What is the relationship between the p waves and the s waves and their travel times?
Answers
P-waves and S-waves have different propagation characteristics, speeds of travel, paths of travel, and effects on materials. P-waves are faster, travel through both solid and liquid mediums, and arrive before S-waves, while S-waves are slower, can only travel through solids, and arrive after P-waves.
P-waves (primary waves) and S-waves (secondary waves) are two types of seismic waves generated by earthquakes or other sources of energy. They travel through the Earth and provide valuable information about its interior.
The key differences between P-waves and S-waves are their propagation characteristics and travel times. Here's a summary of their properties:
1. Propagation:
- P-waves: P-waves are longitudinal waves, which means that they propagate by compressing and expanding the material in the same direction as their wave travel. They can travel through both solid and liquid mediums.
- S-waves: S-waves are transverse waves, which means that they propagate by moving the material perpendicular to the direction of wave travel. They can only travel through solid mediums.
2. Speed of Travel:
- P-waves: P-waves are faster than S-waves and typically have a speed of about 1.7 times that of S-waves. They are the first seismic waves to arrive at a seismograph station after an earthquake.
- S-waves: S-waves are slower than P-waves and have a speed of about 3.5 km/s. They arrive at seismograph stations after P-waves.
3. Path of Travel:
- P-waves: P-waves travel in a straight line, and they can pass through the Earth's interior, including the core, mantle, and crust.
- S-waves: S-waves travel in a more complex path, as they cannot pass through the Earth's liquid outer core. Therefore, they only propagate through the solid parts of the Earth, such as the mantle and crust.
4. Effects on Material:
- P-waves: P-waves cause compression and expansion of the material they pass through. They result in the oscillation of particles in the same direction as the wave travel.
- S-waves: S-waves cause shear motion in the material they pass through. This motion is perpendicular to the direction of wave travel and causes particles to move in a transverse pattern.
In terms of travel times, P-waves reach a given location before S-waves during an earthquake. This time difference between the arrival of P-waves and S-waves is used to determine the epicenter of an earthquake. By measuring the time lag between the arrival of P-waves and S-waves at different seismograph stations, can triangulate the earthquake's origin point.
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Related Questions
A 20.0-kg cannon ball is fired from a cannon with a muzzle speed of 100 m/s at an angle of 20.0° with the horizontal. Use the conservation of energy principle to find the maximum height reached by ba
Answers
A 20.0 kg cannonball is fired from a cannon with a muzzle speed of 100 m/s at an angle of 20.0°. Using conservation of energy, the maximum height reached by the cannonball is approximately 510.2 meters.
A cannon ball weighing 20.0 kg is launched from a cannon with an initial velocity of 100 m/s at an angle of 20.0° above the horizontal.
To determine the maximum height reached by the cannonball using the conservation of energy principle, we consider the conversion of kinetic energy into gravitational potential energy.
Initially, the cannonball has only kinetic energy, given by the equation KE = (1/2)mv², where m is the mass and v is the velocity.
At the highest point of its trajectory, the cannonball has no vertical velocity, meaning it has no kinetic energy but possesses gravitational potential energy, given by the equation PE = mgh, where h is the height and g is the acceleration due to gravity (approximately 9.8 m/s²).
Using the conservation of energy, we equate the initial kinetic energy to the maximum potential energy:
(1/2)mv² = mgh
Canceling the mass and rearranging the equation, we find:
v²/2g = h
Plugging in the given values, we have:
(100²)/(2*9.8) = h
Simplifying the equation, we find:
h ≈ 510.2 m
Therefore, the maximum height reached by the cannonball is approximately 510.2 meters.
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A student with a body mass of 74.0 kilograms climbed several flights of stairs to a final height 7.0 meters from the bottom. A second
student, using a stopwatch, determined that the climb was completed in 13.0 seconds. The body mass, time, and vertical height
reached by the student is given in the table. (Estimate g as 10 m/s2)
How many watts of power were generated by the student during the climb?
Answers
Answer:398.5 watts
Explanation:
E-mail is usually a poor choice for the distribution of sensitive electronic files because
A paper copies seem more official than e-mail
B. not all computers can read e-mails correctly
C. it is easy to send e-mail to the wrong person
D. e-mail is saved on the server that transfers it
Answers
Answer:
it's D
Explanation:
its on edge
an ideal heat-engine is to be used in an environment where the ambient temperature is 35.0 °c. what should be the minimum temperature of the hot heat reservoir in order to reach at least 46.2 percent efficiency with the heat-engine? (give your answer in celsius.)
Answers
The minimum temperature is found to be approximately 72.4 °C obtained using the Carnot efficiency equation.
The efficiency of an ideal heat engine operating between two reservoirs can be determined using the Carnot efficiency formula:
Efficiency = 1 - (T_cold / T_hot)
Where T_cold is the temperature of the cold reservoir (ambient temperature) and T_hot is the temperature of the hot reservoir.
To find the minimum temperature of the hot heat reservoir, we need to solve for T_hot. Rearranging the Carnot efficiency equation, we have:
T_hot = T_cold / (1 - Efficiency)
Substituting the given values, T_cold = 35.0 °C and Efficiency = 0.462, we get:T_hot = 35.0 / (1 - 0.462)
Calculating this expression, we find that the minimum temperature of the hot heat reservoir should be approximately 72.4 °C.
Therefore, in order to achieve at least 46.2 percent efficiency with the heat engine in an environment where the ambient temperature is 35.0 °C, the minimum temperature of the hot heat reservoir should be around 72.4 °C.
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Montesquieu believed that in order for one person not to have all the power government should
Answers
Answer:
Montesquieu called the idea of dividing government power into three branches the "separation of powers." He thought it most important to create separate branches of government with equal but different powers. That way, the government would avoid placing too much power with one individual or group of individuals.
Explanation:
An engineer is designing a small toy car that will be launched from rest. The engineer wants to maximize the kinetic energy of the car when it is launched by a compressed spring. He can only make one adjustment to the initial conditions of the car. Which of the following modifications to the car design would have the greatest effect on increasing the kinetic energy of the car?
A. Decrease the mass of the car slightly.
B. Increase the mass of the car slightly.
C. Decrease the launch speed of the car slightly.
D. Increase the weight of the car slightly.
Answers
The modifications to the car design that would have the greatest effect on increasing the kinetic energy of the car is to increase the mass of the car slightly (option B).
What is kinetic energy?Kinetic energy is the energy possessed by an object because of its motion. The kinetic energy equal (nonrelativistically) to one half the mass of the body times the square of its speed.
According to this question, an engineer is designing a small toy car that will be launched from rest. The engineer wants to maximize the kinetic energy of the car when it is launched by a compressed spring.
However, he can only make one adjustment to the initial conditions of the car. Considering the fact that the mass of an object is directly proportional to the kinetic energy.
This suggests that the modifications to the car design that would have the greatest effect on increasing the kinetic energy of the car is to increase the mass of the car slightly.
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[Provide a solution for every item] A particle moves in a straight line whose position from starting point at any time (t) minutes is s(t) = 2t3 + 3t2 + t. a. What is the acceleration after 1 minute?
Answers
The acceleration of the particle after 1 minute is \(18 units/min^2.\)
To find the acceleration, we need to differentiate the position function twice with respect to time.
Given:
\(s(t) = 2t^3 + 3t^2 + t\)
To find the velocity, differentiate s(t) with respect to t:
\(v(t) = d/dt [2t^3 + 3t^2 + t]\)
\(v(t) = 6t^2 + 6t + 1\)
To find the acceleration, differentiate v(t) with respect to t:
\(a(t) = d/dt [6t^2 + 6t + 1]\)
\(a(t) = 12t + 6\)
Now, substitute t = 1 to find the acceleration after 1 minute:
\(a(1) = 12(1) + 6\)
\(= 12 + 6\)
\(= 18\)
Therefore, the acceleration after 1 minute is \(18 units/min^2\)
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What evidence is there to explain the energy of two blocks?
Answers
Answer:
To explain the energy of two blocks, several types of evidence can be used depending on the context and the specific question being asked. Here are some examples:
Kinetic energy: The kinetic energy of a moving object is given by the formula KE = 0.5 * m * v^2, where m is the mass of the object and v is its velocity. If the two blocks are moving, their kinetic energy can be calculated using this formula.
Potential energy: The potential energy of an object is the energy it possesses by virtue of its position or configuration. If the two blocks are lifted to a certain height, they will possess potential energy due to their position in the Earth's gravitational field. The potential energy of an object is given by the formula PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above a reference point.
Work done: If a force is applied to move the two blocks, work is done on them. The work done on an object is given by the formula W = F * d, where F is the force applied, and d is the distance over which the force is applied.
Conservation of energy: The law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another. Therefore, if the energy of the two blocks changes, it must be due to the transfer of energy from one form to another, such as from potential energy to kinetic energy or vice versa.
Overall, the evidence used to explain the energy of two blocks will depend on the specific context of the question being asked and the type of energy being considered.
The molar specific heat of mixture at constant volume, if one mole of a monoatomic gas is mixed with three moles of a diatomic gas is :
a.)3.33r b.)2.25r c.)1.15r d.)6.72r
Answers
The molar specific heat of the mixture at constant volume, when one mole of a monoatomic gas is mixed with three moles of a diatomic gas, is 2.25r. The correct option is b.
The molar specific heat at constant volume (Cv) is a measure of the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius while keeping the volume constant.
For a monoatomic gas, the molar specific heat at constant volume is given by Cv = (3/2)R, where R is the molar gas constant.
For a diatomic gas, the molar specific heat at constant volume is given by Cv = (5/2)R.
When one mole of a monoatomic gas is mixed with three moles of a diatomic gas, the total moles of gas in the mixture is four. The molar specific heat of the mixture at constant volume can be calculated by taking the weighted average of the molar specific heats of the individual gases, based on their respective mole ratios.
In this case, the mixture consists of one mole of the monoatomic gas and three moles of the diatomic gas, giving a mole ratio of 1:3. Using the weighted average formula, the molar specific heat of the mixture is calculated as:
Cv_mixture = (1/4) × (Cv_monoatomic) + (3/4) × (Cv_diatomic)
= (1/4) × (3/2)R + (3/4) × (5/2)R
= (3/8)R + (15/8)R
= (18/8)R
= 2.25R
Therefore, the molar specific heat of the mixture at constant volume is 2.25R. The correct option is b.
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The acceleration due to gravity on the moon is 1.62 m/s^2, approximately a sixth of the value on earth. for a given initial velocity v0, and a given launch angle θ0, the ratio of the range of an ideal projectile on the moon to the range of the same projectile on earth, rmoon/rearth, will be approximately?
Answers
The ratio of the ideal projectile distance on the moon to the same projectile distance on earth, moon/back, is approximately (the acceleration of gravity on the moon is 1.62 m/s², about one-sixth of the acceleration due to gravity on earth. for a given initial velocity v0 , and the specified launch angle θ0) is ⅙ (option B)
The initial velocity, launch angle, and acceleration due to gravity all affect a projectile's range. The formula for an ideal projectile's range is as follows:
R = v0²sin (2θ0) / g
Where,
v0 = the initial velocity (m/s)
θ0 = the launch angle
g = the acceleration due to gravity
The acceleration caused by gravity is 1.62 m/s² for the moon and 9.8 m/s² for the earth. Ranges on the moon and ranges on earth can be expressed as follows:
R moon / R earth = (1.62 sin (2θ0)) / g
sin (2θ0) = 1.62 / 9.8
Approximately ⅙
Consequently, an ideal projectile's range on the moon is around a sixth of its range on Earth.
The question is incomplete, it should be:
The acceleration due to gravity on the moon is 1.62 m/s², approximately a sixth of the value on earth. for a given initial velocity v0, and a given launch angle θ0, the ratio of the range of an ideal projectile on the moon to the range of the same projectile on earth, rmoon/rearth, will be approximately?
A. ⅓
B. ⅙
C. 1
D. 1/12
E. ⅕
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A coin falls off a table and is traveling to the ground. Which claim about the forces acting on the coin must be true?
(Choice A)
There is a net force on the coin.
(Choice B)
There are no forces on the coin.
(Choice C)
There is no net force on the coin.
(Choice D)
There is not enough information.
Answers
A coin falls off a table and is traveling to the ground. There is a net force on the coin which is responsible for the motion of the coin. Thus, the correct option is A.
What is Net force?The net force can be defined as is the sum of all the forces which are acting on an object. Net force acting upon an object can accelerate its mass. Some other forces also acts on a body either at rest or motion. The net force is used in a system when there is a significant number of forces acting on the object.
A coin which falls off a table and is still traveling to the ground. Then, it can be concluded that there is a net force which is acting on that coin which is responsible for the motion of the coin.
Therefore, the correct option is A.
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What is the range of an arrow shot horizontally at 85.3 m/s if it is initially 1.50 m above the ground?
range of arrow =
Answers
Answer:
47.2m
Explanation:
help asap please!
calculate the answer to the correct number of significant digits.
-3.22 x 5.1
Answers
The sun is the ultimate source of energy for nearly all of life. plants and certain other organisms convert solar energy into ____________ energy through the process of ____________ .
Answers
The sun is the ultimate source of energy for nearly all of life. plants and certain other organisms convert solar energy into chemical energy through the process of photosynthesis.
Photosynthesis is the process to convert light energy into chemical energy to be used for cellular purposes. Plants and other microorganisms use photosynthesis to get nutrients using sunlight, carbon dioxide and water.
The photosynthesis reactions is represented as follows
Carbon dioxide + water (sunlight)→ glucose + oxygen
Photosynthesis occur in the chloroplasts of the plants or algae. They are located within mesophyll cells of leaves.
The photosynthesis pigments include Chlorophyll a, Chlorophyll b, Xanthophylls, and Carotenoids.
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A bond between two or more nonmetals is called a/an
Answers
The answer is ionic bond.
a. your friend's ball converts all of its initia
energy into kinetic energy.
b. Your ball is in the air longer, which result
in a greater changing in the kinetic
energy.
c. The changing in gravitational potential
energy is the same for each ball, which
means that the change in kinetic energ'
must also be the same.
Answers
The change in gravitational potential energy is the same for both balls, leading to the conclusion that the change in kinetic energy must also be the same.
a) The ball will have maximum kinetic energy.
When all the initial energy of the ball is converted into kinetic energy, the ball will have the maximum possible kinetic energy. This occurs when the ball is released from a height and falls to the ground without any loss of energy due to friction or air resistance.
The ball will be moving at its maximum speed when all its initial energy is converted into kinetic energy.
b.The ball will experience a greater change in kinetic energy.
The amount of kinetic energy of a moving object is proportional to its velocity squared. Therefore, if the ball is in the air longer, it will have more time to accelerate due to the force of gravity and gain more velocity, resulting in a greater change in kinetic energy.
A longer duration in the air will result in a greater change in kinetic energy for the ball.
c. The change in kinetic energy must be the same for both balls.
The change in gravitational potential energy of a ball that is dropped from a certain height is determined by the height of the drop and the gravitational field strength. Since the height and gravitational field strength are the same for both balls, the change in gravitational potential energy will be the same.
According to the law of conservation of energy, the change in gravitational potential energy must be equal to the change in kinetic energy. Therefore, the change in kinetic energy must be the same for both balls.
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Jason writes a report about how the land changes due to the movement of magma in earth's mantle. which of the following is he most likely including in his report?
Answers
Answer: can I have answer choices
Explanation:
Question
Which experience of colonial America most likely influenced George Washington to discourage future presidents from serving more than 2 terms?
Responses
European traditions and holidays
tyrannical rule of King George III
encountering Native Americans
exploring land west of the colonies
Answers
Answer: encountering Native Americans and Exploring land west of the Colonies
Explanation:
America was buit from people form europe who were white man who wanted power over other people
Answer:C
Explanation:
two crates, of mass 65 kg and 125 kg, are in contact and at rest on a horizontal surface. a 650 n force is exerted on the 65 kg crate. if the coefficient of kinetic friction is 0.18, calculate the (a) the acceleration of the system, and (b) the force that each crate exert on the other. (c) repeat with the crates reversed.
Answers
The apparatus accelerates at a speed of 1.65 m/s2. One crate presses down on another with a force of 426.75 N. The force applied by one crate to the other when the containers are flipped around is 221.91 N.
Acceleration in mechanics refers to the rate of change in a moving object's velocity with respect to time. A measure of acceleration in a vector (in that they have magnitude and direction). An object's acceleration with respect to a force depends on the direction of the net force acting on it.
Although it could seem challenging, velocity is just the act of travelling swiftly in a specific direction. The rate of change in an object's location relative to a frame of reference and time is referred to as its velocity.
As a result,
The initial containers weighed 65 kg.
Weight of the second crates is 125 kg.
650 N of force
Kinetic friction coefficient is equal to 0.18 a, or 650/(65+120) - 0.18*9.8 a, which equals 1.65 m/s2.
Each box presses on the others with a force of F= 125*1.65*0.18*125*9.8 F= 426.75N.
When the containers are turned around, the force each one applies to the other
F=125*1.65*0.18*125*9.8\s
F=221.91N
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" Sensation " occurs in the while perception occurs in the 1) brain; body 2) skin; nerves 3 ) brainstem spinal cord 4 ) body brain
Answers
Hence the complete statement will be, " Sensation " occurs in the body while perception occurs in the brain.
Option D
Sensation and its resolveGenerally, senses acquire facts from the surroundings using the sensory receptors which eventually feed into neural inputs.
These neural impulses are then dispatched to the brain there it is prepared and interpreted for in addition evaluation which is recognized as perception.
Therefore,we have the follow statements to be true
Sensation occurs in the body
Perception occurs in the brain
Option D
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Captain Kirk launched into space last year aboard a rocket. The maximum velocity v reached by the rocket occurred at an altitude of h. (a) How long did it take for the rocket to reach that altitude? (b) Will the rocket make it to space (an altitude of 100 km)?
Answers
a) The answer to this part of the question cannot be determined.
b) The rocket will not make it to space.
Captain Kirk launched into space last year aboard a rocket. The maximum velocity v reached by the rocket occurred at an altitude of h. Let's find out the answers to the given questions.
(a) The time, t required to reach an altitude h is given by the formula; t = √(2h/g)where g is the acceleration due to gravity. Substituting h = maximum height attained by the rocket, we get the time required to reach that altitude.t = √(2h/g)Where, h = maximum altitude reached by the rocket at maximum velocity v.g = 9.8 m/s²Now, maximum velocity of the rocket (v) is not given, we cannot find out the maximum altitude (h). Thus, the answer to this part of the question cannot be determined.
(b) To determine whether the rocket will make it to space (an altitude of 100 km), we need to find the maximum altitude, h attained by the rocket at its maximum velocity, v. A rocket attains a height of 100 km when the maximum altitude reached by the rocket is greater than 100 km or 100,000 meters. Let's assume that the maximum altitude attained by the rocket is H. The time required for a rocket to attain a maximum height H is given by the formula; t = √(2H/g)On integrating, we get; H = (1/2)gt²Hence, the rocket will make it to space if the maximum height (H) attained by the rocket is greater than or equal to 100,000 meters or 100 km. If H is less than 100,000 meters, the rocket will not make it to space.
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Please someone help me.
is the block of wood at rest or in motion?
refer to the figure below draw the forces acting on the block of wood use the gas as the origin of the forces.
thank you very much for answering this.
Answers
Answer:
1) The block of wood is at rest.
2) Weight and Normal Reaction (see attached diagram).
Explanation:
Assumptions
The block of wood is a particle (a body whose mass acts at a point, so its dimensions don't matter).There are no other external forces involved.Question 1
"At rest" or "resting" means that the object isn't moving.
Therefore, the block of wood is at rest.
Question 2
Forces that are acting on the block of wood:
Weight (W): Due to the particle's mass, m, and the acceleration due to gravity, g: W = mg(Weight always acts downwards).Normal Reaction (R or N): The reaction from a surface.
(Normal Reaction is always at 90° to the surface).
See attached diagram.
HELP HAVING BAD DAY NEED ANSWER QUICK!!!!
Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track Jan is given
a 25 m head start, and the race ends in a tie. How long is the track?
Answers
Let's call the length of the race track as "x".
To solve for "x", we can use the formula:
\(\implies\text{ Time} = \dfrac{\text{ Distance}}{\text{ Speed}}\)
Since the race ends in a tie, we know that Jan and Mary both took the same amount of time to run the race. Let's call this time "t".
For Jan:\(\implies \text{ Time} = \dfrac{\text{ Distance}}{\text{ Speed}}\)
\(\implies t = \dfrac{x - 25}{7.5}\)
For Mary:\(\implies\text{ Time} = \dfrac{\text{ Distance}}{\text{ Speed}}\)
\(\implies t = \dfrac{x}{8.0}\)
Since both expressions represent the same time, we can set them equal to each other and solve for "x":
\(\implies \dfrac{x - 25}{7.5} = \dfrac{x}{8.0}\)
Multiplying both sides by 60 (the least common multiple of 7.5 and 8.0) to get rid of the decimals:
\(\implies 8(x - 25) = 7.5x\)
\(\implies 8x - 200 = 7.5x\)
\(\implies 0.5x = 200\)
\(\implies x = 400\)
\(\therefore\) The length of the race track is 400 meters.
\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)
When you walk on a floor, what pushes you
along?
Answers
Answer:
In order to walk across the floor, you push backwards on the floor with your foot. Newton's Third Law says that the reaction force to this action force is "floor pushes you forward" (Action: You push floor (backwards). Reaction: floor pushes you (forward).) So, when you walk, it is the floor that pushes you along!
Explanation:
.
Answer friction
Please someone help me with this physics work.
Answers
Answer:
The first reactant is methane, the next is oxygen, the first product is carbon dioxide and the second product is water.
The word equation is:
methane + oxygen → carbon dioxide + water
The balanced symbol equation is:
CH₄ + 2O₂ → CO₂ + 2H₂O
Explanation:
In any combustion reaction, fuel is burned in the presence of oxygen to produce carbon dioxide and water.
An equation is balanced when there are the same number of atoms of each element on both sides of the arrow.
Hope this helps!
how much time will it take to perform 440 joule of work at a rare of 11 w?
Answers
Answer:
40sec
Explanation:
Data
Work = 440 J
Power= 11watt
time = ?
Power = work done/time
===> time = work done/power
= 440/11
= 40sec
What pathway in the rock cycle might rock take nextv if it is subjected to uplift?
Answers
If rock is subjected to uplift, the next pathway in the rock cycle it may undergo is erosion and transportation. Uplift refers to the upward movement of Earth's crust, often caused by tectonic forces. When rocks are uplifted, they are exposed to weathering and erosion processes.
Here is the potential pathway the rock may follow:
1. Weathering: As the rock is exposed to the surface, it is exposed to weathering agents such as wind, water, and ice. This can break down the rock into smaller pieces.
2. Erosion: The smaller pieces of rock produced by weathering can be transported by agents such as water, wind, and glaciers to new locations.
3. Deposition: As the agents of erosion lose energy, they deposit the sediment they are carrying. Over time, the sediment can accumulate and become buried.
4. Lithification: As sediment accumulates, it can become compacted and cemented together by minerals. This process is called lithification, and it can turn the sediment into sedimentary rock.
5. Metamorphism: If the sedimentary rock is subjected to heat and pressure, it can undergo metamorphism and turn into metamorphic rock.
6. Melting: If the metamorphic rock is subjected to enough heat, it can melt and turn into magma.
7. Solidification: The magma can cool and solidify to form igneous rock.
Therefore, if a rock is subjected to uplift, it may undergo any of these pathways in the rock cycle, depending on the conditions it experiences.
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A piece of iron has a density of 7.86 g/cm3 and a mass of 1.09 x 10^-1 kg. Calculate the volume of the piece of iron.
Answers
1.00 cm3 lead x 11.4 g/cm3 = 11.4 g lead on one side of balance
To balance that, one needs 11.4 g of iron on the other pan. Calculate volume of iron to give you 11.4 g:
11.4 g iron x 1 cm3/7.87 g = 1.45 cm3 of iron needed
Brain list please
You jump off a cliff and accelerate at 9.8 m/s ^ 2 due to gravity. How far do you fall in 4.0 seconds?
Answers
Answer:
According to my calculations you will fall untill you are stopped by an equal force
calculate the work done by the force of gravity on a particle of mass m as it moves radially from 8000 km to 10,000 km from the center of the earth
Answers
To calculate the work done by the force of gravity on a particle of mass m as it moves radially from 8000 km to 10,000 km from the center of the earth, we need to use the formula for gravitational potential energy:
U = -GMm/r
where U is the potential energy, G is the gravitational constant, M is the mass of the earth, m is the mass of the particle, and r is the distance from the center of the earth.
We can calculate the potential energy at each of the two distances:
U1 = -GMm/8000 km
U2 = -GMm/10,000 km
The work done by the force of gravity is equal to the change in potential energy:
W = U2 - U1
W = (-GMm/10,000 km) - (-GMm/8000 km)
W = 3.06 x 10^9 J
Therefore, the work done by the force of gravity on a particle of mass m as it moves radially from 8000 km to 10,000 km from the center of the earth is 3.06 x 10^9 J. This work is done because the particle is moving against the force of gravity as it moves away from the earth's center.
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