = <em>745000 units of sun</em>

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Kamila [148]

Answer:

A block of mass M = 5 kg is resting on a rough horizontal surface for which the coefficient of friction is 0.2. When a force F = 40N is applied, the acceleration of the block will be then (g=10ms

2 ).

Mass of the block=5kg

Coeffecient of friction=0.2

external applied force, F=40N

The angle at which the force is applied=30degree

So the horizontal component of force=Fcos30=40×

23 =20 3 N

While the uertical component of the force acting in upward direction=Fsin30=40× 21

​ =20N

The normal reaction from the surface (N)=mg−Fsin30=50−20=30N

So the ualue of limiting friction=μN=0.2×30=6N

Hence the net horizontal force on the block=Fcos30=μN=20

3

​

N−6N=28.64N

The horizontal acceleration of the block=

m

Fcos30−μN = 528.64

​  =5.73m/s 2

8 0
3 years ago
A Porsche challenges a Honda to a 400 m race. Because the Porsche's acceleration of 3.4 m/s2 is larger than the Honda's 3.0 m/s2
padilas [110]

Answer:

Winner wins by 0.969 s

Explanation:

For the Porche:

Given:

Displacement of Porsche s = 400 m

Acceleration of Porsche a = 3.4 m/s^2

From Newton's second equation of motion,

s = ut + (1/2) a t^2 (u = 0 as the car was initially at rest)

Substituting the values into the equation, we have

t^2 = (2 * 400) / 3.4

= 235.29 / 3.4

t = 15.33 s

For the Honda:

Displacement of Honda = 310 m

Acceleration of Honda = 3 m/s^2

Applying Newton's second equation of motion

s = ut + (1/2) a t^2 (u = 0 for same reason)

Substituting the values into the equation, we obtain

t^2 = (2 * 310) / 3

= 620 / 3

t = 14.37 s

Hence

The winner (honda) wins by a time interval of = 15.33 - 14.37    

=0.969 s

8 0
2 years ago
The block slides on a horizontal frictionless surface. The block has a mass of 1.0kg and is pushed 5.0N at 45°. What is the magn
Firlakuza [10]

Answer:

3.5\:\mathrm{m/s^2}

Explanation:

Newton's 2nd law is given as \Sigma F = ma.

To find the acceleration in the horizontal direction, you need the horizontal component of the force being applied.

Using trigonometry to find the horizontal component of the force:

\cos 45^{\circ}=\frac{x}{5},\\\frac{\sqrt{2}}{{2}}=\frac{x}{5},\\x=\frac{5\sqrt{2}}{2}

Use this horizontal component of the force to solve for for the acceleration of the object:

\frac{5\sqrt{2}}{2}=1.0\cdot a,\\a=\frac{5\sqrt{2}}{2}\approx \boxed{3.5\:\mathrm{m/s^2}}

8 0
2 years ago
Advantages of cutting crops with sickle ? please friends give this answer in easy way....​
Eva8 [605]

Answer: The only advantage cutting crops with a sickle is that its very effective for cutting lodged crops.

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Consider a river flowing toward a lake at an average velocity of 3 m/s. the river height is 90m above the lake. what is the tota
strojnjashka [21]

Kinetic energy per unit of mass is

K=\frac{v^{2} }{2}

Given, v=3m/s^{2}

Therefore,

K=\frac{(3^{2} m/s^{2} )^2}{2}

K=4.5 J/kg

Now potential energy per unit mass is

p=g\times h

Given, h=90 m

Therefore,

p= 9.8m/s^2 \times 90

p=882.9 J/kg

Thus, total mechanical energy of the river water per unit mass is

T=K+p=(4.5+882.9)J/kg

T=887.9 J/kg

OR

T=0.887 kJ/kg

6 0
3 years ago
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