The linear momentum of the system the bomb before the explosion, the piece after the explosion is conserved. Therefore, while linear momentum is conserved, other forms of energy are not.
The explosion, the bomb was at rest, so its momentum was zero. After the explosion, the pieces will move in different directions with different velocities, but the sum of their momenta will still be zero. This means that the total momentum of the system is conserved. However, it should be noted that the kinetic energy of the system is not conserved as some of it is lost in the form of heat, sound, and other forms of energy during the explosion. Therefore, while linear momentum is conserved, other forms of energy are not.
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a 12.0g rifle bullet is fired with a speed of 380 m/s into aballistic pendulum with mass 6.00kg suspended from a cord 70.0 cmlong.
a) compute the vertical height through which the pendulumrises
b) compute the initial kinetic energy of the bullet
c) compute the kinetic energyof the bullet and pendulumimmediatly after the bullet becomes embedded in the pendulum
A. the vertical height through which the pendulum rises is 0.416 m. B. the initial kinetic energy of the bullet is 866.4 J, and C. the kinetic energy of the bullet and pendulum immediately after the collision is 0.016 J.
a) To compute the vertical height through which the pendulum rises, we can use the conservation of momentum and conservation of energy principles. The momentum conservation equation is:[tex]m_bullet * v_bullet = (m_bullet + m_pendulum) * v_final[/tex]where m_bullet is the mass of the bullet, v_bullet is the initial velocity of the bullet, m_pendulum is the mass of the pendulum, and v_final is the final velocity of the bullet and pendulum after the collision.Using the conservation of energy principle, the initial kinetic energy of the bullet is converted to the potential energy of the bullet and pendulum at the highest point of their swing. So, we can write:[tex](1/2) * m_bullet * v_bullet^2 = (m_bullet + m_pendulum) * g * h[/tex]where h is the vertical height through which the pendulum rises.Solving these two equations simultaneously, we get:[tex]h = (v_bullet^2 / (2*g)) * ((m_bullet + m_pendulum) / m_pendulum)\\\\h = (380^2 / (2*9.81)) * ((0.012 + 6.00) / 6.00)\\\\h = 0.416 m[/tex]Therefore, the vertical height through which the pendulum rises is 0.416 m.b) The initial kinetic energy of the bullet can be calculated using the formula:[tex]KE = (1/2) * m_bullet * v_bullet^2[/tex][tex]KE = (1/2) * 0.012 * (380)^2[/tex]KE = 866.4 JTherefore, the initial kinetic energy of the bullet is 866.4 J.c) After the bullet becomes embedded in the pendulum, the combined system of bullet and pendulum moves with a common velocity, which we can calculate using the principle of conservation of momentum. The momentum conservation equation is:[tex]m_bullet * v_bullet = (m_bullet + m_pendulum) * v_final[/tex]where v_final is the final velocity of the bullet and pendulum after the collision.Solving for v_final, we get:[tex]v_final = (m_bullet * v_bullet) / (m_bullet + m_pendulum)[/tex]v_final = (0.012 * 380) / (0.012 + 6.00)v_final = 0.236 m/sThe kinetic energy of the bullet and pendulum immediately after the collision is given by:[tex]KE_final = (1/2) * (m_bullet + m_pendulum) * v_final^2[/tex][tex]KE_final = (1/2) * (0.012 + 6.00) * (0.236)^2[/tex]KE_final = 0.016 JTherefore, the kinetic energy of the bullet and pendulum immediately after the collision is 0.016 J.For more such question on kinetic energy
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the null hypothesis, h0, is: no more than 90% of homes in the city are up to the current electric codes.and the alternative hypothesis, ha, is: an electrician claims more than 90% of homes in the city are up to the current electric codes. what is the type ii error in this scenario?select the correct answer below:
The type II error in this scenario would be failing to reject the null hypothesis (H0) when the alternative hypothesis (Ha) is actually true.
This would mean concluding that no more than 90% of homes in the city are up to the current electric codes when in reality, more than 90% of homes are up to code. In this scenario, the Type II error occurs when we fail to reject the null hypothesis (H0) when the alternative hypothesis (Ha) is actually true. So, the Type II error would be:
Failing to reject the null hypothesis (H0) that no more than 90% of homes in the city are up to the current electric codes when, in fact, the electrician's claim (Ha) that more than 90% of homes are up to the current electric codes is true.
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What is the function of the iris diaphragm? The substage condenser?
The iris diaphragm is a part of the microscope that controls the amount of light that enters the microscope. It is located just above the condenser and can be adjusted to increase or decrease the amount of light that passes through the specimen. By adjusting the iris diaphragm, you can control the contrast and brightness of the image.
The substage condenser is another part of the microscope that is located just below the stage. Its function is to focus the light from the light source onto the specimen. By adjusting the height and position of the substage condenser, you can improve the resolution and clarity of the image. It also helps to reduce glare and improve contrast by directing the light through the specimen in a more controlled manner.
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1. Calculate the amount of torque applied to the fastener for the torque wrench shown in the figure. Use
the formula T=FX D.
Torque
The amount of torque can be calculated by Force x Moment arm.
How to calculate torqueIt should be noted that to uncover the quantity of torque, you must comprehend both the force applied and the separation from the pivot point (also referred to as the moment arm) at which the force is exerted. The formula for torque can be put forth as:
Torque = Force x Moment arm
The magnitude of force typically is disseminated in Newtons (N) and the length is relayed using meters (m), thus implying that the unit for torque is Newton-meters (Nm).
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A 90.0 kg man climbs up
a rope. At the top, his
potential energy is
8352.54 J. How high
does the man climb up
the rope?
From the given data and calculations, we can see that the man has climbed 9.46 meters
Given DataMass of the Man =90.0 kg Potential Energy at the Top of the rope = 8352.54 JHeight Climbed = ??We know that the expression for Man's potential energy at the top of the rope can be expressed as
P.E = mgh
Let us take acceleration due to gravity to be
g = 9.81 m/s^2
Substituting our given data into the expression and solving for h we have
8352.54 = 90*9.81*h
8352.54 = 882.9h
Dividing both sides by 882.9 we have
h = 8352.54/882.9
h = 9.46 meters
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If the resitance of 0.17 Ohms was measured across the given length of a conductive material, what is the resistivity?
Diameter is 10cm
Lenght is 1 meter
A) 0.25Ohm cm
B) 2.25Ohm cm
C) 0.13345 Ohm cm
D) 0.29 Ohm cm
E) 0.54 Ohm cm
The resistivity of the conductive material can be calculated using the formula: Resistivity = Resistance x (pi x diameter^2)/4 x Length. The resistivity of the conductive material is C) 0.13345 Ohm cm.
Resistance (R) = 0.17 Ohms
Diameter (d) = 10 cm = 0.1 m
Length (l) = 1 m
Using the formula,
Resistivity (p) = R x (pi x d^2)/4 x l
Substituting the values,
p = 0.17 x (pi x 0.1^2)/4 x 1
p = 0.13345 Ohm cm
Therefore, the resistivity of the given conductive material is 0.13345 Ohm cm.
Note: The resistivity of a material is a measure of its ability to resist the flow of electric current through it. It is an intrinsic property of the material and depends on factors such as the type of material, temperature, and impurities present in the material.
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All other things being equal (so assuming that the value of SS never changes), as sample size increases,
the degrees of freedom for sample variance decrease
the value of sample variance decreases
the value in the numerator for sample variance increases
the value in the denominator for sample variance decreases
As sample size increases, the variance decreases because the increase in the numerator is offset by the decrease in the denominator. This is an important concept to understand when analyzing data and making statistical inferences.
As sample size increases, the value in the denominator for sample variance decreases while the value in the numerator for sample variance increases. This means that the variance of a larger sample will be smaller than that of a smaller sample.
To understand this concept, it is important to know that variance is a measure of how spread out a dataset is. The formula for sample variance involves the sum of squared deviations from the mean, divided by the degrees of freedom. The degrees of freedom represent the number of independent pieces of information used to calculate the sample variance.
As sample size increases, the number of independent pieces of information decreases, hence the degrees of freedom decrease. However, the sum of squared deviations from the mean is likely to increase with a larger sample size, as there will be more data points that deviate from the mean. This increase in the numerator will be offset by a decrease in the denominator, resulting in a smaller variance value.
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When considering a change in momentum what two variables must you consider?
When considering a change in momentum, two variables that must be considered are the mass and velocity of the object in question.
The momentum of an object is directly proportional to its mass and velocity, so changes in either of these variables can have a significant impact on its overall momentum. It's important to consider both of these variables when analyzing the momentum of an object, as they can provide valuable insights into its behavior and potential impact in a given situation.
When considering a change in momentum, the two variables you must consider are mass and velocity. Momentum is the product of an object's mass and its velocity, so to determine the change in momentum, you need to consider changes in either the mass or the velocity of the object.
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find the distance and time the vehicle has moved relative to the driver of the vehicle. (b) how fast has the vehicl g
To find the distance and time the vehicle has moved relative to the driver, we need to consider the speed of the vehicle and the direction of motion. If the vehicle is moving in a straight line, we can use the formula distance = speed × time to calculate the distance covered.
Similarly, we can use the formula time = distance ÷ speed to calculate the time taken to cover a certain distance.
Regarding the speed of the vehicle, we need more information to answer that part of the question. If we know the distance covered and the time taken, we can use the formula speed = distance ÷ time to calculate the speed of the vehicle.
Alternatively, if we know the speed and the time taken, we can use the formula distance = speed × time to calculate the distance covered.
In summary, to find the distance and time the vehicle has moved relative to the driver, we need more information about the motion of the vehicle. Once we have that information, we can use basic formulas of distance, speed, and time to calculate the desired quantities.
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according to stefan's law (see section 3.4 in the textbook), how much more radiation - per square meter, say - is emitted by venus's surface at 730 k than is emitted by earth's surface at 300 k ? express your answer using two significant figures.
The surface of Venus emits about 58.2 times more radiation per square meter than the surface of Earth, assuming they both behave as black bodies.
Stefan's law states that the energy radiated per unit area per unit time, or the radiant emittance, of a black body is proportional to the fourth power of its absolute temperature. Mathematically, this can be written as:
E = [tex]σT^4[/tex]
where E is the radiant emittance, σ is the Stefan-Boltzmann constant ([tex]5.67 x 10^-8 W/m^2K^4[/tex]), and T is the absolute temperature.
Using this formula, we can calculate the ratio of the radiant emittance of Venus's surface at 730 K to that of Earth's surface at 300 K:
([tex]E_venus / E_earth) = (σT_venus^4 / σT_earth^4[/tex])
([tex]E_venus / E_earth) = (T_venus / T_earth[/tex])[tex]^4[/tex]
([tex]E_venus / E_earth) = (730 / 300)^4[/tex]
([tex]E_venus / E_earth) ≈ 58.2[/tex]
Therefore, the surface of Venus emits about 58.2 times more radiation per square meter than the surface of Earth, assuming they both behave as black bodies.
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a and b are two spheres with identical mass and radius. however, they are made of different materials. sphere b is made of a more dense core and a less dense shell around it. compare the moment of inertia of sphere a about its center of mass to the moment of inertia of sphere b about its center of mass? ia. ia > ib ib. ia < ib ic. ia
Spheres A and B have the same mass and radius but are composed of different materials. Sphere B has a denser core and a less dense shell.
Comparing the moment of inertia of spheres A and B. Given that both spheres A and B have identical mass and radius, but sphere B has a more dense core and a less dense shell, we can determine the relationship between their moments of inertia about their centers of mass.
To do this, we'll use the following equation for the moment of inertia of a solid sphere: I = (2/5)MR², where M is the mass of the sphere, R is its radius, and I is its moment of inertia.
For sphere A (uniform density), its moment of inertia can be calculated as:
Ia = (2/5)MaRa²
For sphere B (non-uniform density with a denser core), its moment of inertia can also be calculated using the same equation, but since it has a more dense core and a less dense shell, its moment of inertia will be smaller than that of sphere A. This is because the mass is distributed closer to the center, which reduces the moment of inertia.
So, comparing the moments of inertia for spheres A and B:
Ia > Ib
Thus, the correct answer is (a): Ia > Ib.
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A solenoid of radius 2. 5 cm has 400 turns and a length of 20 cm. Find (a) its inductance and (b) the rate at which current must change through it to produce an emf of 75 mV
a. The inductance of the solenoid is 0.0556 H
b. The rate of change of current to produce an emf of 75 mV is -1.35 A/s.
a) The inductance of a solenoid can be calculated using the formula L = (μ₀n²πr²l) / (2l + 3r), where μ₀ is the permeability of free space, n is the number of turns per unit length, r is the radius, and l is the length of the solenoid.
Plugging in the values given, we get
L = (4π x [tex]10^{-7}[/tex] x 400² x π x 0.025² x 0.2) / (2 x 0.2 + 3 x 0.025) = 0.0556 H.
b) The emf induced in a solenoid can be calculated using the formula emf = -L(dI/dt), where L is the inductance and dI/dt is the rate of change of current.
Solving for dI/dt, we get dI/dt = -emf/L. Plugging in the values given,
we get dI/dt = -(75 x [tex]10^{-3}[/tex] V) / 0.0556 H = -1.35 A/s.
So the rate at which current must change through the solenoid to produce an emf of 75 mV is 1.35 A/s.
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The question is -
A solenoid of radius 2.5 cm has 400 turns and a length of 20 cm. Find
a) its inductance and
b) the rate at which current must change through it to produce an emf of 75 mV.
consider a uniformly distributed massive lever of mass 16.06 and length 10.45 with a fulcrum located at position 3.38 from the left end of the lever. if a 25.31 mass is placed on the left end of the lever, then what mass in the units of must be placed on the other end in order to keep the system in rotational static equilibrium? please round your answer to 1 decimal p
The mass must be placed on the right end to keep the system in rotational static equilibrium assuming the net torque is 11.3 kg.
Mass of lever =16.06kg
Length = 10.45m
Mass of object = 25.31kg
Position of fulcrum = 3.38m left to lever
Distance of fulcrum from right = (10.45 - 3.38) m = 7.07 m.
To maintain the system in rotational static equilibrium, the net torque acting on the lever must be zero.
The torque on the left end is:
T_left = F * d_left
T_left = (25.31 kg) * (9.81 [tex]m/s^2[/tex]) * (3.38 m)
T_left = 838.1 N*m
The torque on the right end is:
T_right = F * d_right
T_right = m * g * d_right
T_right = m * (9.81 m/s^2) * (7.07 m) = 69.2 mN*m
Assuming the system is in rotational static equilibrium, T_left = T_right:
m * (9.81 ) * (7.07 m) = 838.1 N*m
m = 838.1 N*m / (9.81 * 7.07 m)
m = 11.3 kg
Therefore we can conclude that the mass that must be placed on the right end to keep the system in rotational static equilibrium is 11.3 kg.
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The mass that must be placed on the other end to maintain rotational static equilibrium is 8.9 units.
What is the mass required on the other end to achieve rotational static equilibrium?To keep the system in rotational static equilibrium, the torques acting on the lever must balance. The torque exerted by the 25.31 mass on the left end of the lever can be calculated as the product of its weight (mass multiplied by gravitational acceleration) and the distance from the fulcrum. Similarly, the torque exerted by the mass on the other end can be calculated as the product of its weight and the distance from the fulcrum. Since the lever is uniformly distributed, the mass on the other end can be represented by a linear unit. By setting up an equation of torques, we can solve for the required mass on the other end. After calculations, the mass is determined to be 8.9 units.
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If the current is 4 Amps and the Wattage produced is 200, how many volts are present?
Answer:
50 volts
Explanation:
Wattage (W) = Current (I) x Voltage (V)
We know the current is 4 Amps and the wattage produced is 200, so we can plug these values into the formula and solve for voltage:
200 = 4 x V
Dividing both sides by 4 gives:
V = 50
Therefore, the voltage present is 50 volts.
if you look at yourself in a shiny christmas tree ball with a diameter of 8.2 cm c m when your face is 33.0 cm c m away from it, where is your image?
The image of your face will be located 0.105 m or 10.5 cm away from the Christmas tree ball mirror.
What is the location of the image of your face away from the Christmas tree ball mirror?Assuming that the Christmas tree ball forms a perfect spherical mirror, we can use the mirror equation to find the location of the image:
[tex]1/f = 1/d0 + 1/di[/tex]
where f is the focal length of the mirror (which is half of its radius), d0 is the distance of the object from the mirror, and di is the distance of the image from the mirror.
Since the Christmas tree ball is a spherical mirror with a diameter of 8.2 cm, its radius is 4.1 cm or 0.041 m.
The distance of the object from the mirror, d0, is given as 33.0 cm or 0.33 m.
We can rearrange the mirror equation to solve for di:
[tex]1/di = 1/f - 1/d0f = 0.041 m\\d0 = 0.33 m1/di = 1/0.041 - 1/0.33\\1/di = 24.3902di = 0.041 m / 0.3902\\di = 0.105 m[/tex]
Therefore, the image of your face will be located 0.105 m or 10.5 cm away from the Christmas tree ball mirror.
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A liquid rocket engine has an average chamber pressure, Pc = 10 MPa, measured during a test, and a throat area, At = 0. 175 m2. For the test, the average value of thrust measured was 2000 kN, and 100,000 kg of propellant was expended in a test that was run at constant mass flow rate in 120 sec. Determine the average values of CF, c* and specific impulse for this engine. (90 points)
The average values of CF, c*, and specific impulse for this engine are 10.857, 4441.62 m/s, and 240.8 sec, respectively.
Thrust = mass flow rate * exhaust velocity
where the mass flow rate is given by:
mass flow rate = propellant expended / burn time
and the exhaust velocity is given by:
exhaust velocity = c* * √(2 * (k / (k-1)) * ((Pc / p) [tex]^ ((k-1) / k) - 1))[/tex]
We can first calculate the mass flow rate:
mass flow rate = 100,000 kg / 120 sec = 833.33 kg/sec
Pc / p = 10 MPa / 101.325 kPa = 98.68
Then, we can calculate the exhaust velocity:
exhaust velocity = c* * sqrt(2 * (k / (k-1)) * ((Pc / p) [tex]^ ((k-1) / k) - 1))[/tex]
c* = exhaust velocity / sqrt(2 * (k / (k-1)) * ((Pc / p) [tex]^ ((k-1) / k) - 1))[/tex]
Using this, we get:
exhaust velocity = 2573.78 m/s
c* = 2573.78 m/s / √(2 * (1.2 / 0.2) * ((98.68) [tex]^ ((0.2-1.2) / 1.2) - 1))[/tex] = 4441.62 m/s
Now, we can calculate the thrust coefficient:
CF = Thrust / (Pc * At)
CF = 2000 kN / (10 MPa * 0.175 m²) = 10.857
Finally, we can calculate the specific impulse:
specific impulse = thrust / (mass flow rate * g0)
where g0 is the standard acceleration due to gravity (9.81 m/s²)
specific impulse = 2000 kN / (833.33 kg/s * 9.81 m/s²) = 240.8 sec
In physics, an impulse is a force applied to an object for a very short amount of time. It is calculated as the product of the force and the duration of time over which it is applied. Impulse can cause a change in an object's momentum, which is the product of an object's mass and velocity. According to Newton's second law, force is directly proportional to the rate of change in momentum, so a larger impulse will cause a greater change in momentum.
The concept of impulse is particularly useful in understanding collisions and other situations where forces act over a short time period. In these cases, the impulse can be used to calculate the change in an object's momentum, and from there, its new velocity and direction of motion. Overall, the impulse is an important concept in physics that helps us to understand the behavior of objects in motion and the effects of forces on their momentum.
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How can the major source of meteor shower meteoroids be determined?
The major source of meteor shower meteoroids can be determined by observing the direction from which they appear to radiate.
Meteor showers occur when Earth passes through the debris trail of a comet or asteroid. When these small particles, called meteoroids, enter Earth's atmosphere, they heat up and produce a streak of light, known as a meteor or shooting star. By observing the direction from which the meteors appear to radiate, astronomers can determine the source of the meteoroids, which is usually the debris trail left behind by a comet or asteroid. The apparent point of origin is called the radiant. Different meteor showers have different radiant points, which can be used to identify the specific comet or asteroid responsible for the meteor shower. By studying meteor showers, astronomers can learn more about the composition and orbit of comets and asteroids.
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Assume the arrays numberArray1 and numberArray2 each have 100 elements. Design an algorithm that copies the values in nmberArray1 to numberArray2.For index = 0 to 99Set numberArray2[index] = numberArray1[index]End For
An algorithm is a set of steps that are followed in order to solve a specific problem. In the case of copying the values in numberArray1 to numberArray2, the algorithm would involve iterating through each element in numberArray1 and assigning its value to the corresponding element in numberArray2.
To achieve this, we can use a simple loop that goes from index 0 to 99. Inside the loop, we set the value of numberArray2 at the current index to the value of numberArray1 at the same index. This way, we are essentially copying the values from one array to the other.
The algorithm can be expressed in pseudocode as follows:
For index = 0 to 99
Set numberArray2[index] = numberArray1[index]
End For
This algorithm is straightforward and efficient, as it only requires a single loop to copy all the values from one array to another. It is also scalable, meaning that it can be easily adapted to work with arrays of different sizes.
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consider the first image shown in the video, which is the hubble extreme deep field. which of the following statements about this image are true?
The true statements about the Hubble Extreme Deep Field image are:
Careful study of the image shows that the youngest galaxies were mostly irregular in shape.We see the more distant galaxies as they were when they were quite young.The image includes galaxies that are elliptical, spiral, and irregular.The Hubble Extreme Deep Field image is a testament to the immense scale and diversity of our universe. By capturing thousands of galaxies at various stages of development, the XDF allows astronomers to study the intricate processes of galaxy formation and evolution, ultimately enhancing our understanding of the cosmos.
The Hubble Extreme Deep Field (XDF) image is a remarkable snapshot of our universe, showcasing the farthest and most diverse celestial objects. This image contains approximately 5,500 galaxies, with some dating back to just 450 million years after the Big Bang. The XDF is a combination of observations taken by the Hubble Space Telescope over a period of ten years, focusing on a small region of the sky.
The XDF's depth and clarity reveal a wealth of information about the galaxies present in the image. Observing galaxies at different stages of development helps astronomers understand the processes involved in galaxy formation and evolution. The image contains a mix of spiral, elliptical, and irregular galaxies, each with their unique characteristics and histories.
Furthermore, the XDF highlights the vast scale of the universe, as many of the galaxies captured in this image are billions of light-years away from Earth. This vast distance means that the light we see from these galaxies started its journey billions of years ago, providing us with a glimpse into the universe's distant past.
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Complete Question:
Consider the first image shown in the video, which is the Hubble Extreme Deep Field. Which of the following statements about this image are true? Select all the true statements. The galaxies in this image are part of a large galaxy cluster, bound together by gravity. Careful study of the image shows that the youngest galaxies were mostly irregular in shape. We see the more distant galaxies as they were when they were quite young. ООО Careful study of the image shows that all present-day galaxies are spirals. The image includes galaxies that are elliptical, spiral, and irregular.
The first spacecraft which did not merely fly bya jovian (or giant) planet, but actually went into orbit around it for an extended period of time was
a. Galileo
b. Einstein
c. Voyager
d. the Hubble Space Telescope
e. Cassini
Answer:The first spacecraft which did not merely fly by a jovian (or giant) planet, but actually went into orbit around it for an extended period of time was option a, Galileo. The Galileo spacecraft was launched in 1989 and orbited Jupiter for almost eight years, from 1995 to 2003.
Explanation:
Which of the following phenomena is probably not related to the presence of a supermassive black hole?
• A) Quasars • B) The radio emission from radio galaxies • C) The huge jets seen emerging from the centers of some galaxies • D) The presence of globular clusters in the halos of galaxies
The following phenomena is probably not related to the presence of a supermassive black hole : D) The presence of globular clusters in the halos of galaxies. Hence, option D) is the correct answer.
The presence of globular clusters in the halos of galaxies is probably not related to the presence of a supermassive black hole.
Quasars, the radio emission from radio galaxies, and the huge jets seen emerging from the centers of some galaxies are all commonly associated with supermassive black holes. However, globular clusters are typically thought to form independently of supermassive black holes and are instead believed to be remnants from the early stages of galaxy formation.
D) The presence of globular clusters in the halos of galaxies is not directly related to supermassive black holes, as globular clusters are dense groups of stars that orbit galaxies and are not associated with the intense energy processes happening near black holes.
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if Earth has a radius of 6400 km. a satelite orbits the Earth at a distance of 12,800 km from the center of Earth, if the weight of the satelite on Earth is 100 kilonewtons, the gravitational Force on the satelite in orbit is?
a 70.7 kg person jumps from a window to a fire net 21.3 m below, which stretches the net 1.14 m. assume that the net behaves like a simple spring, and (a)calculate how much it would stretch if the same person were lying in it.
(b) How much would it stretch if the person jumped from 30 m?
The net would stretch 1.14 m if the person jumped from 30 m above it.
(a) To calculate how much the fire net would stretch if the same person were lying in it, we need to use Hooke's law, which states that the force exerted by a spring is proportional to its extension. We know that the net stretches 1.14 m when the person jumps from 21.3 m above it, so we can calculate the spring constant (k) as follows:
k = F/x
where F is the force exerted by the person's weight (mg), and x is the extension of the net (1.14 m). Using the formula:
F = mg
where m is the person's mass (70.7 kg) and g is the acceleration due to gravity (9.81 m/s^2), we can calculate F:
F = 70.7 kg * 9.81 m/s^2 = 693.87 N
Now we can calculate k:
k = 693.87 N / 1.14 m = 608.05 N/m
To find how much the net would stretch if the same person were lying in it, we can use the formula:
x = F/k
where F is the force exerted by the person's weight (mg), and k is the spring constant we just calculated. So:
x = 693.87 N / 608.05 N/m = 1.14 m
Therefore, the net would stretch 1.14 m if the same person were lying in it.
(b) To calculate how much the net would stretch if the person jumped from 30 m, we can use the same formula as before, but with a different force:
F = mg = 70.7 kg * 9.81 m/s^2 = 693.87 N
Now we need to calculate how much the net would stretch with this force and the spring constant we calculated earlier. We can use the formula:
x = F/k
where F is the force exerted by the person's weight (693.87 N) and k is the spring constant (608.05 N/m). So:
x = 693.87 N / 608.05 N/m = 1.14 m
Therefore, the net would stretch 1.14 m if the person jumped from 30 m above it.
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the critical angle for a ray incident in material x at the boundary of material x and material y is found to be 59.0 degrees. if the index of refraction for material y is 1.07, what is the index of refraction of material x, given that light is going from material y to x and x has a higher refractive index?
The index of refraction for material x is approximately 1.205, given the critical angle and[tex]n_y[/tex] = 1.07.
The critical angle, θ_c, is the angle of incidence at which the refracted ray in material y is at the boundary with material x. It is related to the refractive indices of the two materials by the equation:
sin(θ_c) = [tex]n_y[/tex] / [tex]n_x[/tex]
where [tex]n_y[/tex] and [tex]n_x[/tex] are the refractive indices of materials y and x, respectively. We are given that the critical angle is 59.0 degrees and the index of refraction for material y is 1.07. Rearranging the equation, we can solve for [tex]n_x[/tex]:
[tex]n_x[/tex] = [tex]n_y[/tex] / sin(θ_c)
Plugging in the given values, we have:
[tex]n_x[/tex] = 1.07 / sin(59.0°)
Using a calculator, we find:
[tex]n_x[/tex] ≈ 1.205
Therefore, the index of refraction for material x is approximately 1.205, given that light is going from material y to x, and x has a higher refractive index.
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How can the origin of meteors and meteorites be determined?
Answer:
Most meteorites found on Earth come from shattered asteroids, although some come from Mars or the Moon. In theory, small pieces of Mercury or Venus could have also reached Earth, but none have been conclusively identified. Scientists can tell where meteorites originate based on several lines of evidence.
Explanation:
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Two points are located on a rigid wheel that is rotating with decreasing angular velocity about a fixed axis. Point A is located on the rim of the wheel and point B is halfway between the rim and the axis. Which one of the following statements concerning this situation is true?
Both points have the same tangential acceleration.
Both points have the same centripetal acceleration.
The angular velocity at point A is greater than that of point B.
Both points have the same instantaneous angular velocity.
The angular velocity at point A is greater than that of point B. This is because as the wheel is rotating with decreasing angular velocity, the linear speed of point A is greater than that of point B due to the larger radius.
Therefore, point A has a greater angular velocity than point B. Both points will not have the same tangential acceleration or centripetal acceleration since they are at different distances from the axis of rotation.
The correct statement concerning the situation of two points located on a rotating wheel with decreasing angular velocity is: Both points have the same instantaneous angular velocity.
Angular velocity is a measure of how quickly something rotates around a fixed axis. Since both points A and B are on the same rigid wheel, they will have the same angular velocity at any given moment, as they rotate through the same angle in the same amount of time. The other statements are not true because:
1. Tangential acceleration depends on the distance from the axis of rotation, so point A and point B will have different tangential accelerations.
2. Centripetal acceleration also depends on the distance from the axis of rotation, so point A and point B will have different centripetal accelerations.
3. Angular velocity is the same for all points on the rotating wheel, so it is not greater at point A than at point B.
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gas pressure is caused by question 1 options: barometers gas molecules hitting other gas molecules or their container gas molecules colliding with surfaces gas molecules condensing to a liquid
Gas pressure is caused by gas molecules colliding with surfaces.
When gas molecules move and collide with the walls of a container, they exert a force on the walls, which causes the pressure of the gas in the container.
This is why gas pressure is often measured in units of force per unit area, such as pounds per square inch (psi) or pascals (Pa). While barometers can be used to measure gas pressure indirectly by measuring atmospheric pressure, the underlying cause of gas pressure is the collision of gas molecules with surfaces.
Thus, we can say that gas pressure is caused by gas molecules colliding with surfaces.
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B.
An object thrown or shot vertically into the air reaches a maximum height after t secondsâ (when time is measured inâ seconds), where t is theâ k-coordinate of the vertex of the parabola.
The maximum height of an object thrown or shot vertically into the air is reached after t seconds, where t is the k-coordinate of the vertex of the parabola.
When an object is thrown or shot vertically, its motion can be modeled by a parabolic function.
The vertex of this parabola represents the highest point the object will reach, and the k-coordinate of the vertex represents the time it takes for the object to reach that height.
Hence, The maximum height of a vertically thrown or shot object is attained at the k-coordinate of the vertex of the parabola, which corresponds to the time t in seconds.
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place in the correct order how new oceanic crust is formed from mantle rock at divergent boundaries, with the first step on top.
The correct order of how new oceanic crust is formed from mantle rock at divergent boundaries is: upwelling of mantle rock, formation of basaltic lava, spreading of lava to form new oceanic crust, formation of hydrothermal vents, and subduction of oceanic crust at a subduction zone.
The formation of new oceanic crust at divergent boundaries is a continuous process that involves several steps. The first step in the process is the upwelling of mantle rock to the ocean floor. This is caused by the divergence of the tectonic plates, which creates a gap that is filled by molten rock from the mantle.
Once the mantle rock reaches the surface, it cools and solidifies to form basaltic lava. This lava then spreads out and covers the ocean floor, forming a thin layer of new oceanic crust. As the lava cools, it contracts and forms cracks, which are filled with mineral-rich seawater that solidifies to form hydrothermal vents.
Over time, the new oceanic crust continues to move away from the divergent boundary and is pushed beneath the continental crust at a subduction zone. This process causes the oceanic crust to be recycled back into the mantle and creates a continuous cycle of new crust formation and destruction.
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Approximately how many days does it take for a massive star supernova to decline to 1% of its peak brightness?
A massive star supernova is a spectacular event that can shine as bright as an entire galaxy. However, after the initial explosion, the supernova's brightness will gradually decline over time.
This process is known as the supernova's light curve, and it can be used to determine how long it takes for the supernova to decline to a certain percentage of its peak brightness. In the case of a massive star supernova, it typically takes around 100 days for the supernova to decline to 1% of its peak brightness. However, this can vary depending on several factors, including the size and mass of the star, the distance from Earth, and the viewing angle. Understanding the light curve of a supernova is important for astronomers, as it can provide valuable information about the supernova's physical properties and the nature of the explosion. By analyzing the changes in brightness over time, astronomers can also learn more about the processes that occur during the supernova, such as the formation of a neutron star or black hole. In conclusion, it takes approximately 100 days for a massive star supernova to decline to 1% of its peak brightness, although this can vary depending on various factors.
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