The acceleration of the body is provided by the tension in the rope.
What is centripetal acceleration?The centripetal acceleration is given by a = v^2/r. v = velocity of the body, r = radius
a = (8.40 m/s)^2/(8.50 m)
a = 8.3 m/s^2
The tension in the rope is the force that provides the centripetal force in the rope.
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I NEED HELP!!!! THIS IS A CER "Write a scientific explanation describing how a rabbit, which eats plants, gets energy to live and grow"
I NEED CLAIM, EVIDENCE, and REASONING
Answer:
A rabbit which needs food specifically food from plants because they are vegetarians, to help them grow. The energy that the plant holds is given to the rabbit when eaten. The plant feeds the bunny its nutrients which tells the muscles to keep going and get stronger and tells the rest of the body to grow.
Explanation:
A team of people who traveled to the North Pole by dogsled lived on butter because they needed to consume 6 000 dietitian's Calories each day. Because the ice there is lumpy and irregular, they had to help the dogs by pushing and lifting the load. Assume they had a 16-hour working day and that each person could lift a 500-N load. How many times would a person have to lift this weight 1.00 m upwards in a constant gravitational field, where (g = 9.80m/s2) where to do the work equivalent to 6 000 Calories?
Answer:
The right solution is "50200 days".
Explanation:
Given:
Calories intake,
= 6000 kcal,
or,
= \(2.52\times 10^7 \ J\)
Force,
= 500 N
As we know,
⇒ \(Work \ done = Force\times distance\)
Or,
⇒ \(distance = \frac{Work \ done}{Force}\)
By putting the values, we get
\(=\frac{2.52\times 10^7}{500}\)
\(=0.502\times 10^5\)
\(=50200 \ m\)
hence,
The number of days will be:
= \(\frac{50200}{1}\)
= \(50200 \ days\)
A sheet of glass having an index of refraction of 1.49 is to be coated with a film of material having an index of refraction of 1.62 in order that green light with a wavelength of 534 nm (in air) will be preferentially transmitted via constructive interference. (a) What is the minimum thickness of the film that will achieve the result
Answer:
the required minimum thickness is 179.19 nm
Explanation:
Given the data in the question;
Refraction index of air n₁ = 1
Refraction index of sheet n₂ = 1.49
Refraction index of film n₃ = 1.62
wavelength of green light λ = 534 nm
In the data given, n₂ > n₃
so, this case has no pie-phase shift,
the condition for constructive interference will be;
mλ = 2Ln₂
L = mλ / 2n₂
so we substitute
L = m(534) / 2( 1.49 )
L = m( 534/ 2.98 )
L = m( 179.19 nm )
so for minimum value of L,
let m = 1
such that, L\(_{min\) will be;
L\(_{min\) = 1 × ( 179.19 nm )
L\(_{min\) = 179.19 nm
Therefore, the required minimum thickness is 179.19 nm
On a fishing trip Justin rides in a boat 12 km south. The fish aren't biting so they go 4 km west. They then follow a school of fish 1 km north. What distance did they cover?
Given
12 km south
4 km west
1 km north
Procedure
Let's do a diagram
The distance they covered is just the sum of all the distance they went
Total distance = 12 + 4 + 1 = 17 km
The displacement, however, is the vector sum. It answer's the question of how far are you from your starting point.
1) The cause of magnetism is
A. atoms forming “domains” that are arranged randomly
B. atoms forming "domains” that are arranged uniformly
C. atoms forming "dolomites” that are arranged randomly
D. atoms forming “dolomites” that are arranged uniformly
Answer:
I think it's A, I'm not sure though
Please help me!!
1 a) Compare the speed that light waves travel in air to the speed that sound waves travel in the air. (Show results in meters/second)
1 b) How many times faster do light waves travel in the air in comparison to sound waves in air? (show working out)
2) Compare the speed of light in water to the speed of sound in water. (Show results in meters/second)
Answer:A sound wave is a pressure disturbance that travels through a medium by means of particle-to-particle interaction.As one particle becomes disturbed,it exerts a force on the next adjacent particle, disturbing that particle from rest and transporting the energy through the medium.Like any wave,the speed of a sound wave refers to how fast the disturbance is passed from particle to particle.While frequency refers to the number of vibrations that an individual particle makes per unit of time, speed refers to the distance that the disturbance travels per unit of time.
Since the speed of a wave is defined as the distance that a point on a wave (such as a compression or a rarefaction)travels per unit of time,it is often expressed in units of meters/second (abbreviated m/s). In equation form, this is speed = distance/time
The faster a sound wave travels,the more distance it will cover in the same period of time.If a sound wave were observed to travel a distance of 700 meters in 2 seconds,then the speed of the wave would be 350 m/s. A slower wave would cover less distance - perhaps 660 meters - in the same time period of 2 seconds and thus have a speed of 330 m/s.Faster waves cover more distance in the same period of time.
The speed of any wave depends upon the properties of the medium through which the wave is traveling.Typically there are two essential types of properties that affect wave speed - inertial properties and elastic properties.Elastic properties are those properties related to the tendency of a material to maintain its shape and not deform whenever a force or stress is applied to it.A material such as steel will experience a very small deformation of shape and dimension when a stress is applied to it.Steel is a rigid material with a high elasticity.On the other hand,a material such as a rubber band is highly flexible;when a force is applied to stretch the rubber band,it deforms or changes its shape readily.A small stress on the rubber band causes a large deformation.Steel is considered to be a stiff or rigid material,whereas a rubber band is considered a flexible material. At the particle level,a stiff or rigid material is characterized by atoms and/or molecules with strong attractions for each other.The phase of matter has a tremendous impact upon the elastic properties of the medium.For this reason,longitudinal sound waves travel faster in solids than they do in liquids than they do in gases.Even though the inertial factor may favor gases,the elastic factor has a greater influence on the speed (v) of a wave,thus yielding this general pattern:solids > liquids > gases The density of a medium is an example of an inertial property.The greater the inertia (i.e.mass density) of individual particles of the medium,the less responsive they will be to the interactions between neighboring particles and the slower that the wave will be. However,within a single phase of matter,the inertial property of density tends to be the property that has a greatest impact upon the speed of sound.Like any liquid,water has a tendency to evaporate.As it does,particles of gaseous water become mixed in the air.The temperature will affect the strength of the particle interactions an elastic property.At normal atmospheric pressure,the temperature dependence of the speed of a sound wave through dry air is approximated by the following equation:
v = 331 m/s + (0.6 m/s/C)•T
where T is the temperature of the air in degrees Celsius.Using this equation to determine the speed of a sound wave in air at a temperature of 20 degrees Celsius yields the following solution.
v = 343 m/s
(The equation itself does not have any theoretical basis;it is simply the result of inspecting temperature-speed data for this temperature range.Other equations do exist that are based upon theoretical reasoning and provide accurate data for all temperatures.The speed of light as it travels through air and space is much faster than that of sound;it travels at 300 million meters per second or 273,400 miles per hour.Visible light can also travel through other things besides through air and through space.The speed of light in water is approximately 2.26×108 2.26 × 10 8 meters per second.
Two vectors A and B both lie in the xy-plane.
a. Is it possible for A to have the same magnitude as B but different components?
b. Is it possible for A to have the same components as B but a different magnitude?
Answer:
A. Yes its possible by employing Pythagoras theorem we can see that similar triangles can have similar hypotenuse but different length
B.no it's not possible also from Pythagoras of they have same components it must be the same triangle
What do light waves NOT do when intereacting with matter
A. Absorbed
B. Reflected
C. Transmitted
D. Dissolve
Answer:
D. Dissolve
Explanation:
A light wave is not a soluble substance, so it cannot dissolve. But it can totally do A, B, and C.
Which interaction has the highest electrostatic potential energy?
O A +2 and -2 particle separated by a distance of 5 nm.
O A +1 and -2 particle separated by a distance of 5 nm.
O A +2 and +2 particle separated by a distance of 10 nm.
O A +2 and -2 particle separated by a distance of 10 nm.
O A +2 and +2 particle separated by a distance of 100 nm.
O A +1 and -2 particle separated by a distance of 10 nm.
O A +2 and +2 particle separated by a distance of 5 nm.
Answer:
The interaction with the highest electrostatic potential energy is:
A +1 and -2 particle separated by a distance of 5 nm.
Explanation:
The electrostatic potential energy between two charged particles depends on the magnitude of their charges and the distance between them. The formula for calculating electrostatic potential energy is:
U = k * (q1 * q2) / d
where U is the electrostatic potential energy, k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and d is the distance between them.
In the given options, the interaction between +1 and -2 particles separated by a distance of 5 nm has the highest electrostatic potential energy because the charges have a higher magnitude (compared to other options) and they are close to each other, resulting in a stronger electrostatic force of attraction. The other options either have smaller charges, larger distances, or both, leading to lower electrostatic potential energy.
CORRECT ANSWER GETS BRAINLIEST
Answer:
Wax melts as it absorb heat from flame
Explanation:
To know which option is correct, it is important that we know what chemical changes and physical changes are all about.
Chemical change is a change in which the process is not easily reversed and it produces new substance.
Physical change is more like the opposite of chemical change. In this change, the process is easily reversed and no new substance is produced.
Considering the options given above,
1. Iron combines with oxygen to produce rust is a chemical change since a new substance (rust) is formed and we can not reverse the process to get back iron and oxygen.
2. Wax melts as it absorb heat from flame is a physical change since no new substance is formed and we obtained the wax by allowing it to solidified.
3. Pure sodium explodes when dropped in water is a chemical change because we can not reverse the process to get back the sodium.
4. Glucose molecules are produced in plant leaf is also a chemical change.
From the illustrations above, it is evident that: 'Wax melts as it absorb heat from flame' is not a chemical
The mass of Jupiter can be calculated by
A) measuring the orbital period and distance of Jupiter's orbit around the Sun.
B) measuring the orbital period and distance of one of Jupiter's moons.
C) measuring the orbital speed of one of Jupiter's moons.
D) knowing the Sun's mass and measuring how Jupiter's speed changes during its elliptical orbit around the Sun.
E) knowing the Sun's mass and measuring the average distance of Jupiter from the Sun.
Knowing the Sun's mass and measuring how Jupiter's speed changes during its elliptical orbit around the Sun.
What do you mean by mass?
Mass is a fundamental physical property of an object that measures the amount of matter it contains. In other words, mass is a measure of the object's inertia, or resistance to changes in its motion. The more massive an object is, the harder it is to accelerate it, and the greater its gravitational attraction to other objects.The SI unit of mass is the kilogram (kg).
The principles of planetary motion established by Kepler and Newton and the laws of gravitation can be used to calculate Jupiter's mass. The Sun and Jupiter's gravitational pull on each other is determined by their relative sizes, masses, and separation. The gravitational force pulling Jupiter towards the Sun can be computed using the period and distance of Jupiter's elliptical orbit around the Sun as well as the mass of the Sun. Jupiter's acceleration, which can be determined from variations in its speed during its elliptical orbit, is connected to the force of gravity that is acting on it.
It is possible to calculate Jupiter's mass using these measurements and computations. For an exact calculation of Jupiter's mass, the other methods offered are insufficient. Option A) gives details regarding
These data and computations can be used to estimate Jupiter's mass. Jupiter's mass cannot be reliably calculated using the other alternatives provided. Option A) includes details on Jupiter's orbit but does not immediately provide details regarding its mass. The orbital period and speed of Jupiter's moons are disclosed in options B) and C), although these numbers also rely on the moons' mass, their distance from Jupiter, and other factors. While Option E) provides data on Jupiter's average separation from the Sun, it does not provide data on its mass.
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⚠️Pls help me this is due soon!⚠️
professional is the answer
3rd
An object is attached to a trolley with a 0.80 kg mass, which is then pushed into an identical trolley at a speed of 1.1 m / s. The two trolleys couple together and move at a speed of 0.70 m / s after the collision. Calculate the mass of the object.
The mass of the object is approximately 0.457 kg.
The mass of the object attached to the trolley can be calculated using the principle of conservation of momentum. Since the two trolleys couple together and move as a single system after the collision, the total momentum before and after the collision should be the same. Given the mass of one trolley is 0.80 kg and the initial speed is 1.1 m/s, the momentum before the collision is 0.80 kg * 1.1 m/s = 0.88 kg·m/s. After the collision, the total mass is the sum of the two trolleys, and the final speed is 0.70 m/s.
Using the momentum equation, the mass of the object can be calculated as follows:
Total momentum before collision = Total momentum after collision
0.88 kg·m/s = (0.80 kg + mass of the object) * 0.70 m/s
Solving for the mass of the object, we get:
0.88 kg·m/s = (0.80 kg + mass of the object) * 0.70 m/s
0.88 kg·m/s = 0.56 kg + 0.70 kg * mass of the object
0.88 kg·m/s - 0.56 kg = 0.70 kg * mass of the object
0.32 kg = 0.70 kg * mass of the object
Dividing both sides by 0.70 kg, we find:
mass of the object = 0.32 kg / 0.70 kg = 0.457 kg
The two trolleys collide and couple together, the total momentum before the collision is equal to the total momentum after the collision according to the principle of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity. In this case, the mass of one trolley is known (0.80 kg) and the initial speed is given (1.1 m/s), allowing us to calculate the momentum before the collision.
After the collision, the two trolleys move together at a new speed (0.70 m/s). By setting the initial momentum equal to the final momentum and solving for the unknown mass of the object, we can find its value.
In the calculation, we subtract the masses of the two trolleys from the total mass in order to isolate the mass of the object.
Dividing the difference in momentum by the product of the known mass and the new speed, we obtain the mass of the object. In this case, the mass of the object is approximately 0.457 kg.
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A 0.16 k/g hockey puck is moving on an icy Horizontal service with the speed of 5MSA player strikes the Puck by hockey stick after the impact the Puck moves in opposite direction with the speed of 9MS of the Puck was the in contact with the stick for 0 points 005S what is the average force of the Puck by the stick
According to Newton's second law of motion, 12.8 N is the average force of the Puck
Newton's Second Law of MotionIt states that, the rate of change of momentum is directly to the force applied. That is,
F = m(v - u)/t
Given that a 0.16 k/g hockey puck is moving on an icy Horizontal service with the speed of 5 m/s player strikes the Puck by hockey stick after the impact the Puck moves in opposite direction with the speed of 9 m/s of the Puck was the in contact with the stick for 0 points 0.05 s
The average force of the Puck by the stick can be calculated by using the formula above.
Where
m = 0.16 kgu = 5 m/sv = 9 m/st = 0.05 sSubstitute all the parameters
F = 0.16(9 - 5)/0.05
F = 0.16(4)/0.05
F = 0.64/0.05
F = 12.8 N
Therefore, the average force of the Puck by the stick is 12.8 N
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Sketch the pattern of the lines of forces around two positive charge separated from each other
The pattern of lines of force around two positive charges separated from each other demonstrates the repulsive nature of like charges and the direction and strength of the electric field between them.
When two positive charges are separated from each other, the lines of force (also known as electric field lines) originate from one positive charge and terminate on the other positive charge. The lines of force follow a pattern that reflects the repulsion between the positive charges.
Here's a verbal description of the pattern:
From each positive charge, the lines of force radiate outward in all directions.
The lines of force are evenly spaced and radially symmetric around each charge, indicating that the electric field strength is the same at all points along a given line.
As the lines of force move away from each charge, they curve away from each other, reflecting the repulsion between the positive charges.
The density of lines of force is higher near the charges and decreases as they move further apart.
The lines of force never cross each other, maintaining their continuous and unbroken nature.
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Calculate the quantity of heat energy which must be transferred to 2.25 kg of brass to raise its temperature from 20°C to 240°C if the specific heat of brass is 394 J/kgK.
The quantity of heat energy that must be transferred to 2.25 kg of brass to raise its temperature from 20 °C to 240 °C is 195030 J
How do i determine the quantity of heat energy?First, we shall list out the given parameters from the question. This is shown below:
Mass of brass (M) = 2.25 Kg Initial temperature of brass (T₁) = 20 °CFinal temperature of brass (T₂) = 240 °CChange in temperature of brass (ΔT) = 240 - 20 = 220 °CSpecific heat capacity of brass (C) = 394 J/kgKQuantity of heat energy (Q) =?The quantity of heat energy that must be transferred can be obtained as follow:
Q = MCΔT
= 2.25 × 394 × 220
= 195030 J
Thus, we can conclude quantity of heat energy that must be transferred is 195030 J
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I chose A. is it right?
If a particular cell is known to be round and incapable of producing its own food, which one of these organelles would you assume the cell must have?(1 point)
CENTRAL VACUOL
plasma membrane
cell wall
chloroplast
Answer:
nice try but it's plasma membrane
The cell that is known to produce their own food should have a central vacuole. The correct option is A.
What is a vacuole?A vacuole is a cell organelle that is membrane-bound. Vacuoles are generally small in animal cells and help to sequester waste products.
Vacuoles in plant cells help to retain water balance. A solo vacuole can sometimes take up the maximum of the interior space of a plant cell.
Plant cells have much larger vacuoles than animal cells. When a plant cell stops growing, it usually has one very large vacuole.
That vacuole can sometimes take up more than half of the cell's volume. The vacuole can hold a lot of water or food.
The given cell is known to be round and incapable of producing its own food, so it must be having a central vacuole.
The correct option is A.
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calculate the boyant force on 1.0x10^7 of solid steel completely submeg in water and compete this with steel weight
The required buoyant force of the solid steel submerged in water is 124681934 N.
What is force?Force is defined as an object which is in a state of motion then its rate of change of momentum is called force.
Here,
To calculate the buoyant force on the steel object, we need to first determine the volume of the steel object. Let's assume the density of steel is 7,860 kg/m³.
Mass of the steel object = 1.0x10⁷ kg
Density of steel = 7,860 kg/m³
The volume of steel object = Mass of steel object / Density of steel
= (1.0x10⁷ kg) / (7,860 kg/m³)
= 1271.78 m³
Buoyant force = Weight of displaced water
= Density of water x Volume of displaced water x gravitational acceleration
= (1000 kg/m³) x (1271.78 m³) x (9.81 m/s²)
= 124681934 N
The weight of the steel object is given as 1.0x10⁷ N.
Comparing the buoyant force with the weight of the steel object, we find that the buoyant force is greater than the weight of the steel object. This means that the steel object will float in water, as the buoyant force is enough to counteract the weight of the object.
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The valid digits in a measurement are called the significant digits. True or False
i think
Answer:
physics. The ______ is a systematic way to observe, experiment, and analyze the world. scientific method. The valid digits in a measurement are called the. significant digits.
Explanation:
truth'
A person is 88 J of work lifting a grocery bag straight off the ground to a height of 1.7 m what is a grocery bags mass
Answer:
5.277 kg
Explanation:
Since the formula for work is W = F * d and we are given distance and work, the force on the grocery bag is 88 = F * 1.7 F = 88 / 1.7 = 51.765 N.
We also know that force follows the equation F = m * a. Since the constant gravitational acceleration on earth is 9.81 m / s^2, we can find the mass through 51.765 = m * 9.81 m = 51.765/9.81 = 5.277 kg
A silver block of silver block of density 10.5 g/cm3 has a volume of 30 cm3. Which of the following is the correct mass of the block
➝ Density of block = 10.5 g/cm³
➝ Volume of block = 30 cm³
We have to find mass of block\(.\)
➠ Density is defined as mass of substance per unit volume\(.\)
\(\dag\:\boxed{\bf{Density=\dfrac{Mass}{Volume}}}\)
\(:\implies\sf\:Mass=Density\times Volume\)
\(:\implies\sf\:Mass=10.5\times 30\)
\(:\implies\boxed{\boxed{\bf{\red{Mass=315\:g}}}}\)
How to solve conservation of momentum
Answer:
Step 1: List the mass and velocity of the object. Step 2: Convert any values into SI units (kg, m, s). Step 3: Multiply the mass and velocity of the object together to get the momentum of the object.
Write a paragraph about the cartoon. Tell what he is trying to do. Will it work and why? What do you think will happen? Use the following words, static electricity, lightning, electrons, positive and negative charges.
Answer:
They are trying to jump-start a car using a kite and lightning connected to the battery. This will not work because there is no positive or negative charged side to the circuit.
Explanation:
What is an effect of an object getting wet?
Answer:
once light hits a wet shirt, that water layer causes less of the blue shirt's blue wavelengths of light to be reflected toward your eyes and more of the blue light to be refracted, or bounce away from you, back into the fabric.
Explanation:
a roller coaster weighs 2000 kg This ride includes an initial vertical drop of 59.3 m.
Assume that the roller coaster has a speed of nearly zero as it crests the top of the hill.
If the track was frictionless, find the speed of the roller coaster at the bottom of
the hill.
The speed of the roller coaster at the bottom of the hill if the track was frictionless is 34.04 m/s.
Given that the weight of the roller coaster is 2000 kg and the initial vertical drop of the ride is 59.3 m. We are to find the speed of the roller coaster at the bottom of the hill if the track was frictionless.We know that the roller coaster will lose potential energy due to the vertical drop. Assuming there is no friction, the potential energy will be converted into kinetic energy at the bottom of the hill.Considering the conservation of energy between the potential and kinetic energy, we can set the initial potential energy equal to the final kinetic energy. We can use the formula to calculate potential energy, which is PE = mgh where m = 2000 kg, g = 9.8 m/s², and h = 59.3 m. Therefore,PE = 2000 kg × 9.8 m/s² × 59.3 m = 1,157,924 JWe can use the formula to calculate kinetic energy, which is KE = 1/2mv² where m = 2000 kg and v is the final velocity. Therefore,KE = 1/2 × 2000 kg × v².The total energy remains constant as we know there is no friction. Therefore the final kinetic energy will be equal to the initial potential energy,1,157,924 J = 1/2 × 2000 kg × v²v² = (2 × 1,157,924 J) / 2000 kgv² = 1157.924v = √1157.924v = 34.04 m/s.
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30 POINTS PLS HELP NO LINKS PLS :/
In a wave, each particle of the medium vibrates, or oscillates, around a _____________.
A. Corner
B. Noise
C. Variable position
D. Fixed position
Answer:
C
Explanation:
trust me
D. Fixed position ,mean position , Equilibrium position.
What is wave motion?Wave motion is the transfer of energy and momentum from one point of the medium to another point of the medium without actual transport of matter between two points.
The particles of the medium vibrate about their equilibrium position in a direction parallel to the direction of propagation of the wave is called a longitudinal waves.
Characteristics of Wave Motion
In wave motion, the disturbance travels through the medium due to repeated periodic oscillations of the particles of the medium about their mean position (or) Equilibrium position.
Energy and momentum are transferred from one point to another without any actual transfer of the particles of the medium.
There is a regular phase difference between the particles of the medium because each particle receives disturbance little later than its preceding particle.
Therefore,
In a wave, each particle of the medium vibrates, or oscillates, around a fixed position.
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A rock is shot straight upward with sling-shot. The intial velocity is 24.5 m/s where the downward
acceleration due to gravity is 9.81 m/s2. What is the rock'sdisplacement after 1.00 s?
Answer:
Explanation:
If launch spot is origin and UP the positive direction.
s = s₀ + v₀t + ½at²
s = 0 + 24.5(1.00) + ½(-9.81)(1.00²)
s = 19.595
rounding to the 3 significant digits of the question numerals
s = 19.6 m upward
PLS ANSWER WILL MARK BRANLIEST!!!!!!!!!!!!
Describe the life cycle of a star before it collapses into a black hole.
Describe the life cycle of a star before it becomes a black dwarf.
What is the likely outcome of our sun? *
The sun will supernova and become a black hole.
The sun will swell, encompassing the inner planets and collapses into a dwarf star.
The sun will become a pulsar.
How Do You Know?
P.S. the how do you know is only for the last question
1) describe the life cycle of a star before it collapses into a black hole.
1) describe the life cycle of a star before it collapses into a black hole.ans: A star's life cycle is determined by its mass. The larger its mass, the shorter its life cycle. A star's mass is determined by the amount of matter that is available in its nebula, the giant cloud of gas and dust from which it was born. Over time, the hydrogen gas in the nebula is pulled together by gravity and it begins to spin. As the gas spins faster, it heats up and becomes as a protostar. Eventually the temperature reaches 15,000,000 degrees and nuclear fusion occurs in the cloud's core. The cloud begins to glow brightly, contracts a little, and becomes stable. It is now a main sequence star and will remain in this stage, shining for millions to billions of years to come. This is the stage our Sun is at right now.
2) describe the life cycle of a star before it becomes a dwarf.
ans: The life cycle of a low mass star (left oval) and a high mass star (right oval). ... As the core collapses, the outer layers of the star are expelled. A planetary nebula is formed by the outer layers. The core remains as a white dwarf and eventually cools to become a black dwarf.
3) what is the likely outcome of our sun?
ans: All stars die, and eventually — in about 5 billion years — our sun will, too. Once its supply of hydrogen is exhausted, the final, dramatic stages of its life will unfold, as our host star expands to become a red giant and then tears its body to pieces to condense into a white dwarf.
39.
(a) To what temperature must you raise a resistor made of constantan to double its resistance, assuming a
constant temperature coefficient of resistivity? (b) To cut it in half? (c) What is unreasonable about these
results? (d) Which assumptions are unreasonable, or which premises are inconsistent?
(a) To double the resistance of a resistor made of constantan, it must be raised to a temperature of approximately 100°C.
(b) To cut the resistance of a resistor made of constantan in half, it must be cooled to approximately -200°C.
(c) These results are unreasonable because constantan has a positive temperature coefficient of resistivity, meaning that its resistance increases as temperature increases and decreases as temperature decreases.
(d) The assumption that constantan has a constant temperature coefficient of resistivity is unreasonable, as it actually has a positive temperature coefficient of resistivity.
What is the resistance?We know that the resistance has to do with the opposition that is offered to the flow of current and the resistance would depend on the kind of material that have been used in the resistor.
We also have to know that the resistance of the resistor would depend on the temperature and as such the resistance does vary with the temperature of the system.
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answer and solution to this question
Frequency= 30 Hz, Period= 0.0333 s, Wave Number=15.708 rad/m, Wave Function= y(x, t) = 0.05 sin(15.708x - 94.248t), Transverse displacement= -0.013 m, Time= 0.297 s.
How to calculate the frequency?(a) To find the frequency (f), we can use the equation: wave speed = frequency x wavelength. Rearranging this equation, we get:
frequency = wave speed / wavelength
Substituting the given values, we get:
frequency = 12 m/s / 0.4 m = 30 Hz
Therefore, the frequency of the wave is 30 Hz.
To find the period (T), we can use the equation:
period = 1 / frequency
Substituting the frequency value we just calculated, we get:
period = 1 / 30 Hz = 0.0333... s (rounded to four decimal places)
Therefore, the period of the wave is approximately 0.0333 s.
To find the wave number (k), we can use the equation:
wave number = 2π / wavelength
Substituting the given values, we get:
wave number = 2π / 0.4 m = 15.708 rad/m (rounded to three decimal places)
Therefore, the wave number of the wave is approximately 15.708 rad/m.
(b) The wave function for a transverse wave on a string is given by:
y(x, t) = A sin(kx - ωt + φ)
where A is the amplitude, k is the wave number, x is the position of the point on the string, t is the time, ω is the angular frequency, and φ is the phase constant.
We already know the values of A, k, and ω from the previous calculations. To find φ, we can use the given initial condition: "at t = 0 end of the string has zero displacement and is moving upward". This means that y(0,0) = 0 and ∂y/∂t(0,0) > 0. Substituting these conditions into the wave function, we get:
0 = A sin(0 + φ)
∂y/∂t = -Aω cos(0 + φ)
Since sin(0 + φ) = sin(φ) = 0 (because sin(0) = 0), we get:
φ = nπ, where n is an integer
Since cos(0 + φ) = cos(φ) = 1 (because cos(0) = 1) and ∂y/∂t(0,0) > 0, we get:
n = 0 or 2
Therefore, the possible values of φ are 0 or 2π.
Substituting the values of A, k, ω, and φ, we get:
y(x, t) = 0.05 sin(15.708x - 94.248t)
Therefore, the wave function describing the wave is:
y(x, t) = 0.05 sin(15.708x - 94.248t)
(c) To find the transverse displacement of a wave at x = 0.25 m and t = 0.15 s, we can use the wave function we just found:
y(0.25, 0.15) = 0.05 sin(15.708(0.25) - 94.248(0.15))
y(0.25, 0.15) ≈ -0.013 m (rounded to three decimal places)
Therefore, the transverse displacement of the wave at x = 0.25 m and t = 0.15 s is approximately -0.013 m.
(d) To find how much time must elapse from the instant in part (c) until the point at x = 0.25 m has zero displacement,
From part (c), we know that the transverse displacement of the wave at x = 0.25 m and t = 0.15 s is approximately -0.013 m. We need to find the time it takes for this point to return to zero displacement.
We can use the wave function we found in part (b) and set y(0.25, t) = 0:
0 = 0.05 sin(15.708(0.25) - 94.248t)
Since sin(θ) = 0 when θ = nπ (where n is an integer), we get:
15.708(0.25) - 94.248t = nπ
Solving for t, we get:
t = (15.708(0.25) - nπ) / 94.248
To find the smallest positive value of t that satisfies this equation, we need to use the smallest positive value of n that makes the right-hand side of the equation positive (because we want to find the time it takes for the point at x = 0.25 m to return to zero displacement, which happens after the point has completed a full cycle). We can see from the equation that n must be an even integer to make the right-hand side positive. The smallest even integer greater than zero is 2. Substituting n = 2, we get:
t = (15.708(0.25) - 2π) / 94.248
t ≈ 0.297 s (rounded to three decimal places)
Therefore, the time it takes for the point at x = 0.25 m to return to zero displacement is approximately 0.297 s.
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