200 g mass is placed on meter stick 20 cm from fulcrum. a 170 g mass is used to balance the system and placed the meter stick at 23.52cm.
What is equilibrium?A dynamic or static equilibrium between opposing forces or actions, such as when forces are acting on a body and the resultant is zero (as in a reversible chemical reaction when rates of reaction in both the directions are equal)
The word "equilibrium" derives from the Latin word "libra," which means "weight" or "balance." As a constellation, astrological sign, and representation of the zodiac, Libra is sometimes shown as a set of balance scales, frequently held by the blindfolded goddess of justice, which stands for justice, fairness, and equality. Biology, chemistry, physics, and economics all have different definitions of equilibrium, yet they all refer to the harmony of opposing forces.
F₁d₁ = F₂d₂
m₁gd₁ = m₂gd₂
m₁d₁ = m₂d₂
here,
m₁ is mass of known object = 200 g
m₂ is mass of unknown object = 170 g
d₁ is distance from fulcrum of known object = 20 cm
d₂ is distance from fulcrum of unknown object = ?
∴ 200 × 20 = 170 × d₂
4000 = 170 × d₂
4000/170 = d₂
d₂ = 23.52 cm
170 g mass is placed at the distance of 23.52 cm.
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x. a 0.015-kg marble moving to the right at 0.40 m/s has a head-on, elastic collision with a 0.045-kg marble sitting at rest on a smooth, level surface. a) what are the magnitudes and directions of the velocities of the two marbles after the collision? b) show that the ke is conserved.
The magnitudes and directions of the velocities of the two marbles after the collision is: v1f is left and v2f is right.
What is collision?The initial marble weighs m1 = 0.015 kg.
Second marble's mass is m2=0.045kg.
The first marble's initial velocity is v1i=0.40m/8 before to contact.
The second marble's initial velocity is v2i=0m/8 prior to impact.
After the impact, the first marble's final speed is v1f.
Following the collision, the initial marble's final velocity is v2f.
If the collision is elastic, the kinetic energy is preserved.
We'll write 1/2 m1 for KE = 1/2 mv2 (v1i)
2 + 1/2 m2(vi) (vi)
2 = 1/2 m1(v1f)2 + 1/2 m2 (v2f) (v2f)
2.
Using this equation, we can establish a new relationship between velocities and determine each marble's post-collision velocity:
v1f=(m1-m2)/(m1+m2)
v1\sv1f=(0.015kg-0.045kg)/(0.015kg+0.045kg)
0.40m/s\s=-0.20m/s
First marble is moving leftward at 0.20 m/s, as indicated by the negative sign.
Find the second marble's final velocity.
v2f=2m1v1/(m1+m2)\s
v2f=2⋅0.015kg⋅0.40m/s/(0.015kg+0.045kg)\s
v2f=0.20
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A brick is thrown upward from the top of a building at an angle of 25 to the horizontal and with an initial speed of 15 m/s. The brick hits the ground after 3.0s of flight.
(a) Calculate the height of the building.
The vertical height of the building is determined as 44.1 m.
What is the height of the building?
The height of the building is calculated by applying the following kinematic equation as shown below.
h = vyt + ¹/₂gt²
where;
vy is the initial vertical velocity of the brickt is the time of motion of the brickh is the height of fall of the brickg is acceleration due to gravityh = (v sinθ)t + ¹/₂gt²
where
θ is the angle of inclination of the velocityThe given parameters include the following;
initial vertical velocity of the brick, vy = 0the time of motion of the brick, t = 3.0 sthe height of fall of the brick, h = ?acceleration due to gravity = 9.8 m/s²h = (0 x sin25)(3) + ¹/₂(9.8)(3²)
h = 44.1 m
Thus, the height of the building is equal to the vertical distance travelled by the brick thrown at the given initial velocity.
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a satellite moves on a circular earth orbit that has a radius of 6.7 x 106 m. a model airplane is flying on a 15-m guideline in a horizaontal circle. the guideline is parallel to the ground. find the speed of the plane such that the plane and the satellite have the same centripetal acceleration.
The speed of the plane will have a factor of 0.668 with the satellite speed at the same centripetal acceleration.
We need to know about centripetal acceleration to solve this problem. The centripetal acceleration depends on the angular velocity and the radius. It can be written as
a = v² / R
where a is centripetal acceleration, v is velocity and R is radius.
From the question above, the given parameters are
R1 = 6.7 x 10⁶ m
R2 = 15 m
a1 = a2
By substituting the given parameters, we can calculate the speed of plane
a1 = a2
v1² / R1 = v2² / R2
v2² / v1² = R1 / R2
v2² / v1² = 6.7 x 10⁶ / 15
v2² / v1² = 6.7 x 10⁶ / 15
v2/v1 = 0.668
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a 70 kg man is floating at rest near his spaceship. he throws a 1.5 kg wrench away from the ship at a speed of 10 m/s in order to move himself toward it. with what speed does he move toward the ship?
0.218 m/s speed does he move toward the ship.
use the formula from conservation of Momentum
mu + MV = (m-M)V'
u = o
so
MV = (m-M)V'
V' = (1.5 * 10)/(70-1.5)
V' = 0.218 m/s
What is speed?The most crucial scientific notion is measurement. Base or physical fundamental units are used to quantify a wide range of quantifiable quantities. One such measurable metric is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance. Let's explore speed in-depth in this session.
The distance traveled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
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a mass m is attached to an ideal massless spring. when this system is set in motion with amplitude a, it has a period t. how does the period of the motion change if the amplitude of the motion is increased to 2a? explain.
System is set in motion with an amplitude of a and a period of T. If the amplitude of the motion is increased to 2a, the period of the motion changes.
A straightforward harmonic oscillator's period is independent of its amplitude. with the graphs of acceleration and velocity produced by the time derivatives. These oscillators also show how kinetic and potential energy can be transferred.
The acceleration of the mass increases proportionally with the increase in force, causing the mass to travel farther in the same amount of time. Therefore, increasing the amplitude has no overall impact on the oscillation's period.
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A diver runs horizontally off the end of a 3.0-m-high diving board with an initial speed of 1.8 m/s. Find her y positions at the times t = 0.25 s , t = 0.50 s , and t = 0.75 s .
(a) At time, t = 0.25 s, the y position of the driver is 0.31 m.
(b) At time, t = 0.50 s, the y position of the driver is 1.2 m
(c) At time, t = 0.75 s, the y position of the driver is 2.76 m
What is the position of the driver?The position of the driver at the various time is determined by applying the following kinematic equation.
y = vt + ¹/₂gt²
where;
v is the initial vertical velocity of the drivert is the time of motion of the drivery is the vertical position of the driver at various timet is the time of motionSince the driver runs horizontally, the initial vertical velocity = 0
y = 0 + ¹/₂gt²
y = ¹/₂gt²
at time, t = 0.25 s, the y position of the driver is calculated as;
y = ¹/₂gt²
y = ¹/₂(9.8)(0.25)²
y = 0.31 m
at time, t = 0.5 s, the y position of the driver is calculated as;
y = ¹/₂gt²
y = ¹/₂(9.8)(0.5)²
y = 1.2 m
at time, t = 0.75 s, the y position of the driver is calculated as;
y = ¹/₂gt²
y = ¹/₂(9.8)(0.75)²
y = 2.76 m
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an object has mass 0.2 kg, how much force is required to throw it vertically with velocity 5ms
0.2×51000)
Explanation:
change 5ms into cms before multiplying by 0/2 kgs
A skier (m = 100 kg) is on level ground with a coefficient of kinetic friction of 0.05 m
moving at a speed of 100m/s. Calculate the distance the skier will go before they stop.
Use conservation of energy.
The distance the skier will go before they stop is 10193.68m.
Given ; Mass =100kg
coefficient of kinetic friction μ=0.05m
u=100m/s
v=0
μg=a
a= μg=0.05 x 9.81=0.4905 m/s²
v²-u²=2as
[v²-u²]/2a= s
-100²/2(0.4905)
s=10193.68m (neglecting the negative sign)
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How many moles of CaCo2 are in 50g of calcium carbonate
An aeroplane lands on a runway at a speed of 180 km/hr and is brought uniformly in 30 seconds.what distance does it covers on the run way before coming to rest
This can be calculated by using motion equations, The distance covered on the runway before coming to rest
Initial speed is 180 km/hr = 50 m/s
time took to come to rest is = 30 sec
so we can write, here we are assuming that there is no frictional force is applied externally or internally to the system.
u = 50 m/s
v = 0 m/s
t = 30 s
we know that distance travelled = x
so, x =
putting the appropriate values, we get that
x = [tex](\frac{50+0}{2} ) 30[/tex]
x = 750 m
Hence the distance travelled before coming to rest is 750 m.
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A 65-kg diver jumps off a 9.7-m tower.
(a) Find the diver's velocity when he hits the water.
____m/s
(b) The diver comes to a stop 2.0 m below the surface. Find the net force exerted on the diver while in the water.
______N
(a) The diver's velocity when he hits the water is 13.795 m/s.
(b) The diver's net force while in the water was -3092.7N.
Newton's second law states that the force F acting on a body is equal to the mass m of the body multiplied by the acceleration an of its center of mass, F = ma.
The three equations of motion are: v = u + at, v2 = u2 + 2as, and s = ut + 12at2.
Given
A 65-kg diver jumps off a 9.7-m tower
(a) Using newton's equation of motion,
v² = u² + 2gs ......... (1)
Where v = final velocity,
u = initial velocity,
s = height of the tower,
g = acceleration due to gravity.
Given: s = 9.7 m, u = 0 m/s (height jump), g = 9.81 m/s2.
Substitute into equation 1
v² = 0² + 2×9.81×9.7
v² = 190.314
v = √(190.314)
v = 13.795 m/s.
As a result, the driver's velocity when he hits the water is 13.795 m/s.
(b)
F = ma. ......... (2)
Where F is the force applied to the diver, m is the diver's mass, and an is the diver's acceleration below the water's surface.
Also using
v² = u² + 2as ......... (3)
When the diver enters the water, u = 13.795 m/s, and when the diver comes to a complete stop, v = 0 m/s.
Given are the following values: s = 2.0 m, u = 13.795 m/s, and v = 0 m/s.
Substitute in equation 3
0² = 13.795²+2(2a)
0 = 190.30203 + 4a
-4a = 190.30203
a = 190.30203/-4
a = -47.58 m/s²
Also given: m = 65 kg,
Substitute into equation 3
F = (-47.58)(65)
F = -3092.7
The Force is negative because it acts against the diver's motion.
As a result, the net force exerted on the diver while in the water equals -3092.7N.
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a playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.350 rev/s. what is its angular velocity (in rev/s) after a 15.0 kg child gets onto it by grabbing its outer edge? the child is initially at rest.
Angular velocity (in rev/s) after a 15.0 kg child gets onto it by grabbing its outer edge is 1.575 rad/s.
The angular velocity of the merry-go-round after a child gets on it is equal to the angular velocity of the child plus the angular velocity of the merry-go-round.
The angular velocity of a rotating object can be calculated using a formula:
ω = ω + (m/r)
where ω is the original angular velocity, m is the mass of an object that's been added to it, r is its radius, and (m/r) is the change in mass divided by its radius. When we plug in our values for this problem, we get:
ω = 0.350 rad/s + ((15 kg)/(1.8 m)) rad/s
= 0.350 rad/s + 1.25 rad/s
= 1.575 rad/s
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a solenoid of length 1.50 cm and radius 0.550 cm has 37 turns. if the wire of the solenoid has 1.15 amps of current, what is the magnitude of the magnetic field inside the solenoid? magnitude of the magnetic field: t ignoring the weak magnetic field outside the solenoid, find the magnetic energy density inside the solenoid. magnetic energy density: j/m3 what is the total magnetic energy inside the solenoid? total magnetic energy: j
a) magnitude of the magnetic field = 8.02 X [tex]10^{-3}[/tex] T
b)Energy Density = 5.03 J/[tex]m^{3}[/tex]
c) Total magnetic energy inside the solenoid = 2.01 X [tex]10^{-5}[/tex] J
What is magnetic field?A magnetic field, a vector field in the vicinity of a magnet, an electric current, or a changing electric field in which magnetic forces can be observed. Magnetic fields, such as those found on Earth, cause magnetic compass needles and other permanent magnets to align in the field's direction. Magnetic fields cause electrically charged particles to move in a circular or helical pattern. The operation of electric motors is based on this force, which is exerted on electric currents in wires in a magnetic field.Calculation
a) B = uNI/L
B = (4π X [tex]10^{-7}[/tex])(37)(1.15)/(.015)
B = 8.02 X [tex]10^{-3}[/tex] T
b) Energy Density = [tex]B^{2}[/tex]/2u
Energy Density = [tex](8.02 *10^{-3} )^{2}[/tex]/(2)(4π X [tex]10^{-7}[/tex])
Energy Density = 5.03 J/[tex]m^{3}[/tex]
c) Total magnetic energy inside the solenoid
Multiply by volume for total energy.
Total Energy = 5.03(π[tex]r^{2}[/tex])(L)
Total Energy = (5.03)(π)[tex](8.5*10^{-3})^{2}[/tex])(.015)
Total Energy = 2.01 X [tex]10^{-5}[/tex] J
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a)The magnitude of the magnetic field [tex]$=\mathbf{8 . 0 2} \times 10^{-3} \mathbf{T}$[/tex]
b)The Energy Density [tex]$=\mathbf{5 . 0 3} \mathrm{J} / \mathrm{m}^3$[/tex]
c) Total magnetic energy inside the solenoid [tex]$=\mathbf{2} . \mathbf{0 1} \mathbf{X} 10^{-5} \mathbf{J}$[/tex]
What is magnetic field?A magnetic field, a vector field in the vicinity of a magnet, an electric current, or a changing electric field in which magnetic forces can be observed.Magnetic fields, such as those found on Earth, cause magnetic compass needles and other permanent magnets to align in the field's direction.Magnetic fields cause electrically charged particles to move in a circular or helical pattern.The operation of electric motors is based on this force, which is exerted on electric currents in wires in a magnetic field.a) [tex]$B=u N I / L$[/tex]
[tex]&B=\left(4 \pi \times 10^{-7}\right)(37)(1.15) /(.015) \\[/tex]
[tex]&B=8.02 \times 10^{-3} \mathrm{~T}[/tex]
b) Energy Density[tex]$=B^2 / 2 \mathrm{u}$[/tex]
Energy Density[tex]$=\left(8.02 * 10^{-3}\right)^2 /(2)\left(4 \Pi \times 10^{-7}\right)$[/tex]
Energy Density [tex]$=5.03 \mathrm{~J} / \mathrm{m}^3$[/tex]
c) Total magnetic energy inside the solenoid
Multiply by volume for total energy.
Total Energy [tex]$=5.03\left(\pi r^2\right)(\mathrm{L})$[/tex]
Total Energy [tex]$\left.=(5.03)(\pi)\left(8.5 * 10^{-3}\right)^2\right)(.015)$[/tex]
Total Energy [tex]$=2.01 \times 10^{-5} \mathrm{~J}$[/tex]
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robin started at point a. she walked 4m south, then 8m east, then 4m north, then 8m west so that she was back at point a. if her walk took 5 minutes, what was her velocity in meters per minute?
Robin started at point a. she walked 4m south, then 8m east, then 4m north, then 8m west so that she was back at point a. if her walk took 5 minutes her velocity in meters per minute is 0.96.
Displacement = distance / time = 24m/5 = 4.8
Velocity = displacement / Time = 4.8/5 = 0.96m/min
Its scientific definition and velocity are presumably similar. You are aware that a significant displacement over a short period of time indicates a large velocity, and that velocity has measures of distance / time, like miles/hour or kilometers/hour.
The change in position divided by the distance travelled is the definition of average velocity. However, the average speed of an object tells us nothing about what happens to it between the starting and finishing points. For instance, average velocity does not allow us to determine whether a passenger in an airplane briefly stops or reverses before relocating to the rear of the aircraft. We must consider shorter distances travelled over shorter times in order to obtain more information.
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2. It takes 1,200 J of work to lift a car high enough to change a tire.
How much work must be done by the person operating the jack
if the jack is 25% efficient?
The work done by the person operating the jack is 4,800 J
Efficiency is described as the potential to perform something with the least quantity of wasted time, cash, and attempt or competency in performance. Effectiveness is described because the diploma to which some thing is successful in producing a preferred result; achievement.
calculation:-
work input = (1200 J)/(0.25)
= 4800 J.
There are numerous styles of performance, consisting of allocative and effective performance, technical efficiency, 'X' efficiency, dynamic performance and social efficiency.
The prime focus of performance is for customers to get the goods and offerings they want at the bottom possible resource price. Inside the have a look at of economics, the dreams of efficiency and equity are frequently in warfare with each other.
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what is the wavelength (in pm) of an electron with a mass of 9.11 x 10-31 kg and a velocity of 2.963 x 106 m/s aleks
The wavelength of an electron is 215.5nm.
The de Broglie wavelength is calculated in what way?A description of the de Broglie wavelength is as follows:
The formula for wavelength is = h/mv, where h stands for Planck's constant, m for mass, and v for velocity.
The equation p = h/λ, where h is the Planck constant and is the wavelength, expresses the De Broglie relation, which states that there is a correlation between an electron's wavelength and momentum.
The wavelength of a wave is the distance between its two subsequent crests or troughs.
h = 6.62607015 × 10⁻³⁴ joule second.
m =9.11 x 10 ⁻³¹Kg
v = 2.963 x 10⁶m/s
λ = h / ( mv)
λ = 6.62607015 × 10⁻³⁴/9.11 x 10 ⁻³¹×2.963 x 10⁶
λ = 2.155×10⁻⁷
λ = 215.5nm.
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what is the magnification of an astronomical telescope whose objective lens has a focal length of 79 cm and whose eyepiece has a focal length of 2.9 cm ? follow the sign conventions.
The magnification of an astronomical telescope is -27.24 .
The magnification of a telescope is actually a relationship between two independent optical systems: the telescope itself and the eyepiece that is being used.
To determine the power, divide the focal length of the telescope (in mm) by the focal length of the eyepiece (in mm)Magnification is denoted by MMathematically it is M = -(T/E)Focal length of the telescope = T = 79 cm = 790mm
Focal length of the eyepiece = E = 2.9 cm = 29mm
M = -[tex]\frac{T}{E}[/tex]
M = -[tex]\frac{79}{2.9}[/tex]
M = -27.24
Therefore, the magnification of an astronomical telescope is -27.24.
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A 0. 25-kg toy car experiences a net force of 9. 0 n while slowing down to a complete stop. What is the magnitude of its acceleration?.
Answer:
a = 36 m/s
Explanation:
Given:
F = 9 N
m = 0.25 kg
a= ?
Use the equation:
F = ma (divide by m on both sides to get a alone)
a = F/m= 9/0.25 = 36 m/s
the frequency content of an analog signal to be digitized has a range roughly covering the range of the auditory system of a young child: 200 hz to 20,000 hz. for accurate sampling, what is the minimal sampling rate necessary for an a/d convertor?
For accurate sampling, -44.1khz is minimum sampling rate for an a/d convertor.
What is sampling rate?The number of samples per second (or other unit) taken from a continuous signal to form a discrete or digital signal. The sample rate or sample rate specifies the number of samples per second (or other unit). of a continuous signal to form a discrete or digital signal..
The sampling rate can be thought of as the audio version of frames per second. This is the number of "clips" taken from an analogue sound wave to make a digital file. In addition, the sample rate also controls the highest frequency that can be accurately reproduced by a digital file.
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Calculate the efficiency of a machine that requires 20 J of input work to do 10 J of output work. What is the efficiency of the machine? (in percent, but write the number only)
The efficiency of a machine that requires 20 J of input work to do 10 J of output work. The efficiency of the machine η = 50 %
The engine efficiency is defined as ratio of the useful work done to the heat provided.
By using the formula for efficiency of a machine and substituting the values in it, we get :
η = (Wo/Wi × 100)%
η = (10/20 × 100)%
η = 50 %
The efficiency of the machine will be η = 50 %
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what is the rotational inertia of a solid iron disk of mass 41.0 kg with a thickness of 5.00 cm and radius of 30.0 cm, about an axis perpendicular to the disk and passing through its center?
Answer:
I = 1/2 M R^2 moment of inertia of solid disk
I = 1/2 * 41.0 kg * (.3 m)^2
I = 20.5 kg * .09 m^2 = 1.85 kg-m^2
an electron is released within a uniform electric field of a magnitude of 28,000 n/c generated by two parallel plates. the plates are separated by 4 cm. if the electron has moved across the entire gap between the plates, what is its speed?
Within a uniform electric field of magnitude 28,000 n/c produced by two parallel plates, an electron is expelled at a speed of 3.51 * 10^15 m/s^2. The distance between the plates is 4 cm.
The electron is a subatomic particle with the symbol e or with an electric field of one elementary negative charge. Due to their lack of known components or substructure, electrons, which are part of the first generation of the lepton particle family, are typically considered to be elementary particles. When the electric field strength at the electron's location, E, is taken into account, the force acting on it has the size F=eE. Newton's second law provides the electron's acceleration as follows:
a= F/m = eE/m
= (1.60*10^-19)(2.00*10^4)/9.11*10^-31
= 3.51 *10^15 m/s^2
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a car traveling with a constant velocity quickly comes to rest. while slowing down, the passengers inside the car are pushed forward by the force of .
Using the concepts of motion, we got that Ma is the force exerted on the passengers inside the car when a car traveling with a constant velocity quickly comes to rest.
We know very well that according to newton second law of motion,
if a moving object is moving with some velocity v at any particular time t, then there is force acting on that object and that force is given by
F= dp /dt,
where dp is defines as change in momentum of the object. In other words,
dp=M×([tex]v_f_i_n_a_l[/tex] - [tex]v_i_n_i_t_i_a_l[/tex])
where [tex]v_f_i_n_a_l[/tex] and v[tex]_i_n_i_t_i_a_l[/tex] are the velocities of the object in different time.
So suppose car has some mass M kg
It is given that final velocity of the object is =0 as the car comes to rest,
suppose initial velocity is v
Therefore, F=[M×(0-v)]/t
=> F= -M×(v/t)
=> F= -Ma because acceleration =velocity/time
Here negative sign shows that force acts on the person in opposite direction of frictional force applied by the road.
Hence, when a car traveling with a constant velocity quickly comes to rest. while slowing down, the passengers inside the car are pushed forward by the force - Ma.
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How does a white dwarf differ from a neutron star? how does each form? what keeps each from collapsing under its own weight?.
An electron degenerate object is a white dwarf, whereas a neutron star is a neutron degenerate object. A white dwarf is less compact and has a larger radius than a neutron star.
How is a white dwarf transformed into a neutron star?A white dwarf would collapse into a denser entity known as a neutron star if it reached the Chandrasekhar limit and nuclear reactions were to stop. This would happen if nuclear reactions continued to occur.
How is a white dwarf prevented from exploding into a neutron star?White dwarf stars are prevented from collapsing by the fact that electrons are fermions, while neutron stars are prevented from collapsing by the fact that electrons are fermions.
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the tide that results from a lunar wave is larger than the solar wave. group of answer choices true false
The given statement is true. A lunar eclipse happens when the Moon passes into the shadow of the Earth. A solar eclipse happens when the Moon passes between Earth and the Sun.
What is lunar wave and solar wave?A lunar eclipse happens when the Moon passes into the shadow of the Earth. This is only possible when the Sun, Earth, and Moon are precisely or extremely closely aligned with Earth between the other two, which can happen only on a full moon night when the Moon is close to either lunar node.
A solar eclipse happens when the Moon passes between Earth and the Sun, completely or partially blocking Earth's view of the Sun. A new moon corresponds with such an alignment, showing that the Moon is closest to the plane of the Earth's orbit. The Moon completely obscures the disk of the Sun during a total eclipse.
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The given statement is true. A lunar eclipse happens when the Moon passes into the shadow of the Earth. A solar eclipse happens when the Moon passes between Earth and the Sun.
What is lunar wave and solar wave?When the Moon enters the shadow of the Earth, an eclipse occurs. This can only occur on a full moon night when the Moon is close to either lunar node, when the Sun, Earth, and Moon are precisely or extremely closely aligned with Earth between the other two.When the Moon passes in front of Earth and the Sun, covering Earth's view of the Sun entirely or in part, a solar eclipse occurs. Such an alignment is accompanied by a new moon, demonstrating that the Moon is closest to the plane of the Earth's orbit. A total eclipse occurs when the Moon totally blocks out the Sun's disk.To learn more about Lunar and solar eclipse refer to:
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many astronomers believe that the massive object at the center of the milky way galaxy is a black hole. if so, what must the schwarzschild radius rs of this black hole be?
The Schwarzschild Radius Rs of this black hole is 5.69 x [tex]10^{10}[/tex] m
The Schwarzschild radius or gravitational radius is a physical parameter in the Schwarzschild solution of Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole.
Let's assume that the ring shaped disk is circular and thus, to find the mass of the object at the center of the milky way, we can use the circular orbit equation;
v = √(GM/r)
where;
G is the gravitational constant and has a value of 6.67 x 10^(-11) Nm²/kg²
R is the radius of the orbit,
M is the mass of the larger object
v = velocity = 190km/s = 190000 m/s
Also
1 light year = 9.4605 x 10^(15) m
Thus,7.5 light years = 7.5 x 9.4605 x 10^(15) m
so, M = v²r/G
Putting all the values in the equation,
M = [190000² x 7.5 x 9.4605 x 10^(15)]/6.67 x 10^(-11)
M = 3.84 x 10^(37) kg
Now, mass of the sun generally has a value of 1.9891 x 10^(30) kg
Thus, value of mass of object in solar masses = 3.84 x 10^(37)/1.9891 x 10^(30) = 1.931 x 10^(7) solar masses
The formula for Schwarzschild radius is given as;
Rs = 2GM/c²
Where c is speed of light = 3 x 10^(8) m/s
Thus,
Rs = 2 x 6.67 x 10^(-11) x 3.84 x 10^(37)/(3 x 10^(8))² = 5.69 x [tex]10^{10}[/tex] m
The Schwarzschild radius Rs of this black hole is 5.69 x [tex]10^{10}[/tex] m
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A small nail stuck in your car tire moves on a circular path with a radius of 35 cm. when the nail has traveled a linear distance of 5.5 m, through what angle has the tire rotated in both radians and degrees?
To cover 5.5 meters in a straight line, the tire rotated at an angle of 15.714rad.
What is a circle's simple definition?To put it simply, a circle is a spherical shape without any corners or line segments. In geometry, it has the shape of a closed curve.
A definition from Euclid
A circle is a plane figure that is bounded by a single curved line and in which all straight lines drawn from any point inside the circle to the boundary are equal. Its center is the point, and its circumference is the bounding line. — Book I of Euclid's Elements.
Given,
circular path with a radius of 35cm,
Circumference of car tire is 2πr = 2×3.14×0.35 = 2.198m
For traveling a distance of 5.5m
5.5 = angle in rads ×radius
angle = 5.5/0.35
angle = 15.714 rad
To cover 5.5 meters in a straight line, the tire rotated at an angle of 15.714rad.
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(b) The cars collide and car B experiences an impulse. Car A continues to move in the same
direction, with a momentum of 21 000 kg m/s.
(i) Calculate the momentum of car B immediately after the collision.
momentum =
llicion
[1]
The momentum of car B immediately after the collision if the momentum of car A is 21 000 kg m/s after collision is 15000 kg m / s
p = m v
p = Momentum
m = Mass
v = Velocity
m1 = 2000 kg
u1 = 18 m / s
pi1 = 2000 * 18
pi1 = 36000 kg m / s
m2 = 1200 kg
u2 = 0
pi2 = 0
pf1 = 21000
According to law of conservation of momentum
pi1 + pi2 = pf1 + pf2
pi1 = Initial momentum of car A
pi2 = Initial momentum of car B
pf1 = Final momentum of car A
pf2 = Final momentum of car B
pf2 = pi1 + pi2 - pf1
pf2 = 36000 + 0 - 21000
pf2 = 15000 kg m / s
Therefore, the momentum of car B immediately after the collision is 15000 kg m / s
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how is the energy that powers radio galaxies, quasars, and other active galactic nuclei thought to be produced?
The energy that powers radio galaxies, quasars, and other active galactic nuclei is thought to be produced by accreting matter onto a supermassive black hole. This process is called active galactic nucleus (AGN) fueling.
The gas that surrounds the black hole is heated to millions of degrees as it falls into the black hole. Because the gas is so hot, it emits a great deal of radiation in many different wavelengths.
This radiation can be seen across the electromagnetic spectrum, from low-energy gamma rays to high-energy X-rays. In some cases, jets of charged particles are ejected at nearly the speed of light along magnetic field lines; these jets can create shock waves in the surrounding medium that emit radio waves.
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explain the differences between linear speed and angular speed when describing motion along a circular path.
The difference between linear speed and angular speed is linear speed calculates the distance to time whereas angular speed calculates the angle to time.
The difference between the linear speed and the angular speed is that linear speed is just a measurement determined by calculating the distance of an arc versus time taken, and angular velocity is also a measurement determined by calculating the angle of an arc versus time taken.
The formula of the linear speed is
s = d / t
where s is the speed
d is the distance
t is the time taken
The formula of the angular speed is
ω = θ / t
where ω is the angular speed
θ is the angular rotation
t is the time taken.
The relation between the linear speed and angular speed in a uniform circular motion is
s = rω
where s is the linear speed
r is the radius
ω is the angular speed.
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