Answer: Helium=4 is the answer
Explanation:
took the test and got it right that'
s the answer.
Answer:
It's b
Explanation:
I took the quiz on EDGE and got it right.
(b) A cylinder of cross-sectional area 0.65m2 and
height 0.32m has a mass of 2. Ikg. If there is a
cavity inside, find the volume of the cavity.
(Density of cylinder = 11.053 kg/m^3)
Answer:
The volume of the cavity is 0.013m^3
Explanation:
To find the volume of the cavity, the major parameter missing is the diameter of the cavity itself. we can obtain this using the following steps:
Step one:
Obtain the volume of the cylinder by dividing the mass of the cylinder by the density.
Volume of the cylinder = 2.1 / 11.053 =0.19[tex]m^{3}[/tex]
Step two:
From the volume of the cylinder, we can get the radius of the cylinder.
[tex]radius = \sqrt{\frac{V}{\pi \times h}} = \sqrt{\frac{0.19}{\pi \times 0.32}} =0.44m[/tex]
Step three:
From the cross-sectional area, we can obtain the radius of the cavity.
Let the radius of the cavity be = r, while the radius of the cylinder be = R
CSA of cavity =
[tex]\pi({R^2}-r^2) = CSA\\0.65 = \pi (0.32^2-r^2)\\r= 0.115m[/tex]
Step Four:
calculate the volume of the cavity using volume =[tex]\pi r^2 \times h[/tex]
Recall that the cavity has the same height as the original cylinder
[tex]volume = \pi \times 0.115^2\times 0.32= 0.013m^3[/tex]
Will mark as BRAINLIEST......
A balloon is ascending at the rate of 4.9 m/s. A packet is dropped from from the balloon when situated at a height of 100m.
How long does it take the packet to reach the ground ?
What is it's final velocity ?
Answer:
t = 5.04secsv = -44.49m/sExplanation:
Given parameters
initial velocity u = 4.9m/s
height of drop H = 100m
acceleration due to gravity g = -9.8m/s²(since the body is ascending i.e moving against gravity)
Required
time taken by the packet to reach the ground 't'
Using the equation of motion
S = ut+1/2gt²
0-100 = 4.9t+1/2(-9.8)t²
-100 = 4.9t-1/2(9.8)t²
-100 = 4.9t-4.9t²
4.9t-4.9t² +100 = 0
4.9t²-4.9t² -100 = 0
Multiplying through by 10
49t²-49t-1000 = 0
Using the general equation t = (-b±√b²-4ac)/2a
t = -(-49)±√(-49)²-4(49)(-1000)/2(49)
t = 49±√(2401+196000)/2(49)
t = 49±√(198401)/98
t = 49±√(198401)/98
t = 49±449.42/98
t = (49+449.42)/98
t = 494.42/98
t = 5.04secs
Hence, it took the packet 5.04secs to reach the ground
The final velocity is calculated using the formula v = u + at
v = u-gt
v = 4.9-(9.8)(5.04)
v = 4.9-49.392
v = -44.492m/s
This shows that the final velocity is 44.49m/s(moving downwards)
what is the function of eye lens of human eye
Answer:
the lens is located in the eye. by changing its shape, the lens changes the focal distance of the eye. in other words,it focuses the light rays that pass through it (and onto the retina) in order to create clear images of objects that are positioned
at various distances.
Help!!! Line B touches the circle at a single point. Line A extends through the center of the circle.
I. What is line b in reference to the circle?
2. How large is the angle between lines A and B?
Answer:
If I understand correctly. Line B is parallel to the circle. Also, the angle is less than 90.
The size of the circle determines. The diameter should not be fixed either.'Circle' is characterized as "a two-dimensional geometric figure comprising of the set of all those points in a plane that are at equal distance from the center."
1). Line B would be considered as the 'tangent' in association with the given circle.
2). The angle lying among the lines A and B would be of 90° i.e. right angle.
Given that,
A circle with line A drawn through its center
Line B moves while touching the edge of the circle and intersects line A outside the circle.
Since 'Tangent' is described as a 'straight-line touching the curve at one point without crossing it,' thus, line B would be considered as the tangent of the circle as it touches the circle's curve once. The angle that is formed at the intersection of the line A and B at the curve of the circle would be a right angle because they are perpendicular to one another. Thus, the perpendicular lines A and B form an angle of 90°.Learn more about 'circle' here:
brainly.com/question/11833983
This is the question
Explanation:
a) The displacement is the area under the curve.
Δx = ½ (10 s) (20 m/s) + (20 s) (20 m/s) + ½ (10 s) (20 m/s)
Δx = 600 m
b) The car is accelerating when the velocity is changing. This happens between t = 0 and t = 10, and between t = 30 and t = 40.
c) Average speed = displacement / time
v_avg = 600 m / 40 s
v_avg = 15 m/s
Un auto se mueve con MRU y recorre un espacio de 5km en un cuarto de hora (15 minutos) calcule la velocidad en m/s
Explanation:
5 km en 15 min.
= 5000 metros en 900 segundos
dividimos
la velocidad es de 5,56m/s
Espero que te sirva
Which atomic number corresponds to the element which is most stable?
01
03
28
36
Answer:
Which atomic number corresponds to the element which is most stable?
01
03
28
36
36 is your answer.
The rhinestones in costume jewelry are glass with index of refraction 1.50. To make them more reflective, they are often coated with a layer of silicon monoxide of index of refraction 2.00. What is the minimum coating thickness needed to ensure that light of wavelength 480 nm and of perpendicular incidence will be reflected from the two surfaces of the coating with fully constructive interference?
Answer:
60
Explanation:
According to the given question, the computation of minimum coating thickness is shown below:-
The condition for constructive interference is
[tex]2t_{min} = (m + \frac{1}{2} )\times \frac{\lambda}{^nmateral}[/tex]
[tex]= (0 + \frac{1}{2} )\times \frac{\lambda}{^nmateral}[/tex]
[tex]t = \frac{\lambda}{4n}[/tex]
Now we will put the values to the above formula to reach the answer
[tex]= \frac{480nm}{4\times 2.0}[/tex]
= 60
Therefore we simply applied the above formula to determine the minimum coating thickness
The minimum coating thickness needed to ensure that light of wavelength 480 nm and of perpendicular incidence will be reflected from the two surfaces of the coating with fully constructive interference is 60.
Given that, the index of refraction of glass is 1.50 and the index of refraction of silicon monoxide is 2.00. The wavelength light of 480 nm.
If [tex]\lambda {c}[/tex] is the wavelength in the coating and λ is the wavelength in vacuum, then [tex]\lambda_{c} = \dfrac {\lambda}{n}[/tex] where n is the index of refraction of the coating.
Thus, the minimum coating thickness [tex]T_{min}[/tex] can be calculated as,
[tex]2T_{min} = (m+\dfrac {1}{2})\times\dfrac {\lambda} {n}\\\\T_{min} = (m+\dfrac {1}{2}) \times\dfrac {\lambda} {2n}[/tex].
For the constructive interference, m = 0.
So [tex]T_{min} = \dfrac {\lambda} {4n}[/tex]
[tex]T_{min} = \dfrac {480\rm nm} {4\times2.0}[/tex]
[tex]T_{min} = 60[/tex]
The minimum coating thickness needed to ensure that light of wavelength 480 nm and of perpendicular incidence will be reflected from the two surfaces of the coating with fully constructive interference is 60.
For more details, follow the link given below.
https://brainly.com/question/15541641.
Shortly after receiving a traffic ticket for speeding, Fred made numerous comments about the road signs being inadequate and is GPS telling him a different speed limit. This would be an example of:
Answer:
External locus of control
Explanation:
External locus of control is an attitude people possess that makes them attribute their failures or successes to factors other than themselves. The opposite of this type of attitude is the Internal locus of control where the individuals take responsibility for the outcomes of their actions whether good or bad. One good thing about the external locus of control is that when the individuals with this characteristic record successes, they attribute it to others and this presents them as people with team spirit. However, when they record failures, they do not want to take the blame, but rather attribute it to others.
Fred exhibits an external locus of control because he attributed his speeding to other factors like the road signs and GPS instead of fully admitting that it was his fault.
The radius of a small ball is around 3.79747 cm. The radius of a basketball is about 3.16 times larger. What is the ratio of the surface areas of the small ball and a basketball? 2. What is the ratio of their volumes?
Explanation:
The ratio of the areas is the square of the ratio of the radii.
A/A = 3.16² = 9.99
The ratio of the volumes is the cube of the ratio of the radii.
V/V = 3.16³ = 31.6
An electric lamp is marked 240v, 60w
It is left to operate for 1h. How much
heat is generated by the lamp
Answer:
H = 0.06 kWh
Explanation:
Given that,
Power of an electric lamp, P = 60 W
Voltage, V = 240 V
It is operated for 1 hour
We need to find the heat generated by the lamp. Heat generated is given by :
[tex]H=P\times t\\\\H=60\ W\times 1\ h\\\\H=60\ Wh\\\\H=0.06\ kWh[/tex]
So, 0.06 kWh of the heat is generated by the lamp.
Students are going to conduct an experiment to study the effect of a net force applied to an object on the object’s motion. In each trial of the experiment, the students will apply a net force on the object. They also need to take two other measurements. What are the other quantities they should measure in each trial of the experiment?(1 point) velocity and time mass and acceleration mass and velocity acceleration and time
Answer:
A. velocity and time
Explanation:
A force can be define as an agent which has the capacity to change the state of an object. It can either increase the velocity of a body, change its direction of motion or cause a moving object to come to rest.
From Newton's second law of motion;
F = ma
where F is the force on the object, m is the mass of the object and a is the acceleration of the object. The unit of force is kgm/[tex]s^{2}[/tex] or Newtons.
a = [tex]\frac{change in velocity}{change in time}[/tex]
In the given question, apart from the mass of the object which is constant, the students should take the measurements of the velocity and time in each trial so as to calculate the required acceleration.
Answer:
mass and acceleration!
Explanation:
Because i am in class just like you and got it wrong because i didn't choose my first answer:(
a uniform rod of length 1.5m is placed over a wedge at 0.5m from one end .a force of 100 N is applied at its one end near the wedge to keep it horizontal .find weight of rod and reaction of wedge
Explanation:
The rod is uniform, so the center of gravity is at the center, or 0.75 m from the end. The wedge is 0.5 m from the end, so the center is 0.25 m from the wedge.
Sum the torques about the wedge (it may help to draw a diagram first). Take counterclockwise to be positive.
∑τ = Iα
W (0.25 m) − (100 N) (0.50 m) = 0
W = 200 N
Sum the forces in the y direction.
∑F = ma
F − 100 N − 200 N = 0
F = 300 N
in how many ways can five basketball players be placed in three postitions?
Answer:
Well if they playing a game like that
The energy consumed by a home during a month is 90 kWh, how many Joules are we talking about? a good explanation please is for today
Answer:
3.24×10⁸ J, or 324 MJ
Explanation:
"kWh" is a kilowatt-hour. It's the energy used by 1 kilowatt of power after one hour.
A kilowatt is a kilojoule per second.
90 kWh
= 90 kW × 1 hr
= 90 kJ/s × 1 hr
= 90 kJ/s × 3600 s
= 324,000 kJ
= 324,000,000 J
The energy is 3.24×10⁸ J, or 324 megajoules.
B. La velocidad de los electrones en los conductores metálicos es muy pequeña, del orden de algunos mm por segundo. ¿Cómo podrías explicar que cuando se cierra el interruptor de, una bombilla situada a 10m de distancia se ilumina casi instantáneamente? (explica tu respuesta construyendo una hipótesis deductiva a partir de la relación de algunas leyes físicas y teorías científicas.)
Answer:
electromagnetic wave. this energy is what lights the bulb.
Explanation:
When you close an electrical circuit, the electrons have a small drag speed, but the fluctuation of the electric field that is created originates by Lenz's law a magnetic field and the appearance of this magnetic field creates a fluctuating elective field, these two fields together forms a wave called an electromagnetic wave.
This electromagnetic wave has a speed given by the relation
v = √1 /ε μ
in a vacuum this speed is equal to the speed of light, which is worth 3 10⁸ m/s this very high value so the energy transported by this wave can travel the distance of 10 m in less than 10⁻⁷ s, This energy is what lights the bulb.
calculate the power of an engine which can supply 60kg of energy per minute
Answer:
1 Watt
Explanation:
Power (P) = w / Δt
w = work done
Δt = change in time
Power (P) = 60kg / 60 seconds
Power (P) = 1 Watt
Will mark as BRAINLIEST....... The Displacement x of particle moving in one dimension under the action of constant force is related to the time by equation 4x³+3x²-5x+2 , where x is in meters and t is in sec. a)Find velocity of particle at i) t=2 sec ii) t=4 sec. b) Find the acceleration of the particle at t=3 sec.
Explanation:
It is given that,
The Displacement x of particle moving in one dimension under the action of constant force is related to the time by equation as:
[tex]x=4t^3+3t^2-5t+2[/tex]
Where,
x is in meters and t is in sec
We know that,
Velocity,
[tex]v=\dfrac{dx}{dt}\\\\v=\dfrac{d(4t^3+3t^2-5t+2)}{dt}\\\\v=12t^2+6t-5[/tex]
(a) i. t = 2 s
[tex]v=12(2)^2+6(2)-5=55\ m/s[/tex]
At t = 4 s
[tex]v=12(4)^2+6(4)-5=211\ m/s[/tex]
(b) Acceleration,
[tex]a=\dfrac{dv}{dt}\\\\a=\dfrac{d(12t^2+6t-5)}{dt}\\\\a=24t+6[/tex]
Pu t = 3 s in the above equation
So,
[tex]a=24(3)+6\\\\a=78\ m/s^2[/tex]
Hence, this is the required solution.
Two objects, one of mass m and the other of mass 2m, are dropped from the top of a building. If there is no air resistance, when they hit the ground A) both will have the same kinetic energy. B) the heavier one will have twice the kinetic energy of the lighter one. C) the heavier one will have four times the kinetic energy of the lighter one. D) the heavier one will have half the kinetic energy of the lighter one. E) the heavier one will have one-fourth the kinetic energy of the lighter one.
Answer:
option b
Explanation:
the heavier one will have twice the kinetic energy of the lighter one
The heavier one will have twice the kinetic energy of the lighter one. Hence, option (B) is correct.
Given data:
The mass of object 1 is, m.
The mass of object 2 is, 2m.
Here, the concept of kinetic energy is used. The kinetic energy of an object is the energy possessed by the object by virtue of its motion. Motion means something related with the speed.
And the mathematical expression for the kinetic energy is given as,
[tex]KE =\dfrac{1}{2}mv^{2}[/tex]
Here,
m is the mass of body.
v is the speed of body.
Now considering the kinetic energy for the two given objects as,
[tex]KE=\dfrac{1}{2}mv^{2}\\\\KE'=\dfrac{1}{2}(2m)v^{2}[/tex]
Comparing both the values of kinetic energies, we find that,
KE' = 2KE
Thus, we can conclude that the heavier one will have twice the kinetic energy of the lighter one. Hence, option (B) is correct.
Learn more about the kinetic energy here:
https://brainly.com/question/12669551
Please Help
A skydiver jumps out of a hovering helicopter, so there is no forward velocity. Use this information to answer questions. Ignore wind resistance for this exercise.
What is the skydiver's velocity after one second? Show your work and include direction.
Answer:
I suppose that by forward velocity the question refers to horizontal velocity
Since the acceleration due to gravity is 10 m/s2.The object gains an increase of 10 m/s in speed per second.In after one second its speed will be 10M/S
The direction will be downward i.e vertical
what is the function of eye lens of the human eye
Answer:
Lens of the human Eye is a important and one of that most complex sense organ.
Explanation:
Lens of the human eye it helps that in visualizing light and color perception and objects , glance on the human eye structure and function.
Sense organs are much pretty similar to the camera they help us see the objects clear.
A human eye is the 2.3 cm in diameter and all filled some fluid, and there are following parts in eye:- cornea, Retina , Lens ,Pupil , optic nerves.
cornea :- the cornea is the first transparent part of is called cornea, enters the light through the cornea.
Retina :-it is light sensitive layer that consists of nerve cells,then transmitted to the brain through nerves.
Lens:- behind the pupil there is a transparent structure called lens,it shape focus light on the retina.
Pupil:-it control the value of light that enters the human eye.
Optic nerves is are the two types :- (1) cones (2) Rods .
Answer:
It causes Light Rays to converge on the retina
Explanation:
I took the K12 Test
A narrow beam of light containing red (660 nm) and blue (470 nm) wavelengths travels from air through a 1.00 cm thick flat piece of crown glass and back to air again. The beam strikes at an incident angle of 30 degrees. (a) At what angles do the two colors emerge
Answer:
The color blue emerges at 19.16° and the color red emerges at 19.32°.
Explanation:
The angle at which the two colors emerge can be calculated using the Snell's Law:
[tex]n_{1}sin(\theta_{1}) = n_{2}sin(\theta_{2})[/tex]
Where:
n₁ is the refractive index of the incident medium (air) = 1.0003
n₂ is the refractive index of the refractive medium:
blue light in crown glass = 1.524
red light in crown glass = 1.512
θ₁ is the angle of the incident light = 30°
θ₂ is the angle of the refracted light
For the red wavelengths we have:
[tex] \theta_{2} = arcsin(\frac{n_{1}sin(\theta_{1})}{n_{2}}) = arcsin(\frac{1.0003*sin(30)}{1.512}) = 19.32 ^{\circ} [/tex]
For the blue wavelengths we have:
[tex] \theta_{2} = arcsin(\frac{n_{1}sin(\theta_{1})}{n_{2}}) = arcsin(\frac{1.0003*sin(30)}{1.524}) = 19.16 ^{\circ} [/tex]
Therefore, the color blue emerges at 19.16° and the color red emerges at 19.32°.
I hope it helps you!
What is CGS unit of weight
Answer:
[tex] \boxed{dyne}[/tex]Explanation:
The weight of a body is defined as the force with which it is attracted towards the centre of a planet. A spring balance measures it. It's unit is Newton ( N ) in the SI system and dyne in the CGS system.
Hope I helped!
Best regards!
Weight is force.
The CGS unit of force is the dyne.
The SI unit of force is the Newton.
Explain.
4. State the limitations of our senses to obtain accurate in
formation concerning
our environment.
Answer:
The limits of our senses are
Limits of Sight
Our vision field of view is 120° sideways and 135° vertically
Angular visual resolution is about an 1/60 of one degree
The presence of blind spots in the eyes
Limits of sound
The hearing range is within 20 - 20,000 Hz and our threshold hearing above 0 to 5 decibel of sound
Limits of taste
We have very limited sense of taste which is partly dependent on our sense of smell with little objectivity in distinguishing tastes
Sense of smell
The establishing of the effectiveness of human sense of smell is gauged on numerous parameters with certain tests being inconsistent, as such, it is difficult to clearly establish the effectiveness of the human sense of smell
In comparison with the sense of smell of other living things such as dogs, the human sense organ is comparatively low
Explanation:
A model rocket blasts off from the ground, rising straight upward with a constant acceleration that has a magnitude of 76.8 m/s2 for 1.99 seconds, at which point its fuel abruptly runs out. Air resistance has no effect on its flight. What maximum altitude (above the ground) will the rocket reach?
Answer:
Explanation:
Take note that when the fuel of the rocket is consumed, the acceleration would be zero. However, at this phase the rocket would still be moving up until all the forces of gravity would dominate and change the direction of the rocket. Hence, there will be a need to calculate two distances, one from the ground until the point where the fuel is consumed and from that point to the point where the gravity would change the direction.
Given:
a = 76.8 m/s^2
t = 1.99 s
Solution:
d = vi (t) + 0.5 (a) (t^2)
d = (0) (1.99) + 0.5 (76.8) (1.99)^2
d = 0+38.4×3.9601
d = 152.068m
vf = vi + at
vf = 0 + 76.8 (1.99)
vf = 152.83 m/s (velocity when the fuel is consumed completely)
Then, we calculate the time it takes until it reaches the maximum height.
vf = vi + at
0 = 152.83+(-9.8) (t)
0 = 152.83 + (-9.8) (t)
-152.83 = -9.8t
t = 152.83/9.8 s
t = 15.59s
Then, the second distance
d= vi (t) + 0.5 (a) (t^2)
d = 152.83 (15.59) + 0.5 (-9.8) (15.59^2)
d = 2382.6197- 1190.93
d = 1191.68m
Then, we determine the maximum altitude:
d1 + d2 = 152.068 m + 1191.68m = 1343.748m
A 1 kg object accelerated at a constant rate of 5m/s? Estimate the net force needed to accelerate the object
Answer:
5 N.
Explanation:
Data obtained from the question include the following:
Mass (m) of object = 1 kg
Acceleration (a) = 5 m/s²
Force (F) =?
Force is simple defined as the product of mass and acceleration. Mathematically, it is expressed as:
Force (F) = mass (m) x acceleration (a)
F = ma
With the above formula, we can obtain the net force needed to accelerate the object as follow:
Mass (m) of object = 1 kg
Acceleration (a) = 5 m/s²
Force (F) =?
F = ma
F = 1 x 5
F = 5 N.
Therefore, the net force needed to accelerate the object is 5 N.
the indiscriminate use of drugs without the doctor's prescription is called
Answer:
drug misuse
Explanation:
this is because the person is using those drugs but indiscriminately meaning without correct judgement or in this context without a prescription therefore without following guidelines and legal standards eg self medication
but it is not abuse because it is being used for its intended purpose just without any guidelines
Gravity is affected by the ?
Answer:
Mass and distance
Explanation:
The force of gravity the masses exert on each other. If one of the masses is doubled, the force of gravity between the objects is doubled. increases, the force of gravity decreases. Hence, answer is mass and distance
Calculate the Schwarzschild radius (in kilometers) for each of the following.1.) A 1 ×108MSun black hole in the center of a quasar. Express your answer using two significant figures.2.) A 6 MSun black hole that formed in the supernova of a massive star. Express your answer using two significant figures.3.) A mini-black hole with the mass of the Moon. Express your answer using two significant figures.4.) Estimate the Schwarzschild radius (in kilometers) for a mini-black hole formed when a superadvanced civilization decides to punish you (unfairly) by squeezing you until you become so small that you disappear inside your own event horizon. (Assume that your weight is 50 kg.) Express your answer using one significant figure.
Answer:
(I). The Schwarzschild radius is [tex]2.94\times10^{8}\ km[/tex]
(II). The Schwarzschild radius is 17.7 km.
(III). The Schwarzschild radius is [tex]1.1\times10^{-7}\ km[/tex]
(IV). The Schwarzschild radius is [tex]7.4\times10^{-29}\ km[/tex]
Explanation:
Given that,
Mass of black hole [tex]m= 1\times10^{8} M_{sun}[/tex]
(I). We need to calculate the Schwarzschild radius
Using formula of radius
[tex]R_{g}=\dfrac{2MG}{c^2}[/tex]
Where, G = gravitational constant
M = mass
c = speed of light
Put the value into the formula
[tex]R_{g}=\dfrac{2\times6.67\times10^{-11}\times1\times10^{8}\times1.989\times10^{30}}{(3\times10^{8})^2}[/tex]
[tex]R_{g}=2.94\times10^{8}\ km[/tex]
(II). Mass of block hole [tex]m= 6 M_{sun}[/tex]
We need to calculate the Schwarzschild radius
Using formula of radius
[tex]R_{g}=\dfrac{2MG}{c^2}[/tex]
Put the value into the formula
[tex]R_{g}=\dfrac{2\times6.67\times10^{-11}\times6\times1.989\times10^{30}}{(3\times10^{8})^2}[/tex]
[tex]R_{g}=17.7\ km[/tex]
(III). Mass of block hole m= mass of moon
We need to calculate the Schwarzschild radius
Using formula of radius
[tex]R_{g}=\dfrac{2MG}{c^2}[/tex]
Put the value into the formula
[tex]R_{g}=\dfrac{2\times6.67\times10^{-11}\times7.35\times10^{22}}{(3\times10^{8})^2}[/tex]
[tex]R_{g}=1.1\times10^{-7}\ km[/tex]
(IV). Mass = 50 kg
We need to calculate the Schwarzschild radius
Using formula of radius
[tex]R_{g}=\dfrac{2MG}{c^2}[/tex]
Put the value into the formula
[tex]R_{g}=\dfrac{2\times6.67\times10^{-11}\times50}{(3\times10^{8})^2}[/tex]
[tex]R_{g}=7.4\times10^{-29}\ km[/tex]
Hence, (I). The Schwarzschild radius is [tex]2.94\times10^{8}\ km[/tex]
(II). The Schwarzschild radius is 17.7 km.
(III). The Schwarzschild radius is [tex]1.1\times10^{-7}\ km[/tex]
(IV). The Schwarzschild radius is [tex]7.4\times10^{-29}\ km[/tex]
The energy conservation allows to find the Schwarschild radius for several bodies of different masses are:
1) Black hole quasar is: r = 2.9 10⁸ km
2) Blsck hole supernove is: r = 17.7 km
3) Mini black hole is: r = 1.1 10⁻⁷ km
4) Human body is: r= 7 10⁻²⁹ km
The schwarschild radius is defined as the distance from a black hole center at radius which the escape velocity is equal to the light speed, in some cases it is also called the event horizon.
Let's use Newton's second law where force is the universal law of attraction and acceleration is centripetal.
F = ma
F = [tex]G \frac{Mm}{r^2}[/tex]
Where F is the force, M the mass of the black hole, m the handle of the body, r the radius and v the speed of the body.
The energy of the gravitational field is
F = [tex]- \frac{dU}{dr }[/tex]
U = [tex]-G \frac{Mm}{r}[/tex]
Let's use conservation of energy
Em₀ = K + U = ½ m v² - [tex]G \frac{Mm}{r}[/tex]
In infinity the energy
Em_f = 0
energy is conserved
Em₀ = Em_f
½ m v² - [tex]G \frac{Mm }{r}[/tex] = 0
r = [tex]\frac{2GM}{v^2}[/tex]
From the definition of the Schwarschild radius this speed is equal to the light speed
v = c
r = [tex]\frac{2GM}{c^2 }[/tex]
They ask to calculate the radius for several cases of different mass, claculate the constant value
V = [tex]\frac{2 \ 6.67 \ 10^{-11} }{(3 \ 10^8) ^2 }[/tex]
V = 1.482 10⁻²⁷
1) A black hole of mass M = 1 10⁸ [tex]M_{sum}[/tex]
The tabulated mass of the sun is [tex]M_{sum}[/tex] = 1.989 10³⁰ kg
Let's substitute
r = 1.482 10⁻²⁷ 1 10⁸ 1.989 10³⁰
r = 2.94 10⁸ km
With two significant figures
r = 2.9 10⁸ km
2) A black hole of mass M = 6 [tex]M_{sum}[/tex]
r = 1.482 10⁻²⁷ 6 1.989 10-30
r = 17.7 km
3) a mini black hole with the mass of the moon
Tabulated mass of the moon M = 7.35 10²² kg
r = 1.482 10⁻²⁷ 7.35 10²²
r = 1.1 10⁻⁷ km
4) A person of M = 50 kg
r = 1.482 10⁻²⁷ 50
r= 7 10-29 km
In conclusion using the conservation of energy we can find the Schwarschild radius for several bodies of different masses are:
1) Black hole quasar is: r = 2.9 10⁸ km
2) Blsck hole supernove is: r = 17.7 km
3) Mini black hole is: r = 1.1 10⁻⁷ km
4) Human body is: r= 7 10⁻²⁹ km
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Forensic toxicologist analyze and identify drugs that are confiscated from criminals
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