The amplitude of the current at resonant frequency is 5 A
What is a R L C circuit?R L C is acronym representing Resistor Inductor and Capacitor. A circuit containing Resistor, Inductor, and Capacitor is called R L C circuit. The connection of the circuit can be in series or in parallel;
For connection in series, like we have the end of the connection point of the resistor marks the beginning of the connection point of the inductor and the end of the inductor marks the beginning of the connection point for the capacitor. The sequence of the connection may not be exactly R L C however connection of the three components end to end represents the R L C series connection
How to solve for current. I at resonant frequencyGiven values:
L=20.0mH,
C=100 nF,
R=20.0 Ω ,
ΔVmax = 100V
I = ΔVmax / R
I = 100 / 20
I = 5.0 Amp
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2 An air rifle pellet of mass 2 g is fired into a block of modelling clay mounted
on a model railway truck. The truck and modelling clay have a mass of
0.1 kg. The truck moves off after the pellet hits the modelling clay with an
initial velocity of 0.8 m/s.
State the momentum of the pellet just before it hits the modelling clay.
c Use your answers to a and b to calculate the velocity of the pellet just
before it hits the modelling clay.
d State any assumptions you made in this calculation.
The momentum of the pellet just before it hits the modelling clay is 0.0816 kg-m/s the velocity of the pellet just before it hits the modelling clay is 40m/s.
Assumption:
1)the pallet embeds into the clay.
A perfectly inelastic collision is one where the two objects that collide together become one object, losing the maximum amount of kinetic energy.
e=0
In perfectly inelastic collision the momentum is conserved.
given:
velocity of the truck + clay = 0.8m/s
mass of the truck + clay = 0.1 kg
mass of the pallet = 2g=0.002kg
a)
now since the example is of perfectly inelastic collision the momentum will be conserved .
i.e. momentum before collision = momentum after collision
momentum of pallet = momentum of( truck + clay)
momentum of pallet = (0.1+0.002)×0.8
momentum of pallet =0.0816 kg-m/s
b)
momentum before collision= mass of pallet ×velocity of pallet + mass of truck × velocity of truck
velocity of pallet =0.0816/0.002
velocity of pallet =40m/s
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A conductor carrying a current I = 15.0 A is directed along the positive x axis and perpendicular to a uniform magnetic field. A magnetic force per unit length of 0.120 N/m acts on the conductor in the negative y direction. Deter- mine (b) the direction of the magnetic field in the region through which the current passes.
The magnitude of the magnetic field in the region through the current passes is 8×10⁻³ T.
What is a magnetic field?The magnetic field is defined as the field the magnetic materials generate or when an electric charge moves in a field region that generates the magnetic field.
It is given that:
A conductor carrying a current I = 15.0 A is directed along the positive x-axis and perpendicular to a uniform magnetic field.
As we know,
F = ilB
i = 15 A
F/l = 0.120 N/m
B = (F/l)(1/i)
B = 0.120(1/15)
B = 8×10⁻³ T
Thus, the magnitude of the magnetic field in the region through the current passes is 8×10⁻³ T.
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HELP PLEASE IMMEDIATILY !!!!!!
- Determine the force required to accelerate a block of ice with a mass of 3.5 kg from 0 to 8 m/s2.
- Determine the acceleration that a cart with a mass of 25 kg experiences when it is being pulled with a force of 50 Newtons.
- Determine the mass of a block of ice that is accelerated to 6 m/s2 by a force of 3 Newtons.
- What is a free body diagram and what information does it contain?
Answer all of them please
The force required to accelerate the block is 28 N.
The acceleration of a cart with a mass of 25 kg and applied force of 50 N is 2 m/s².
The mass of a block of ice that is accelerated to 6 m/s2 by a force of 3 Newtons is 0.5kg.
A free body diagram is a sketch of forces acting on an object. It consists of the applied force, weight of the object, frictional force and normal reaction.
Force required to accelerate the blockThe force required to accelerate the block is calculated as follows;
F = ma
F = 3.5 kg x 8 m/s²
F = 28 N
Acceleration that cartThe acceleration of a cart with a mass of 25 kg and applied force of 50 N is calculated as follows;
a = F/m
a = 50/25
a = 2 m/s²
Mass of the block of iceThe mass of a block of ice that is accelerated to 6 m/s2 by a force of 3 Newtons is calculated as follows;
m = F/a
m = 3 N / 6 m/s²
m = 0.5 kg
What is a free body diagram?A free body diagram is a sketch of forces acting on an object. It consists of the applied force, weight of the object, frictional force and normal reaction.
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An alien spaceship traveling at 0.600 c toward the Earth launches a landing craft. The landing craft travels in the same direction with a speed of 0.800 c relative to the mother ship. As measured on the Earth, the spaceship is 0.200 ly from the Earth when the landing craft is launched.(a) What speed do the Earth-based observers measure for the approaching landing craft?
The speed does the Earth-based observers measure for the approaching landing craft is 1.016 times the speed of light.
To find the answer, we have to know about the Lorentz transformation.
What speed do the Earth-based observers measure for the approaching landing craft?It is given that, an alien spaceship traveling at 0.600 c toward the Earth, in the same direction the landing craft travels with a speed of 0.800 c relative to the mother ship. We have to find the speed do the Earth-based observers measure for the approaching landing craft.
Let us consider the earth as S frame and space craft as S' frame, then the expression for the value of speed of the approaching landing craft with respect to the earth frame as,[tex]V_x=V_x'(1-\frac{VV_x}{c^2} )+V\\where,\\V_x'=0.8c\\V=0.6c[/tex]
Substituting values, we get,[tex]V_x=0.8c(1-\frac{0.8c*0.6c}{c^2} )+0.6c=1.016c[/tex]
Thus, we can conclude that, the speed does the Earth-based observers measure for the approaching landing craft is 1.016 times the speed of light.
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a ball is shot from the ground straight up into the air with initial velocity of 50 50 ft/sec. assuming that the air resistance can be ignored, how high does it go?
The height attained by the ball is 11.86m
a ball is shot from the ground straight up into the air its initial and final velocity is
initial velocity, u = 50 ft/s = 50×0.305 = 15.25m/s
final velocity ,v = 0 m/s
gravity =-9.8 m/s²
( negative sign shows acceleration in opposite direction)
height =?
using the newton motion of equation
v² = u² + 2as
where
a= acceleration due to gravity(g)
s = height
v² = u² + 2gs
(0)² = (15.25)² + 2×(-9.8)×s
0 = (15.25)² - 19.6 × s
s= - (15.25)²/ 19.6
s = 11.86m
after ignoring the air resistance the maximum height of the ball is 11.86m
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If more electric field lines leave a gaussian surface than enter it, what can you conclude about the net charge enclosed by that surface?
The net charge enclosed within the electric field is positive when more electric field lines leave a gaussian surface than enter it.
Remember, that a Gaussian surface is a three-dimensional closed surface that determines the flux of a vector field, often the gravity field, electric field, or magnetic field. A surface with more electric field lines departing than coming in indicates a net positive charge. It is important to note that E-field lines begin with positive charges and end with negative charges. This is characteristic of most gaussian surfaces. So, if more electric field lines exit than enter a gaussian surface, we may deduce that the enclosing net charge is generally positive.
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a plastic rod that has been charged to − 15 nc touches a metal sphere. afterward, the rod's charge is − 1.0 nc .
According to the question a plastic rod that has been charged to − 15nc touches a metal sphere. Afterward, the rod's charge is − 1.0nc.The electrons will be transferred from the plastic rod to the metal sphere and the number of electrons ( n ) = 8.73 * 10^10
First of all, write the initial charge on the plastic rod, and then it touches the metallic sphere. Then, a few amounts of charge are transferred to the steel sphere. Later, calculating the price difference between the plastic rod and metal sphere, the kind of charged particle transferred may be decided. Ultimately, the number of electrons may be calculated by the use of the overall charge and the rate of the electron.
The expression of the total charge in electrostatics is Q = ne
Q = charge
n = number of electrons
e = charge of the electron
The initial charge on the plastic rod ( Qplastic ) = -15nC
Final charge on the metal sphere after it was touched by the plastic rod ( Qmetal ) = -1nC
The charge transferred from the metal rod to the sphere = ( Q = Qplastic - Qmetal )
Therefore Q = - 15nC - ( -1nC )
Q = -14nC
The plastic rod is negatively charged, so the electrons will be transferred to the metal sphere. The electrons will be transferred from the plastic rod to the metal sphere.
The expression of the total charge in electrostatics is Q = ne
The expression for n = Q / e
Q = -14nC
The charge on 1 electron = 1.602 * 10^-19 C.
Number of electrons ( n ) = -14nC ( 10^-9C/1nC ) / -1.602 * 10^-19 C.
Number of electrons ( n ) = 8.73 * 10^10
Threfore the number of electrons ( n ) = 8.73 * 10^10
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this average velocity results because she hikes for 6.44 km with an average velocity of 2.68 m/s, due west turns around, and hikes with an average velocity of 0.447 m /s, due east. how far east did she walk?
0.81 km far east she walked.
What do you mean by average velocity?The ratio of the sum of quantities to the entire number of quantities is what is simply meant by the word "average." In Physics, an alternative strategy is used. Let's first define velocity precisely as well as speed and how the two are related before moving on to average velocity. The change in location of an object with respect to time is referred to as its speed. On the other hand, velocity is nothing more than the speed that is specified in relation to the direction that an item travels. For now, let's return to the average velocity before we get into further detail regarding the distinction between speed and velocity.
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Scientific theories are able to be changed true or false
Answer:
true
Explanation:
A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of λ, and the cylinder has a net charge per unit length of 2λ . From this information, use Gauss's law to find (b) the charge per unit length on the outer surface of the
The charge per unit length on the outer surface is [tex]3\lambda[/tex]
Charge per unit length of the wire [tex]= {\lambda}[/tex].
Charge per unit length of the cylinder =[tex]{2\lambda}[/tex]
Gauss's law is a principle that connects the distribution of electric charge to the resulting electric field. In its integral form, it asserts that the flux of the electric field out of any closed surface, regardless of how that charge is distributed, is proportional to the electric charge enclosed by the surface.
The total charge per unit length of the cylinder is equal to the charge per unit length of the inner part of the cylinder plus the charge per unit length of the outer part:
Solve for [tex]{\lambda_{\text{out}}}[/tex] :
[tex]\lambda_{\text{out}}=2\lambda-\lambda_{\text{in}}[/tex]
Substitute for [tex]{\lambda_{\text{in}}}[/tex] :
[tex]\lambda_{\text{out}}&=2\lambda-(-\lambda)\\ &={3\lambda}}[/tex]
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Imagine that the entire Sun, of mass MS , collapses to a sphere of radius Rg such that the work required to remove a small mass m from the surface would be equal to its rest energy mc² . This radius is called the gravitational radius for the Sun.(a) Use this approach to show that Rg = GMS / c² .
It is proved for gravitational radius that Rg=GMs/c^2 .
Given,
The mass of sun = Ms
Sphere of radius = Rg
Sun collapses to a sphere such that the work required to remove a small mass (m) from the surface would be equal to its rest energy mc^2 .
The given radius (Rg) is called as gravitational radius for sun.
We know,
gravitational potential energy Ug = G ×Ms×m/Rg
given, the rest energy, E =mc^2
As it is given that work required to remove small mass is equal to rest energy,
thus, Ug=E
G×Ms×m/Rg = mc^2
Rg =GMs/c^2
Hence, it is proved for gravitational radius that Rg=GMs/c^2 .
What is gravitational potential energy?Total work done in assembling bodies together,in their respective places, is called gravitational potential energy of the system.
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The tank is 51m long and 20m wide.The sea water in the tank is 11m deep and has a density of 1030 kilograms per cubic meters.
Calculate the mass of water in the tank.
Answer: 1.2 x 10^7kg
Explanation:
Volume of tank = length x width x height
Volume = 51 x 20 x 11
Volume = 11220 m^3
Density = Mass/Volume
Density = 1030 kg/m^3
Volume = 11220 m^3
Mass = m
1030 = m/11220
m = 1030 x 11220
m = 11,556,600 kg or 1.2 x 10^7kg
Which type of energy does not describe potential energy being changed into kenetic energy
The type of energy that does not describe potential energy being changed into kinetic energy is the energy that exists in the Compression of the spring.
Usually, in many energy sources, the potential energy is changed into kinetic energy but no such energy transmission takes place when a spring is compressed.
Potential energy is considered as the stored energy occupied by an object or system by virtue of its respective position or by the arrangement of parts. However, this energy is not affected by the environment existing outside of the system or subject including air or height. Potential energy is changed into kinetic energy is also not described in the compression of rubber foam.
On the other hand, the term kinetic energy is termed as the energy of a particular object or particle of a system that is in motion. Contrary to several peculiarities of potential energy, the kinetic energy of a particular object is in relative position to other stationery as well as moving objects present in its own environment which is an immediate type. In general, the kinetic energy of an object will be of higher value if the object is placed at a distance of greater height.
If we take the case of Potential energy, it is not all transferrable in nature and will depend on the height or the distance and also the mass of the object. On the other hand, Kinetic energy can be easily transferable from one moving object to another which includes the vibrational and rotational types of energy and it depends on the speed, velocity, and mass of the object.
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Different types of brain injuries and what they affect
Answer:
Explanation:
Traumatic brain injury (TBI) happens when a sudden, external, physical assault damages the brain. It is one of the most common causes of disability and death in adults. TBI is a broad term that describes a vast array of injuries that happen to the brain. The damage can be focal (confined to one area of the brain) or diffuse (happens in more than one area of the brain). The severity of a brain injury can range from a mild concussion to a severe injury that results in coma or even death.
Brain injury may happen in one of two ways:
CLOSE BRAIN INJURY : Closed brain injuries happen when there is a nonpenetrating injury to the brain with no break in the skull. A closed brain injury is caused by a rapid forward or backward movement and shaking of the brain inside the bony skull that results in bruising and tearing of brain tissue and blood vessels. Closed brain injuries are usually caused by car accidents, falls, and increasingly, in sports. Shaking a baby can also result in this type of injury (called shaken baby syndrome).
PENETRATING BRAIN INJURY: Penetrating, or open head injuries happen when there is a break in the skull, such as when a bullet pierces the brain.
DIFFUSE AXONAL INJURY: Is the shearing (tearing) of the brain's long connecting nerve fibers (axons) that happens when the brain is injured as it shifts and rotates inside the bony skull. DAI usually causes coma and injury to many different parts of the brain. The changes in the brain are often microscopic and may not be evident on computed tomography (CT scan) or magnetic resonance imaging (MRI) scans.
PRIMARY BRAIN INJURY: Refers to the sudden and profound injury to the brain that is considered to be more or less complete at the time of impact. This happens at the time of the car accident, gunshot wound, or fall.
SECONDARY BRAIN INJURY : Refers to the changes that evolve over a period of hours to days after the primary brain injury. It includes an entire series of steps or stages of cellular, chemical, tissue, or blood vessel changes in the brain that contribute to further destruction of brain tissue.
A boy walks 25 meters north along a sidewalk before realizing that he has walked in the wrong direction. He turns around and walks 48 m south. What is the distance he traveled?
if two 6-volt sources are connected in parallel to supply a 24-ohm load and the total current is 0.25 a, how much current would each source supply to the load? (round the final answer to three decimal places.)
V or total voltage is 6 volts because when multiple power supplies of the same voltage are connected in parallel, the applied voltage is same and the current equally divides between the number of power sources.
Divide I(t) or total current 0.25 amps between the two power sources.
Is=I(t)/Ns
Is=0.25amps/2sources
Is=.125amps
Voltage is the difference in electrical potential between two points.
Current is just the rate of flow of electric charge.
Each power source supplies .125amps of current to the load
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the atoms of each element in a compound cannot be pulled apart
Answer:
Element of a compound typically cannot be separated by physical means because atoms are chemically bonded together
Explanation:
Compounds are substances composed of two or more elements chemically combined that can be separated into simpler substances only by chemical means
A table tennis ball with a mass of 0.003 kg and a soccer ball with a mass of 0.43 kg are both set in motion at 16 m/s. Calculate and compare the momenta of both balls.
Answer:
Momentum of tennis ball = 0.048
Momentum of soccer ball = 6.88
momentum of soccer ball is greater than that of tennis ball.
Explanation:
For table tennis ball,
Momentum of tennis the ball is given by,
Momentum = mass × volume
Momentum = 0.003 × 16
Momentum = 0.048
For table soccer ball,
Momentum of the soccer ball is given by,
Momentum = mass × volume
Momentum = 0.43 × 16
Momentum = 6.88
Thus, momentum of soccer ball is greater than that of tennis ball.
In materials with nickel, iron, or cobalt, what moves around inside, creating the magnetic field?
A.protons
B.neutrons
C.electrons
D.All of the above
At what temperature is the temperature in degrees fahrenheit equal to twice the temperature in degrees celsius?.
The temperature in degrees Fahrenheit is 320 equal to twice the temperature in degrees Celsius.
What is a temperature scale?The measurement of temperature as a physical quantity. In order to measure temperature, empirical scales take into account useful and trustworthy factors like the freezing and boiling temperatures of water.
The temperature will be solved as below:-
F = 2C
The temperature in degree centigrade is:-
C = ( 5 / 9 ) ( F - 32 )
Put the value in the equation above:-
F = 2 { 5 / 9 [ F -32 ]}
F = ( 10 / 9 ) [ F - 32 ]
( 9 / 10)F = F - 32
( 9 / 10)F - F = 32
( -1 / 10)F = -32
F = 320°
Therefore, the temperature in degrees Fahrenheit is 320 equal to twice the temperature in degrees Celsius.
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The concrete sections of a certain superhighway are designed to have a length of 25.0m . The sections are poured and cured at 10.0°C . What minimum spacing should the engineer leave between the sections to eliminate buckling if the concrete is to reach a temperature of 50.0°C ?
The minimum spacing the engineer should leave between the sections to eliminate buckling is 0.011 m.
To calculate the minimum space the engineer must leave in other to eliminate bulking, we use the coefficient of linear expansivity of steel.
What is coefficient of linear expansivity?This can be defined as the increase in length, per unit length, per degree rise in temperature.
To calculate the minimum space, we use the fomula below
Formula:
α = ΔL/L₁(t₂-t₁)........... Equation 1
Make L₂ the subject of the equation
ΔL = αL₁(t₂-t₁)........... Equation 2From the question,
Given:
L₁ = 25 mt₁ = 10°Ct₂ = 50°Cα = 11×10⁻⁶ /K ( Cofficient of Linear expansion of steel)Substitute these values into equation 2
ΔL = [11×10⁻⁶×25×(50-10)]ΔL = 0.011 mHence, the minimum spacing the engineer should leave between the sections to eliminate buckling is 0.011 m.
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In Niels Bohr's 1913 model of the hydrogen atom, the single electron is in a circular orbit of radius 5.29×10⁻¹¹m and its speed is 2.19×10⁶ m/s . (a) What is the magnitude of the magnetic moment due to the electron's motion?
The magnitude of the magnetic moment due to the electron's motion is [tex]87.87 * 10^{-37}[/tex].
What is magnetic moment?The magnetic pull and direction of a magnet or other object that produces a magnetic field are referred to as the magnetic moment in electromagnetism. Things that have magnetic moments include electromagnets, permanent magnets, various compounds, elementary particles like electrons, and a number of celestial objects (such as many planets, some moons, stars, etc).
The term "magnetic moment" really refers to the magnetic dipole moment of a system, which is the portion of the magnetic moment that can be represented by an equivalent magnetic dipole or a pair of magnetic north and south poles that are only very slightly apart. The magnetic dipole component is adequate for sufficiently small magnets or over sufficiently large distances.
Calculations:
radius= [tex]5.29 * 10^{-11} m\\[/tex]
velocity=[tex]2.9* 10^{6} m/s[/tex]
Working formula, M=N/A
[tex]I=\frac{charge flow }{time taken} =\frac{e}{time taken\\}[/tex]
[tex]T= \frac{2xr}{v} =\frac{2xx * 5.29 * 10^{-11} }{2.9* 10^{6} }[/tex]
=[tex]15.16 * 10^{-5} s[/tex]
[tex]I= \frac{1.6 * 10^{-19} }{15.16 * 10^{-5} }[/tex][tex]= 0.10 * 10^{-14}[/tex]
=[tex]1 * 10^{-15} C[/tex]
M=[tex]1x (1* 10^{-15} * (5.29 * 10^{-11} )^{2}[/tex]
=[tex]87.87 * 10^{-37}[/tex]
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pls help me!! 100 points!!!
"type a definition for each of the following words in YOUR own words."
1) Constants (also called Controls or Control Variables) –
2) Independent variable –
3) Dependent variable –
Answer:
1) Constants are variables that are kept the same throughout an experiment.
2) An independent variable is a variable that is manipulated by the experimenter.
3) A dependent variable is a variable that is measured by the experimenter.
Explanation:
The charge per unit length on a long, straight filament is -90.0μC/m . Find the electric field (b) 20.0cm
The electric field for 20 cm is 8.09 MN/C
Length of the straight filament = (20cm) (1m/100cm) = 0.2
Electric field for the straight conductor = [tex]E = \frac{2k_{e} \lambda}{r}[/tex]
E = [2(8.99 × 10^9 N·m^2/C^2)(90.0 × 10^-6 C/m)] / 0.2 m
E = 8.09 MN/C
The electric field is directed radially inward, toward the filament.
The electric field is a force produced by a charge near its surroundings. This force is exerted on other charges when brought in the vicinity of this field. SI unit of the electric field is N/C (Force/Charge).
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If I use the author's last name in my sentence, then _________________ (Choose 2)
Group of answer choices
I only put the page number in parentheses.
I do not need to use it in the in-text citation.
I also need to use it in the in-text citation.
I put the year of publication and the page number.
I put the author's last name, a comma, and the publication date.
Even if in a piece of writing, you happen to use the author's last name in my sentence, you also need to use it in the in-text citation.
What is referencing?In academic writing, it is often important to quote the sources that one used in writing up the text. Failure to give accurate citation could be taken as plagiarism by the assessors.
Hence, even if in a piece of writing, you happen to use the author's last name in my sentence, you also need to use it in the in-text citation.
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An athlete is running a race. The athlete’s body needs energy. Which type of organelle in the athlete’s cells supplies the energy for cellular function?.
Mitochondria is a type of organelle in the athlete’s cells supplies the energy for cellular function.
Since mitochondria are the cellular organelles in charge of producing aerobic ATP, the "health" of mitochondria is crucial for proper cellular operation
Which organelles that give energy to the cell?Mitochondria. Dictionary Britannica, Inc. Mitochondria, or "powerhouses," are oval-shaped organelles that are present in the majority of eukaryotic cells. During cellular respiration, substances like glucose are converted by mitochondria into ATP, an energy molecule (adenosine triphosphate).
How Mitochondria produce ROS?The generation of ROS by mitochondria can result in oxidative damage to mitochondrial proteins, membranes, and DNA, impairing their capacity to synthesize ATP and perform a wide range of metabolic processes, including the tricarboxylic acid cycle, fatty acid oxidation, the urea cycle, amino acid metabolism, haem synthesis, and FeS center assembly, which are crucial to the normal functioning of most cells. The tendency of mitochondria to release intermembrane space proteins, such as cytochrome c (cyt c), to the cytosol by mitochondrial outer membrane permeabilization (MOMP), and so trigger the cell's apoptotic machinery, can also be increased by mitochondrial oxidative damage. The mitochondrial permeability transition pore (PTP), which opens up the inner membrane to tiny molecules in conditions like ischaemial reperfusion damage, is also induced by mitochondrial ROS generation. So it should come as no surprise that mitochondrial oxidative damage plays a role in a variety of diseases. Additionally, mitochondrial ROS may behave as a modifiable redox signal, impacting a number of activities in the mitochondria, cytosol, and nucleus in a reversible manner.
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if a gas occupies 15 l at pressure of 2.3 atm what would the volume be at 3.1 atm
The volume occupied by the gas at 3.1 atm pressure will be 11.12 L.
What is Boyle's Law?When a gas is maintained at a constant temperature and with a certain mass, Boyle's law states that the pressure of the gas is inversely proportional to its volume.
To put it another way, as long as the temperature and volume of the gas remain constant, the pressure and volume of the gas are inversely proportional to one another. In 1662, the Anglo-Irish chemist Robert Boyle proposed the Boyle's law.
According to Boyle's law :
P1V1=P2V2 where,
P1 and P2 are the pressure and,
V1 and V2 are the volume of container.
As per the question, the given values are :
V1=15 L
P1= 2.3 atm and,
P2= 3.1 atm
So by using Boyle's theorem :
2.3 atm× 15 L = 3.1 atm× V2
34.5=3.1 atm × V2
V2=11.12 L
Hence, the volume at 3.1 atm pressure will be 11.12 L.
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the earth has a mass of 6x10^24 kg, and a radius of 6400 km. What is the density of the earth in kg/m^2.
The density of the earth is 3.51×10¹⁰ kg/m³
What is Density?Density can be defined as the ratio of mass to the volume of a body. The S.I unit of density is kg/m³
To calculate the density of the earth, we use the formula below.
Formula:
D = m/v............ Equation 1Where:
D = Denstiy of the earthm = Mass of the earthv = Volume of the earthFrom the question,
Given:
m = 6×10²⁴ kgNote: Since the earth is a spherical in shape, we can calculate the volume of the earth using the volume of a sphere
v = 4πr³/3 = (4×3.14×6400000³)/3 = 1.71×10¹⁴ m³Substitute these values into equation 1
D = (6×10²⁴)/(1.71×10¹⁴) D = 3.51×10¹⁰ kg/m³Hence, the density of the earth is 3.51×10¹⁰ kg/m³.
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A train is climbing a gradual hill. The weight of the train creates a downhill force of 150,000 newtons. Friction creates an additional force of 25,000 newtons acting in the same direction (downhill). How much force does the train’s engine need to produce so the train is in equilibrium.
The force produced by the train's engine will be 175000N.
Force is an external agent that has the power to alter an object's state of motion or rest. In a brief, force is a vector quantity that's also defined as a push or pull exerted on an object as a result of the object's contact with another object. The Newton (N) is the unit of force F.
F = ma
Here, F is force, m is mass and a is acceleration of the object.
We are given here,
The force by the train weight = [tex]Fw[/tex] = 150,000N
The force creates by the friction = [tex]F_{f}[/tex] = 25,000N
Thus , to get the total force of the train's engine by adding force by weight and force by friction is given as,
[tex]F_{t} = F_{w}+ F_{f}[/tex]
Then for getting total force of the train's engine putting above values in the expression ,
[tex]F_{t} = 150,000 N +25,000N\\F_{t} = 175,000N[/tex]
Hence, the train’s engine has to produce 175000N force to become in equilibrium.
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How much energy is required to change a 40.0-g ice cube from ice at -10.0°C to steam at 110°C ?
The amount of heat required to warm the ice is 38.317 KJ
What is specific heat capacity ?
In scientific terms, a specific heat capacity is the quantity of heat (J) absorbed by a material every time its temperature goes up 1 K (or 1 °C), given in J/(kg K) or J/(kg °C) per unit mass. formulae for specific heat capacity is given by
Given data:
The mass of ice is, m = 40.0 g.
The initial temperature is, T = - 10 degree Celsius.
The final temperature is, T' = 110.0 degree Celsius.
The heat capacity of ice is, c = 2.09 J/g C.
The heat capacity of steam is, c' = 2.01 J/g C.
When ice absorbs heat, the conversion takes place from ice to water (liquid) and from the liquid to steam at 110 degree Celsius. So,
The amount of heat absorbed is given as,
Q = m[c(T' - T) + c'T']
Q = 40[2.09 x (110-(-10)) + 2.01 x (110+273))]
Q = 38,317.2 J
Convert in kJ as,
Q = 38,317.2/1000
Q = 38.317 kJ
Thus, we can conclude that the amount of heat required to warm the ice is 38.317 kJ.
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