To solve this problem, we derive Newton’s Law of Universal Gravitation as the basis of computation
Where: M₁ = mass of planet #1
M₂ = mass of planet #2
M = total mass
R₁ = radius of planet #1
R₂ = radius of planet #2
d₁ = initial distance between planet centers
d₂ = final distance between planet centers
a = semimajor axis of plunge orbit
v₁ = relative speed of approach at distance d₁
v₂ = relative speed of approach at distance d₂
To determine velocity during the impact of two heavenly bodies, the solution is as follows:
M₁ = M₂ = 1.8986e27 kilograms
M = M₁ + M₂ = 3.7972e27 kg
G = 6.6742e-11 m³ kg⁻¹ sec⁻²
GM = 2.5343e17 m³ sec⁻²
d₁ = 1.4e11 meters
a = d₁/2 = 7e10 meters
R₁ = R₂ = 7.1492e7 meters
d₂ = R₁ + R₂ = 1.42984e8 meters
v₁ = 0
v₂ = √[GM(2/d₂−1/a)]
v₂ = 59508.4 m/s
The final answer is 59508.4 m/s.
Answer:
this verified kid is way too smart for his own good
Explanation:
when you snap your wrist open, the frisbee ____
A. Flips.
B. Tumbles.
C. Spins.
D.Flops.
Starting the moon's cycle with the new moon phase, what phase will it be in after about a week?
A ball is dropped from the roof of a building. the mass of the ball is 3.0 kg. what is the potential energy of the ball in the instant that it is exactly 18.0 meters above the ground?
Frank and Lisa are analyzing the chart, which shows the speed at which light travels through different media. Frank says that light travels through diamond with the greatest frequency. Lisa says that light travels through air with the greatest frequency. Which best describes the accuracy of these statements? a.Frank is correct because light travels through diamond at the slowest speed, and speed and frequency have an inverse relationship. b.Lisa is correct because light travels through air at the fastest speed, and speed and frequency have a direct relationship. c.Neither person is correct because light does not change frequency when it travels through different media. d. Both people are correct because light has both an inverse and a direct relationship with frequency, depending on the media.
Neither person is correct because light does not change frequency when it travels through different media.
How can an electron in an atom lose energy to go from a higher energy level to a lower energy level? select one:
a. it exchanges gravitational potential energy for kinetic energy.
b. it loses gravitational potential energy.
c. it releases a photon equal in energy to its own energy drop.
d. it absorbs a photon equal in energy to its own energy drop.
e. it loses kinetic energy?
A solid steel sphere of density 7.86 g/cm3 and mass 1 kg spin on an axis through its center with a period of 2.3 s. given vsphere = 4 3 π r3 , what is its angular momentum? answer in units of kg m2 /s.
The solution for this problem is:
density = mass / volume
7860 = 1 / ((4/3) pi r^3)
r^3 = 1 / (7860 * 4/3*pi)
r = (1 / (7860 * 4/3*pi))^(1/3)
= 0.067 m
Inertia = (2/5)mr^2
= (2/5) x 1 x 0.067^2
= 0.0017956 kg-m^2
1/2.3 = 0.4348 rev/s
0.4348 x 2pi = 2.732 rad/s
Angular momentum = Inertia x rad/s
0.0017956 x 2.732 = 0.00490557 kg m^2/s
From the graph find the cars speed 5 seconds into the journey
Which statement accurately compares the weight of an object on these two planets
This is a large, rocky body found in space. It often orbits the sun in a belt between Mars and Jupiter.
Final answer:
Asteroids are rocky bodies in space that mostly orbit the Sun within the asteroid belt, located between Mars and Jupiter. They vary in size and are classified by composition as C-type, S-type, or M-type. The largest asteroid and dwarf planet in this belt is Ceres.
Explanation:
The large, rocky bodies that are often found orbiting the sun in a belt between Mars and Jupiter are known as asteroids. The region where most asteroids are found is called the asteroid belt, and this area extends from 2.2 to 3.3 AU from the Sun. Asteroids are mainly remnants of the initial solar system that existed before the planets formed, ranging from a few centimeters to hundreds of kilometers in size. While most asteroids reside within the asteroid belt, they are spread out with significant empty space between them, making navigation for spacecraft like Galileo and Cassini feasible.
Asteroids are classified into different types: C-type (carbonaceous), S-type (stony), and M-type (metallic). The largest known asteroid is Ceres, which is also classified as a dwarf planet. Understanding asteroids is important for planetary defense as well as for exploring the solar system's past.
On which of the following planets or celestial bodies will the mass of the object be the greatest?
The Earth because it has the greatest mass and therefore the largest force of gravity.
The Moon because it has the lowest mass and the weakest force of gravity.
Its mass will be the same on all because mass is constant, no matter the gravity.
Jupiter because it has the greatest mass and therefore the greatest force of gravity.
Answer:
Its mass will be the same on all because mass is constant, no matter the gravity
Explanation:
Inertial property of an object is its mass. Mass is a changeless quantity since it is the amount of matter contained in an object. When an object is on the surface of the earth or any other celestial body, it is influenced by the pull of gravity of that planet . Then it experiences the gravitational force which is called as weight , commonly.
It is weight that changes when an object is taken from one place to another . But it is mass that remains constant.
Suppose that a dominant allele (P) codes for a polka-dot tail and a recessive allele (p) codes for a solid colored tail. In addition, suppose that a dominant allele (L) codes for long eyelashes and a recessive allele (l) codes for short eyelashes. If two individuals heterozygous for both traits (tail color and eyelash length) mate, what's the probability of the phenotypic combinations of the offspring?
A. 9:3:3:1 ratio (9 polka-dot tails and short eyelashes, 3 polka-dot tails and long eyelashes, 3 solid tails and short eyelashes, 1 solid tail and long eyelash)
B. 1:1 ratio (half are polka-dot tails and long eyelashes; half are solid tails and short eyelashes)
C. 1:1 ratio (half are polka-dot tails and short eyelashes; half are solid tails and long eyelashes)
D. 9:3:3:1 ratio (9 polka-dot tails and long eyelashes, 3 polka-dot tails and short eyelashes, 3 solid tails and long eyelashes, 1 solid tail and short eyelash)
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Which of the following statements is true about a current-carrying wire in a magnetic field? @Somy
A. Reversing the current direction will cause the force deflecting the wire to be parallel to the magnetic field.
B. Reversing the current direction will cause the force deflecting the wire to be perpendicular to the magnetic field but in the opposite direction.
C. Reversing the current direction will not affect the force deflecting the wire.
Suppose a star the size of our Sun, but of mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 12 km, losing 3/4 of its mass in the process, what would its rotation speed be? Assume the star is a uniform sphere at all times.
(a) Assume that the thrown-off mass carries off no angular momentum, in rev/s
(b) Assume that the thrown-off mass carries off its proportional share (3/4) of the initial angular momentum, in rev/s
(a) The final angular velocity [tex](\(\omega_2\))[/tex] of the neutron star is approximately [tex]\(1.42 \times 10^{-5}\)[/tex] rad/s.
(b) The final angular velocity [tex](\(\omega_2'\))[/tex] of the neutron star is approximately [tex]\(3.54 \times 10^{-6}\)[/tex] rad/s.
**(a) Assume that the thrown-off mass carries off no angular momentum:**
1. Calculate the initial moment of inertia [tex](\(I_1\)):[/tex]
[tex]\[I_1 = \frac{2}{5} \cdot (8 \cdot \text{mass of the Sun}) \cdot (\text{radius of the Sun})^2\][/tex]
The mass of the Sun is approximately [tex]\(2 \times 10^{30}\)[/tex] kg, and the radius of the Sun is approximately 6.96 x [tex]10^8[/tex] meters. Calculate [tex]\(I_1\): \[I_1 = \frac{2}{5} \cdot (8 \times 2 \times 10^{30} \text{ kg}) \cdot (6.96 \times 10^8 \text{ m})^2\][/tex]
This gives [tex]\(I_1 \approx 3.06 \times 10^{40}\) kg m^2.[/tex]
2. Calculate the initial angular velocity [tex](\(\omega_1\)):[/tex]
The rotation period is 12 days, which is equivalent to [tex]\(12 \times 24 \times 60 \times 60\)[/tex] seconds. Calculate
[tex]\(\omega_1\): \[\omega_1 = \frac{2\pi}{12 \times 24 \times 60 \times 60} \text{ rad/s}\][/tex]
This gives [tex]\(\omega_1 \approx 1.99 \times 10^{-7}\) rad/s.[/tex]
3. Calculate the initial angular momentum [tex](\(L_1\)): \[L_1 = I_1 \cdot \omega_1 = (3.06 \times 10^{40}\, \text{kg·m²}) \cdot (1.99 \times 10^{-7}\, \text{rad/s})\][/tex]
This gives [tex]\(L_1 \approx 6.11 \times 10^{33}\) kg m^2/s.[/tex]
4. Calculate the final moment of inertia [tex](\(I_2\)):[/tex]
The final radius of the neutron star is 12 km, which is equivalent to 12,000 meters. Calculate [tex]\(I_2\):[/tex]
[tex]\[I_2 = \frac{2}{5} \cdot (3/4 \cdot \text{mass of the Sun}) \cdot (12,000 \text{ m})^2\] \[I_2 = \frac{2}{5} \cdot (3/4 \cdot 2 \times 10^{30}\, \text{kg}) \cdot (12,000\, \text{m})^2\][/tex]
This gives [tex]\(I_2 \approx 4.32 \times 10^{38}\)[/tex] kg·m².
5. Use the conservation of angular momentum [tex](\(L_1 = L_2\))[/tex] to find the final angular momentum [tex](\(L_2\)): \[L_2 = L_1 = 6.11 \times 10^{33}\, \text{kg·m²/s}\][/tex]
6. Calculate the final angular velocity [tex](\(\omega_2\))[/tex] of the neutron star:
[tex]\[\omega_2 = \frac{L_2}{I_2} = \frac{6.11 \times 10^{33}\, \text{kg·m²/s}}{4.32 \times 10^{38}\, \text{kg·m²}}\][/tex]
This gives [tex]\(\omega_2 \approx 1.42 \times 10^{-5}\)[/tex] rad/s.
**(b) Assume that the thrown-off mass carries off its proportional share (3/4) of the initial angular momentum:**
1. Calculate the final angular momentum [tex](\(L_2'\))[/tex] considering that 3/4 of the initial angular momentum is carried away by the mass that is thrown off during the collapse:
[tex]\[L_2' = (1 - \frac{3}{4}) \cdot L_1 = (1 - 0.75) \cdot 6.11 \times 10^{33}\, \text{kg·m²/s}\][/tex]
This gives [tex]\(L_2' \approx 1.53 \times 10^{33}\, \text{kg·m²/s}\).[/tex]
2. Calculate the final angular velocity [tex](\(\omega_2'\))[/tex] of the neutron star:
[tex]\[\omega_2' = \frac{L_2'}{I_2} = \frac{1.53 \times 10^{33}\, \text{kg·m²/s}}{4.32 \times 10^{38}\, \text{kg·m²}}\][/tex]
This gives [tex]\(\omega_2' \approx 3.54 \times 10^{-6}\)[/tex] rad/s.
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Which of these alkali metals has the largest atomic radius?
A) Cs
B) Fr
C) Li
D) Na
Answer:
B
Explanation:
Fr
In each of the four situations described below, something is being heated. in which case is the heating caused by radiation?
a. a heat lamp keeps a hamburger warm.
b. cooking an egg in a skillet.
c. hot air pouring from a heat vent.
d. melting ice on your sidewalk by pouring hot water on it.
In the case of a heat lamp keeping a hamburger warm, the heating is caused by radiation (Option A).
What is heat transfer?Heat transfer is the process through which internal energy from one material is transferred to another.
A heat lamp emits thermal radiation, which is a form of electromagnetic radiation in the infrared part of the spectrum. This radiation travels through the air and is absorbed by the hamburger, causing it to heat up. The heat lamp is a source of radiant heat and the hamburger is being heated by the transfer of energy by radiation.
In the case of cooking an egg in a skillet (Option B), the heating is caused by conduction.
In the case of hot air pouring from a heat vent (Option C), the heating is caused by convection.
In the case of melting ice on your sidewalk by pouring hot water on it (Option D), the heating is caused by conduction.
Thus, the heat lamp keeps a hamburger warm, the heating is caused by radiation.
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What voltage would be measured across the 45 ohm resistor?
Answer:
C) 9.0 volts
Explanation:
Describe where to look on the Periodic Table to find elements which have similar reactivity and other properties. Give an example of three elements that have those similarities.
Vast, circular to elliptical dark-colored, smooth areas of the moon are known as ________.
imagine that a tank is filled with water the hight of the liquid column is 7 meters and the area is 1.5 sq meters (m™). what's the force of gravity acting on the column of water.
2. Lower latitudes tend to have __________. (Points : 1)
lower average temperatures than higher latitudes
the same temperatures as higher latitudes
higher average temperatures than higher latitudes
you can't compare temperatures without including pressure data
Answer:
Higher average temperatures then higher latitudes. I TOOK THE TEST!
Explanation:
Calculate the frequency of a water wave that has a wavelength of 0.5 m and a speed of 4.0 m/s
Answer:
f = 8 Hz
Explanation:
Wavelength of wave = 0.5 m
Speed of wave = 4 m/s
Frequency = ?
Solution:
Formula:
f = v/λ
f = frequency
v = speed
λ = wavelength
Now we will put the values in formula.
f = v/λ
f = 4 m/s / 0.5 m
f = 8 s⁻¹
s⁻¹ = Hz
f = 8 Hz
The frequency of the water wave has a wavelength of 0.5 meters and a speed of 4 m/s will be equal to 8 Hz.
What is Wavelength?The distance between two identical locations (adjacent crests) in successive cycles is known as the wavelength, and it is used to describe waveform signals that are transmitted over wires or into space.
Typically, in wireless systems, this length is specified in meters (m), centimeters (cm), or millimeters (mm).
The wavelength is more frequently described in nanometers (nm), which are units of 10-9 m, or angstroms, which are units of 10-10 m, for infrared (IR), visible light (UV), and gamma radiation.
As per the given information provided in the question,
The wavelength, λ = 0.5 m
Speed, v = 4.0 m/s
Frequency, F = v/λ
F = 4/0.5
F = 8 Hz.
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A diver with a mass of 70.0 kg stands motionless at the top of a diving platform 3.0 m high. The diver’s initial vertical speed is zero. What is the diver’s potential energy relative to the water surface?
Final answer:
The diver's potential energy relative to the water surface, calculated using the formula PE = mgh with given values, is 2058 Joules.
Explanation:
To calculate the diver's potential energy relative to the water surface, we use the formula for gravitational potential energy, which is PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s2), and h is the height above the reference point (in this case, the water surface).
Given a diver with a mass of 70.0 kg standing 3.0 m high above the water, the calculation would be as follows:
PE = (70.0 kg) * (9.8 m/s2) * (3.0 m) = 2058 Joules.
Therefore, the diver's potential energy relative to the water surface is 2058 Joules.
Water's heat of fusion is 80 cal/g. Its specific heat is 1.0 cal/g degrees celsius, and its heat of vaporization is 540 cal/g.
A canister is filled with 330g of ice and 100g of liquid water, both at 0 degrees celsius. The canister is placed in an oven until all the water has boiled off and the canister is empty. How much energy in calories was absorbed?
Which correctly lists the outer planets from the least number of moons to the greatest number of moons?
a)Neptune, Uranus, Jupiter, Saturn
b)Saturn, Jupiter, Uranus, Neptune
c)Jupiter, Neptune, Uranus, Saturn
d)Uranus, Neptune, Jupiter, Saturn
In a cathode ray tube, the number of electrons that reach the fluorescent screen is controlled by the A. cathode. B. anode. C. grid. D. deflecting plate.
Answer:
C) The answer is grid .
Explanation:
Grid lies between cathode and anode with varying volts . It controls the no of
electrons reaching screen. It is kept closer to cathode which emits electrons.There may be more than one control grid.
How much force is required to accelerate a 2kg mass at 3 m/s2? answer key?
Using Newton's second law of motion, the force required to accelerate a 2kg mass at 3 m/s² is 6 Newtons.
To calculate the force required to accelerate a 2kg mass at 3 m/s², we can use Newton's second law of motion, which states that the force is equal to mass times acceleration (F = m imes a). Therefore, the force (F) required is:
F = 2kg imes 3 m/s² = 6 N
This means that a force of 6 Newtons is needed to accelerate the 2kg mass at the specified rate.
A coin slides over a frictionless plane and across an xy coordinate system from the origin to a point with xy coordinates (3.30 m, 5.20 m) while a constant force acts on it. the force has magnitude 9.70 n and is directed at a counterclockwise angle of 111.° from the positive direction of the x axis. how much work is done by the force on the coin during the displacement?
Work = force x distance x cos (theta) where theta is the
angle between the force and the direction of motion
component of force in x direction = 9.70N cos 111 = -3.48 N
component of force in y direction = 9.70 sin 111 = 9.06 N
Adding the two = -3.48 x 3.30 m + 9.06N x 5.20 m
= 11.484 + 47.112
= 58.60 Joules
which group in the periodic table is known as salt farmers?
carbon family
copper family
helium family
halogen family
The group in the periodic table known as salt farmers is the halogen family, which consists of fluorine, chlorine, bromine, iodine, and astatine.
The group in the periodic table known as salt farmers is the halogen family. The term 'halogen' comes from Greek roots meaning 'salt forming.' This group consists of the elements fluorine, chlorine, bromine, iodine, and astatine, which are all found in Group 17 of the periodic table. They react readily with metals to form salts, such as sodium chloride (table salt) and calcium chloride (road salt).
Halogens are known for forming compounds with metals to create salts.These elements are very reactive and can be found in Group 17.Examples of halogen compounds include sodium chloride (NaCl) and calcium chloride (CaCl₂).In contrast, the carbon family (Group 14), the copper family (transition elements), and the helium family (noble gases) do not have these properties.
When an object is moving with uniform circular motion, the centropetal acceleration of the object?
Answer:
The correct answer is "is directed toward the center of motion".
Explanation:
When an object moves in a uniform circular motion, the centrifugal acceleration of the object is directed toward the center of the motion. This acceleration is the only acceleration of the object experiences when it has constant velocity on a circular path. This causes the body to be attracted to the center of the trajectory by a centripetal force that prevents the body from entering a rectilinear trajectory.
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Which is not true of the weak nuclear force?
A. It is a repellent force.
B. It acts over a shorter range than the strong nuclear force.
C. It is an attractive force.
D. It is weaker than the strong nuclear force.
Answer: Option (A) is the correct answer.
Explanation:
A force that helps in binding protons and neutrons together in a nucleus is known as nuclear force. It is known that neutrons have no charge whereas protons have positive charge and like charges repel each other but due to the strong nuclear force which over powers the repulsion force between protons, they are held together in a nucleus.
A weak nuclear force is weaker than the strong nuclear force. Also, it acts over a shorter range than the strong nuclear force. A weak nuclear force is also attractive in nature.
But a weak nuclear force is not repellent in nature.
Thus, we can conclude that a weak nuclear force is a repellent force is not true.