Static friction ensures forces are balanced when an object is at rest by matching the applied force up to its limit. This balance means that the net external force on the object is zero. Such conditions imply static equilibrium.
When an object is at rest and static friction is acting on it, the forces are said to be balanced. This state of balance or equilibrium exists because the net external force on the object is zero. According to Newton's first law, an object will remain at rest if no unbalanced force acts on it.
To break it down step-by-step:
The object remains at rest, indicating that all forces acting on it are balanced.The static friction force adjusts to exactly match the applied force, up to its maximum limit, preventing motion.This balance implies that the sum of all forces in any direction is zero.For example, consider a heavy crate on the ground. When you apply a small force to push it, if the crate does not move, the force of static friction equals the applied force but in the opposite direction. This indicates static equilibrium where forces are balanced.
To further understand, let's note that static friction does no work because the point of contact does not move relative to the surface. This characteristic helps in identifying balance as no work is done when forces are perfectly equal and opposite.
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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Starting the moon's cycle with the new moon phase, what phase will it be in after about a week?
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.
Which statement accurately compares the weight of an object on these two planets
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.
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?
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.
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.
What voltage would be measured across the 45 ohm resistor?
Answer:
C) 9.0 volts
Explanation:
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
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?
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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A gas has a volume of 300 ml at 300 kpa. what will its volume be if the pressure is changed to 600 kpa?
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
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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If an element has 10 electrons, how many of them will be in the 2nd energy level?
Answer:
If an element has 10 electrons, 8 of them will be in the second energy level.
Explanation:
There are 7 energy levels, numbered from 1 to 7, and in which electrons are distributed, logically in order according to their energy level.
Each level is divided into sub-levels. These sub-levels into which each level is divided can be up to 4, which are called: s, p, d, f. In the sub-level s there can only be a maximum of 2 electrons, in p there can be a maximum of 6 electrons, in the sub-level d 10 electrons and finally in the sub-level f there can be a maximum of 14 electrons.
In level 1 there is only one sub-level, which will be the s. In level 2 there are 2 sub-levels, the s and the p. At level 3 there are 3 sub-levels s, p and d. And at level 4 there are 4 sub-levels, the s, the p, the d and the f.
Then, in level 1 there is only a maximum two electrons. In level 2 there are a maximum of 8 electrons. At level 3 there are a maximum of 18 electrons. And at level 4 there are a maximum of 32 electrons.
The filling of the orbitals occurs in increasing order of energy, that is, from the orbitals of lower energy to those of higher energy.
So, considering that at level 1 there can only be two electrons and that it is the lowest energy level, 2 of the 10 electrons that the element has will be located at that level. So 8 electrons remain to be located.
The next level to fill with electrons is 2. As this level can enter a maximum of 8 electrons, the electrons that remained to be located in level 1 will be located in level 2.
If an element has 10 electrons, 8 of them will be in the second energy level.
How are ocean ridges formed
when you snap your wrist open, the frisbee ____
A. Flips.
B. Tumbles.
C. Spins.
D.Flops.
What will happen if you rub two different materials together?
From the graph find the cars speed 5 seconds into the journey
A __________ sign on a truck means that the load on the truck is potentially dangerous.
A hazardous sign on a truck means that the load on the truck is potentially dangerous.
A hazardous sign on a truck means that the load on the truck is potentially dangerous. These signs are part of a system of hazard communication that includes symbols, labels, and placards to quickly and effectively convey information about the hazards of the materials being transported. The use of such signs is essential for the safety of everyone on the road, including the truck driver, other motorists, emergency responders, and the general public. It helps to ensure that appropriate precautions are taken when handling, transporting, and in the event of an accident involving, these materials.
The surface pressures at the bases of warm and cold columns of air are equal. air pressure in the warm column of air will ______ with increasing height __________ than in the cold column.
How many neutrons does element X have if its atomic number is 36 and its mass number is 74?
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.
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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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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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.
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.
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: