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svetlana [45]
3 years ago
12

M84, M87, and NGC 4258 all have accretion disks around their central black holes for which the rotational velocities have been m

easured in HST spectra. In M84, the disk extends 8 pc from the center and exhibits Doppler velocities as large as ±400 km/s with respect to the galaxy's overall radial velocity. In M87, the corresponding figures are 20 pc and 500 km/s. In NGC 4258, the figures are 0.5 ly and 1000 km/s. Calculate the black hole masses to two significant figures. Comment also on the assumptions under which you did your calculation (e.g., orbital plane viewed edge-on; note the appearance of the galaxies and their disks in the notes) and the effect this may have on the accuracy of the answers.
Physics
1 answer:
givi [52]3 years ago
3 0

Answer:

<u>For M84:</u>

M = 590.7 * 10³⁶ kg

<u>For M87:</u>

M = 2307.46 * 10³⁶ kg

Explanation:

1 parsec, pc  = 3.08 * 10¹⁶ m

The equation of the orbit speed can be used to calculate the doppler velocity:

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

making m the subject of the formula in the equation above to calculate the mass of the black hole:

M = \frac{v^{2} r}{G}.............(1)

<u>For M84:</u>

r = 8 pc = 8 * 3.08 * 10¹⁶

r = 24.64 * 10¹⁶ m

v = 400 km/s = 4 * 10⁵ m/s

G = 6.674 * 10⁻¹¹ m³/kgs²

Substituting these values into equation (1)

M = \frac{( 4*10^{5}) ^{2} *24.64* 10^{16} }{6.674 * 10^{-11} }

M = 590.7 * 10³⁶ kg

<u>For M87:</u>

r = 20 pc = 20 * 3.08 * 10¹⁶

r = 61.6* 10¹⁶ m

v = 500 km/s = 5 * 10⁵ m/s

G = 6.674 * 10⁻¹¹ m³/kgs²

Substituting these values into equation (1)

M = \frac{( 5*10^{5}) ^{2} *61.6* 10^{16} }{6.674 * 10^{-11} }

M = 2307.46 * 10³⁶ kg

The mass of the black hole in the galaxies is measured using the doppler shift.

The assumption made is that the intrinsic velocity dispersion is needed to match the line widths that are observed.

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Calculate the translational speed of a cylinder when it reaches the foot of an incline 7.05 mm high. Assume it starts from rest
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Height is 7.05 m and not 7.05 mm

Answer:

9.603 m/s

Explanation:

We are dealing with rotation, so velocity of centre of mass is given by;

v_cm = Rω

Since we are working with a solid cylinder, moment of inertia of the cylinder is; I = ½mR²

Since it is rolled from the top to the bottom, at the top it will have potential energy(mgh) while at the bottom it will have kinetic energy (rotational plus translational kinetic energy).

Using conservation of energy, we have:

P.E = K.E_t + K.E_r

Formula for rotational and kinetic energy here are;

K.E_t = ½mv²

K.E_r = ½Iω²

mgh = ½mv² + ½Iω²

Since we want to find translational speed(v), let's get rid of ω.

Earlier, we saw that v_cm = Rω

Thus; ω = v/R

Also, we know that I = ½mR².

Thus;

mgh = ½mv² + ½(½mR²)(v/R)²

This gives;

mgh = ½mv² + ¼mv²

Divide through by m to get;

gh = v²(½ + ¼)

gh = ¾v²

Making v the subject gives;

v = √(4gh/3)

v = √((4 × 9.81 × 7.05)/3)

v = 9.603 m/s

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As she climbs a hill a cyclist slows down from 25 mi/hr to 6mi/hr in 10 seconds what is her acceleration
vesna_86 [32]

|Acceleration| = (change in speed) / (time for the change).

Change in speed = (6 mi/hr - 25 mi/hr) = -19 mi/hr
Time for the change = 10 sec

|Acceleration| = (-19 mi/hr) / (10 sec) = -1.9 mile per hour per second

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3 years ago
Caffeine concentration is 1.99 mg/oz how many cans would be leathal if 10g was leathal and there where 12oz in a can
katovenus [111]

The number of cans that would be considered lethal if 10g was lethal and there where 12oz in a can is 419 cans.

<h3>How to convert mass?</h3>

According to this question, caffeine concentration is 1.99 mg/oz.

1.99 milligrams can be converted to grams as follows:

1.99milligrams ÷ 1000 = 0.00199grams

This means that 0.00199grams per oz is the caffeine concentration.

If there were 12 oz in a can, then, 0.00199grams × 12 = 0.02388 grams in 1 can.

This means that if 10grams is considered lethal, 10grams ÷ 0.02388 grams = 419 cans would be lethal for consumption.

Therefore, the number of cans that would be considered lethal if 10g was lethal and there where 12oz in a can is 419 cans.

Learn more about conversion factor at: brainly.com/question/14479308

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