A neutron has a neutral charge because it is composed of an equal number of protons and electrons. Hence option C is correct.
The neutron is a subatomic particle with a neutral (neither positive nor negative) charge and a slightly larger mass than a proton. Atomic nuclei are made up of protons and neutrons. Protons and neutrons are both referred to as nucleons because they function similarly within the nucleus and each have a mass of around one atomic mass unit. Nuclear physics describes their characteristics and interactions. Protons and neutrons are not elementary particles; they are made up of three quarks apiece.
Hence option C is correct.
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A 20 kg child is on a swing that hangs from 2.6-m-long chains. What is her maximum speed if she swings out to a 50 degree angle?
Two balloons with charges of 8.37 µC and unknown one repel each other with a force of 0.5 Newton in the distance of 30mm. Determine the unknown charge.
help
1. Calculate the Energy of skater at all the positions shown. Position C is the highest point the skater reaches
The energy of the skater at each position is:
A: 1920 JB: 1764 JC: 3528 JHow to calculate conservation of energy?At position A, the skater is at the lowest point, so the PE is zero. The KE can be calculated using the formula KE = (1/2)mv², where m is the mass of the skater and v is the velocity:
KE = (1/2)(60 kg)(8 m/s)²
KE = 1920 J
Therefore, at position A, the skater has 1920 J of kinetic energy and 0 J of potential energy.
At position B, the skater has gained some height, so there is some potential energy. The KE can be calculated as before, and the PE can be calculated using the formula PE = mgh, where m is the mass of the skater, g is the acceleration due to gravity (9.81 m/s²), and h is the height:
KE = (1/2)(60 kg)(8 m/s)²
KE = 1920 J
PE = (60 kg)(9.81 m/s²)(3 m)
PE = 1764 J
Therefore, at position B, the skater has 1920 J of kinetic energy and 1764 J of potential energy.
At position C, the skater has reached the highest point, so the KE is zero. The PE can be calculated as before:
PE = (60 kg)(9.81 m/s²)(6 m)
PE = 3528 J
Therefore, at position C, the skater has 0 J of kinetic energy and 3528 J of potential energy.
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A complete circuit with a capacitor is turned on. What causes that potential energy produced?
The voltage difference across the capacitor.
The switch adds energy to the system through the capacitor.
The electrons are removed from one side of the capacitor and moved to the other side.
The current running through the wire causes the capacitor to heat up, raising the resistance of the wire.
The potential energy produced in a complete circuit with a capacitor is caused by the voltage difference across the capacitor.
A capacitor is an electrical component that stores electric charge. When a capacitor is connected to a complete circuit and a voltage is applied, it becomes charged. The voltage difference across the capacitor creates an electric field between its plates, which stores potential energy in the electric field.
As the capacitor charges, electrons accumulate on one plate, creating a negative charge, while the other plate becomes positively charged due to the loss of electrons. This separation of charge creates an electric potential difference (voltage) between the two plates of the capacitor.
The potential energy stored in the capacitor is directly proportional to the square of the voltage across it and the capacitance (C) of the capacitor, and is given by the formula:
Potential energy (PE) = (1/2) * C * V²
where V is the voltage across the capacitor.
As the voltage across the capacitor increases, more potential energy is stored in the electric field between its plates. When the circuit is turned off or the capacitor is discharged, this stored potential energy is released back into the circuit in the form of electrical energy. Capacitors play a crucial role in many electronic devices and circuits by providing energy storage and smoothing out voltage fluctuations.
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Why do we know so much Earth's Composition?
A.Digging to the inner core
B.Looking at the Earth's Magnetic Field
C.Studying Seismic Waves
Answer:
C
Explanation:
Since we can't go to the center of Earth, we have to rely on indirect observations of the materials of the interior. The seismic waves are generated by earthquakes and explosions that travel through Earth and across its surface. Thanks to that, it reveals the structure of the interior of the planet. Thousands of earthquakes occur every year, and each one provides a glimpse of the Earth's interior.
CAN ANYONE PLEASE HELP!
One long wire lies along an x axis and carries a current of 36 A in the positive x direction. A second long wire is perpendicular to the xy plane, passes through the point (0,5.8 m, 0), and carries a current of 73 A in the positive z direction. What is the magnitude of the resulting magnetic field at the point (0, 2.0 m, 0)?
The resultant magnetic field magnitude at the position (0, 2.0 m, 0) is 1.9 x 10⁻⁵ T.
How to find resulting magnetic field?The magnetic field due to each wire at point P will be:
B₁ = μ₀I₁/2πr₁ and B₂ = μ₀I₂/2πr₂
Where,
μ₀ = 4π x 10⁻⁷ T m/A is the permeability of free space,
I₁ = 36 A is the current in the first wire,
I₂ = 73 A is the current in the second wire,
r₁ = distance between point P and the first wire,
r₂ = distance between point P and the second wire.
As the first wire is along the x-axis, its magnetic field at point P will be purely in the y-direction. The magnitude of B₁:
B₁ = μ₀I₁/2πr₁ = (4π x 10⁻⁷ T m/A)(36 A)/(2π(2.0 m)) = 1.8 x 10⁻⁵ T
The second wire is perpendicular to the xy-plane, so its magnetic field at point P will be purely in the x-direction. The distance r₂ using the Pythagorean theorem:
r₂ = √(5.8 m)² + (2.0 m)² = 6.1 m
The magnitude of B₂:
B₂ = μ₀I₂/2πr₂ = (4π x 10⁻⁷ T m/A)(73 A)/(2π(6.1 m)) = 6.0 x 10⁻⁶ T
The resulting magnetic field at point P will be the vector sum of the magnetic fields due to each wire:
B = √(B₁² + B₂²) = √((1.8 x 10⁻⁵ T)² + (6.0 x 10⁻⁶ T)²) = 1.9 x 10⁻⁵ T
Therefore, the magnitude of the resulting magnetic field at the point (0, 2.0 m, 0) is 1.9 x 10⁻⁵ T.
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In a futuristic scenario, you are assigned the mission of making an enemy satellite that is in a circular orbit around Earth inoperative. You know you cannot destroy the satellite, as it is well protected against attack, but you can try to knock it out of its orbit so it will fly away and never return. What is the minimum amount of work applied to the satellite that is required to accomplish that? The satellite's mass and altitude are 993 kg and 227 km. Earth's mass and radius are 5.98×10^24 kg and 6370 km.
The minimum amount of work required to make the enemy satellite inoperative and push it out of its circular orbit is 6.972 × 10^9 joules.
To calculate the minimum amount of work required to knock the satellite out of its circular orbit, we need to determine the change in kinetic energy required to change the satellite's velocity. This change in kinetic energy can be calculated using the conservation of energy, which states that the total energy in a closed system remains constant.
The kinetic energy of an object in motion can be expressed as:
K = (1/2)mv^2
Where:
K = Kinetic energy
m = Mass of the object
v = Velocity of the object
To determine the velocity of the satellite, we can use the following formula:
v = sqrt(GM/r)
Where:
G = Universal gravitational constant = 6.6743 × 10^-11 N m^2/kg^2
M = Mass of the Earth = 5.98×10^24 kg
r = Altitude of the satellite above the Earth's surface + radius of the Earth = 6,997 km
v = sqrt(6.6743 × 10^-11 × 5.98×10^24 / 6,997×10^3) = 7,650 m/s
To change the satellite's velocity, we need to calculate the new velocity required to push the satellite out of its circular orbit. We can use the following formula to calculate the escape velocity required to leave the Earth's gravitational field:
Ve = sqrt(2GM/r)
Ve = sqrt(2 × 6.6743 × 10^-11 × 5.98×10^24 / 6,997×10^3) = 11,186 m/s
To calculate the change in kinetic energy required to change the satellite's velocity from its initial velocity to the escape velocity, we can use the following formula:
ΔK = (1/2)m(Δv)^2
Where:
ΔK = Change in kinetic energy
m = Mass of the satellite
Δv = Change in velocity required to reach escape velocity = Ve - v
Δv = 11,186 m/s - 7,650 m/s = 3,536 m/s
ΔK = (1/2) × 993 kg × (3,536 m/s)^2 = 6.972 × 10^9 J
Therefore, The adversary spacecraft must be rendered inoperable and forced out of its elliptical orbit with a minimum of 6.972 × 10^9 joules of work.
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What two things can be considered to be substances?
Answer:Classification of Matter According To Composition
When you think about classifying matter, you likely think of the three states of matter: solid, liquid, and gas. But, thinking back to the donut metaphor, we can also classify matter according to what it is made of (aka its chemical composition)! So, what makes up matter? Well, on a molecular level, all matter is made up of atoms that can form elements, compounds, and molecules! Even with all these different components, matter can be split into two broad categories based on its composition: pure substances and mixtures. We will spend most of our time on pure substances, but briefly cover mixtures! So, let’s dive into pure substances!
We will go into more detail on all the components of matter, but for a more thorough review, check out Atomic Structure!
Definition of Pure Substances
A simple way to think about pure substances is as something that is made up of only one type of matter that always has the same properties, such as melting point, boiling point, density, etc.
Pure substances are matter that has a fixed chemical composition and properties that do not change.
Can you guess what are pure substances in your day-to-day life? I bet you may have salt (NaCl) and tin cans (Sn) in your pantry! These are perfect examples of pure substances because salt is made up of purely NaCl molecules, and tin is made up of only tin atoms.
But wait, you may have noticed a difference between salt and tin and asked how exactly salt is only made up of one type of matter when it’s two different atoms bonded together?
Pure substances can be further divided into two classes: elements and compounds.
Pure Substance Examples
We are going to spend some time looking at elements and compounds separately and some common examples of each!
Elements
If you think elements sound familiar, you are correctly thinking of the 118 organized in the periodic table. Tin is an example of an element!
Explanation:
There are two resistors connected in parallel: R1-43 Ohms and R2-43 Ohms.
Determine the equivalent resistance. Round your answer to 2 significant digits only. For example, if the answer is 65.4 Ohms write 65.
The equivalence resistance rounded off to two significant digits is
22 Ohms.How to find the equivalent resistanceThe equation used to work out the equivalent resistance of two resistors in parallel is as follows:
1/Req = 1/R1 + 1/R2
When R1 and R2 are set at 43 Ohms, we can fill in the placed values like so:
1/Req = 1/43 + 1/43
Simplifying to reduce the equation
1/Req = 2/43
cross multiplying the sides of the equation:
2 x Req = 43
Isolating Req
Req = 43/2
Req = 21.5 Ohms
Req = 22 Ohms to 2 significant figures
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A simple circuit contains a battery connected with wires to a small bulb that has a resistance of 150 ohms. If the power dissipated by the bulb is 0.4 W, what is the voltage of the battery?
Remember to identify all data (givens and unknowns), list equations used, show all your work, and include units and the proper number of significant digits to receive full credit.
Answer: The answer is 7.75v
Explanation; As we know,
power dissipated= (voltage)^2/resistance
0.4w = v^2/150
v^2=0.4w*150ohm
v^2=60
v=7.75v
What is the force required to accelerate a 500 kg object at a rate of 10 m/s^2?
Answer:
Therefore, the force required to accelerate a 500 kg object at a rate of 10 m/s^2 is 5000 Newtons (N).
Explanation:
The force required to accelerate an object can be calculated using the formula:
force = mass x acceleration
where "mass" is the mass of the object being accelerated, and "acceleration" is the rate at which the object's velocity is changing.
In this case, the mass of the object is 500 kg, and the acceleration is 10 m/s^2. Plugging these values into the formula gives:
force = mass x acceleration
force = 500 kg x 10 m/s^2
force = 5000 N
Therefore, the force required to accelerate a 500 kg object at a rate of 10 m/s^2 is 5000 Newtons (N).
drawing shows a force vector that has a magnitude of 475 newtons.
Find the
(a) X,
(b) y, and
(c) z components of the vector.
X, Y, and Z components of the vector are 398, 384 and 279 resp.
Vector is a physical quantity which has both magnitude and direction. Vector A can be written as A = a₁i + a₂j + a₃k where a₁, a₂, a₃ are components along X, Y, Z axis resp. and i,j,k, are the unit vectors along X,Y,Z axis resp.
In this figure
vector F is at angle 36° from y axis, hence
x = Fcos33 = 475cos33 = 398 N
y = Fcos36 = 475cos36 = 384 N
z = Fsin36 = 475sin36 = 279 N
The vector can be written as
F = 398i + 384j + 279k
Hence x, y and z components of this force is 398, 384 and 279 resp.
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A radioactive source has decayed to 1/10 of 1% of its initial activity in 100 days. What is its half life period?
The half-life period of the radioactive source is approximately 693.15 days.
The activity of a radioactive source is known to follow an exponential decay law given by:
A(t) = A(0) × (1/2)[tex]^{t/T}[/tex]
where,
A(t) = activity at time t
A(0) = initial activity
T = half-life period and (1/2)[tex]^{t/T}[/tex] is the fraction of the original activity remaining after time t.
We are given that the activity of the source has decayed to 1/10 of 1% of its initial activity, which is equivalent to 0.001 times the initial activity. This means that:
A(t) = 0.001 ) × A(0)
We are also given that this has occurred in 100 days, so:
t = 100
Substituting these values in the equation, we get:
0.001 × A(0) = A(0) × (1/2)¹⁰⁰/[tex]^T[/tex]
Simplifying and solving for T, we get:
T = -100 / In(1/2) × log(0.001))
T ≈ 693.15 days
Therefore, the half-life period of the radioactive source is approximately 693.15 days.
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The half-life of a radioactive source that decayed to 1/10 of 1% of its initial activity in 100 days is approximately 14.61 days.
Explanation:The given problem can be solved using the formula for radioactive decay, which is N = N0 * (1/2)^(t/h), where N is the final quantity, N0 is the initial quantity, t is time passed, and h is the half-life time. Here, the radioactive source has decayed to 1/10 of 1% of its initial activity, meaning N = 0.001 * N0. The time passed is 100 days. Plugging these values into the formula we have: 0.001 = (1/2)^(100/h). Solving for h, the half-life time, gives us a half-life of approximately 14.61 days.
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What areas of daily life are the effects of the laws of physics seen?
Answer: Our day-to-day life highly relates to physics.
Explanation: We know that in physics there are many laws such as gravitational laws, laws of friction, and inertia.For example
When we drive a car, and suddenly apply the bake the drive moves forward. This is actually the LAW OF INERTIA.If we placed a ball on the surface it does not change its position until a force is applied. When we placed an object on the surface of the earth, it does not change its position and size until an external force is applied. This is an example of NEWTON'S FIRST LAW.Writing with a ballpoint pen is another example of a LAW OF GRAVITY. When we write with a ballpoint pen the ball spins and because of the gravity the ink travel to the paper.
Which is an accurate definition of an element?
Question 2 options:
Something that can burn
Something that cannot be broken down into simpler substances through chemical reactions
Something that is essential to living things
Something that combines with hydrogen
Answer:
Explanation:
Something that cannot be broken down into simpler substances through chemical reactions
Which sentence best describes what happens when you turn on a light? (1 point)
A. Potential energy is changed into kinetic energy.
B. Electrical energy is changed into light energy and thermal energy.
C. Light energy is created.
D. Chemical energy is changed into electrical energy and light energy.
A voltage of 32 V generates a work done of 2.10x10^-7 J. Calculate the charge.
Two point charges each carrying a charge of +3.5 E−6 C are located 3.5 meters away from each other.
How strong is the electrostatic force between the two points (k = 9.0 E9 Nm2/C2)?
Is this force a repulsive force or an attractive force?
Remember to identify all data (givens and unknowns), list equations used, show all your work, and include units and the proper number of significant digits to receive full credit.
Answer: the answer is 0.009N
Explanation: as we know, force =KqQ/R^2
F= 9*10^9*3.5*10^-6*3.5*10^-6/(3.5)^2
F=9*10^-3N
A block of mass m is released from the top of a spring and goes through simple harmonic motion. Use equations to show your work (no numerical values).
a. What is the compression of the spring at equilibrium?
b. What is the maximum compression in the spring?
c. Find the maximum acceleration of the block.
How to solve the question, pls ignore my answer ? I don't know how to finsih
The final velocity of the puck, v, is determined as 3 m/s.
What is the impulse received by the puck?The impulse received by the puck is calculated by applying the following formula.
impulse received = change in momentum of the puck = area under the curve
Area under the curve = area of triangle
Area of triangle = ¹/₂ x b x h
where;
b is the base = ( 5 ms - 2 ms) = 3 ms = 0.003 sh is the height = 160 NArea = ¹/₂ x 0.003 s x 160 N
Area = 0.24 Ns
Therefore, impulse (J) = change in momentum (ΔP) = 0.24 Ns
The final velocity of the puck is calculated as follows;
m(vf - vi) = ΔP
where;
vf is the final velocity of the puckvi is the initial velocity of the puckm is the mass of the puckLet vf be in positive direction,
then vi will in negative direction
0.03 kg(vf - (-5 m/s)) = 0.24 Ns
vf + 5 = 0.24/0.03
vf + 5 = 8
vf = 8 - 5
vf = 3 m/s
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Calculate the energy changes corresponding to the transitions of the hydrogen atom. From n = 3 to n = ∞.
Answer: ΔE = -2.42 × 10^-19 J
Explanation:
The energy of an electron in the nth energy level of a hydrogen atom is given by the following formula:
E = (-2.18 × 10^-18 J) × (Z^2 / n^2)
where Z is the atomic number (1 for hydrogen) and n is the principal quantum number.
The energy change corresponding to a transition from energy level n1 to energy level n2 is given by the formula:
ΔE = E2 - E1 = (-2.18 × 10^-18 J) × Z^2 (1/n2^2 - 1/n1^2)
Given that the electron transitions from n = 3 to n = ∞, we can substitute n1 = 3 and n2 = ∞ in the above formula to obtain:
ΔE = (-2.18 × 10^-18 J) × 1^2 (1/∞^2 - 1/3^2)
ΔE = (-2.18 × 10^-18 J) × (1/9)
ΔE = -2.42 × 10^-19 J
Therefore, the energy change corresponding to the transition of the hydrogen atom from n = 3 to n = ∞ is -2.42 × 10^-19 J.
The energy change for the transition of a hydrogen atom from n = 3 to n = ∞ is 1.511 eV. This transition represents the electron moving to an energy level where it is essentially unbound from the nucleus, resulting in an energy increase.
The energy changes corresponding to the transitions of a hydrogen atom can be calculated using the formula for energy levels in hydrogen:
E = -13.6 eV * (Z² / n²)
Where:
E is the energy of the electron in electronvolts (eV).
Z is the atomic number, which is 1 for hydrogen.
n is the principal quantum number, representing the energy level.
Given the transition from n = 3 to n = ∞, we can calculate the energy change:
Calculate the initial energy (n = 3):
Einitial = -13.6 eV * (1² / 3²) = -13.6 eV * (1/9) = -1.511 eV
Calculate the final energy (n = ∞):
Efinal = -13.6 eV * (1² / ∞²)
In the final state, as n approaches infinity, the energy becomes zero.
Calculate the energy change (ΔE):
ΔE = Efinal - Einitial = 0 - (-1.511 eV) = 1.511 eV
So, the energy change corresponding to the transition of a hydrogen atom from n = 3 to n = ∞ is 1.511 electronvolts (eV).
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a) i) Calculate the change in length of a 1.5m long copper bar when its temp is raised from 303K to 353K . (3mks)
Answer:
the change in length of the copper bar is 1.26 x 10^-3 meters (or 1.26 millimeters).
Explanation:
The change in length of a copper bar can be calculated using the formula:
ΔL = L₀αΔT
where:
ΔL = change in length
L₀ = original length of the copper bar (1.5 m)
α = coefficient of linear expansion for copper (16.8 x 10^-6 K^-1)
ΔT = change in temperature (353 K - 303 K = 50 K)
Plugging in the values, we get:
ΔL = (1.5 m)(16.8 x 10^-6 K^-1)(50 K)
ΔL = 1.26 x 10^-3 m
SOMEONE PLEASE HELP ASAP?!
A neutron and a proton combine to form a nucleus. How does the sum of the masses of the nucleons that make up the nucleus compare with the mass of the nucleus itself?
The nucleons have less mass, because matter is converted into binding energy. Option D is correct.
During the process of combining a neutron and a proton to form a nucleus, a small amount of mass is converted into binding energy. This is due to the strong nuclear force that holds the nucleus together. The mass of the nucleus is slightly less than the sum of the masses of the individual nucleons, and the difference in mass is referred to as the mass defect.
This mass defect is related to the binding energy of the nucleus through Einstein's famous equation E=mc², where E is energy, m is mass, and c is the speed of light. The mass defect represents the amount of mass that is converted into binding energy to hold the nucleus together. Option D is correct.
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3) Vector A is 2.8 cm at 60° above the positive x-axis. Vector B is 1.90 cm at 60° below the
positive x-axis. Use components to find the following:
a) A + B
b) A -B
c) B-A
a) A + B: 3.9 cm, 0°
b) A - B: 0.9 cm, 60°
c) B - A: 0.9 cm, 240°
The Gift of the Magi
by O Henry
After Della counted her money she flopped down on the couch and began to scream and cry. Sobs, sniffles and smiles seem to be a progression from sadness to satisfaction.
Read the passage closely and answer the following question:
On reflection, what did Della (Mrs. James Dillingham Young) decide that life was made up of?
On reflection, what did Della (Mrs. James Dillingham Young) decide that life was made up of happiness.
In the context of mental or emotional states, happiness refers to good or pleasant emotions ranging from satisfaction to profound delight. Life satisfaction, well-being, subjective well-being, flourishing, and eudaimonia are some of the other types.
Happiness research has been carried out in a wide range of scientific fields since the 1960s, including gerontology, social psychology and positive psychology, clinical and medical research, and happiness economics.
when he saw how much money he is having he found that he has lots of money, he scream and cry with happiness and joy. Then he decided that the life is made up of happiness.
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A point charge of 1.0 C is 15 m from a second point charge, and the electric force on one of them due to the other is 1.0 N. What is the modulus of the second load? (k = 1/4πε0 = 8.99 × 109N∙m2/C2)
The modulus (or magnitude) of the second charge is approximately 3.34 × 10⁻⁶ C.
We can use Coulomb's law to solve this problem:
F = k * (q₁ * q₂) / r²
where F is the electric force between the two charges, q₁ and q₂ are the magnitudes of the charges, r is the distance between the charges, and k is the Coulomb constant.
We know that the electric force between the two charges is 1.0 N, that one of the charges has a magnitude of 1.0 C, and that the distance between the charges is 15 m. Therefore, we can solve for the magnitude of the second charge:
1.0 N = (8.99 × 10⁹ N∙m²/C²) * (1.0 C) * q₂ / (15 m)²
Solving for q₂, we get:
q₂ = (1.0 N) * (15 m)² / (8.99 × 10⁹ N∙m²/C²) ≈ 3.34 × 10⁻⁶ C
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The figure shows wire 1 in cross section; the wire is long and straight, carries a current of 4.20 mA out of the page, and is at distance d₁ = 2.58 cm from a surface. Wire 2. which is parallel to wire 1 and also long, is at horizontal distance d-5.05 cm from wire 1 and carries a current of 6.88 mA into the page. What is the x component of the magnetic force per unit length on wire 2 due to wire 1?
Wire 1 in cross section; the wire is long and straight, carries a current of 4.20 mA out of the page, and is at distance d₁ = 2.58 cm from a surface. Wire 2. which is parallel to wire 1 and also long, is at horizontal distance d-5.05 cm from wire 1 and carries a current of 6.88 mA.
To find the x component of the magnetic force per unit length on wire 2 due to wire 1, we can use the formula for the magnetic force between two parallel current-carrying wires we get
F = μ₀I₁I₂/(2πd)
Where F is the magnetic force per unit length, μ₀ is the magnetic constant (4π x [tex]10^{-7}[/tex]Tm/A), I₁ and I₂ are the currents in the wires, and d is the distance between the wires.
In this problem, we need to find the x component of the magnetic force per unit length on wire 2 due to wire 1. We can break down the problem into components by considering the direction of the magnetic field due to wire 1 at the position of wire 2. The magnetic field due to wire 1 will be perpendicular to both wire 1 and wire 2, and will be directed into the page.
To find the x component of the magnetic force, we need to consider the component of the magnetic force that is perpendicular to wire 2. This component will be directed along the x axis, and will have a magnitude of
[tex]F_{x}[/tex] = Fsinθ
Where θ is the angle between the direction of the magnetic force and the x axis. Since the magnetic force is directed into the page, θ is 90 degrees, and sinθ = 1.
Substituting the values given in the problem, we get
F = (4π x [tex]10^{-7}[/tex]Tm/A)(4.20 x[tex]10^{-3}[/tex] A)(6.88 x [tex]10^{-3}[/tex]A)/(2π*0.0258 m)
F = 3.99 x [tex]10^{-10}[/tex] N/m
Therefore, the x component of the magnetic force per unit length on wire 2 due to wire 1 is
[tex]F_{x}[/tex] = Fsinθ= (3.99 x [tex]10^{-10}[/tex] N/m)(1) = 3.99 x [tex]10^{-10}[/tex] N/m
Hence, the x component of the magnetic force per unit length on wire 2 due to wire 1 is 3.99 x [tex]10^{-10}[/tex] N/m.
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The magnitude of a uniform electric field between two plates is about 1.7 ✕ 106 N/C. If the distance between these plates is 3.7 cm, find the potential difference between the plates.
The magnitude of a uniform electric field between two plates of capacitor is about 1.7 ✕ 106 N/C. If the distance between these plates is 3.7 cm then the potential difference between the plates is 62.5 kV.
A capacitor is a device that stores electrical energy in an electric field by collecting electric charges on two isolated surfaces. It is a two-terminal passive electrical component.
Electric field of the parallel plate capacitor is given as,
E = V/d
Given,
E = 1.7 ✕ 10⁶ N/C.
d = 3.7 cm,
V= Ed
V = 1.7 ✕ 10⁶ N/C × 3.7 × 10⁻² m
V = 62.5 kV.
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OA. True
OB. False
An unhappy 0.400 kg rodent, moving on the end of a spring with force constant 3.50 N/m , is acted on by a damping force Fx=−bvx .
The equation of motion for the rodent is x(t) = -1.12cos(3.20t), and the damping force is Fd = -0.62*vx(t). The damping force will cause the amplitude of the motion to decrease over time, and the rodent will eventually come to rest at the equilibrium position.
We can use the following equations to solve this problem:
F = -kx (Hooke's Law)
F = ma (Newton's Second Law)
a = d^2x/dt^2 (Definition of Acceleration)
Fd = -bv (Definition of Damping Force)
x(t) = A*cos(ωt + φ) (Equation of Motion for Simple Harmonic Motion)
We will need to use these equations to find the displacement, velocity, and acceleration of the rodent as a function of time, and then use that information to calculate the damping force and solve for the parameters of the motion.
First, let's find the natural frequency of the system:
ω = sqrt(k/m) = sqrt(3.50 N/m / 0.400 kg) = 3.20 rad/s
Next, let's assume that the rodent starts at its maximum displacement and moves in simple harmonic motion. We can use the equation of motion for simple harmonic motion to write:
x(t) = A*cos(ωt + φ)
where A is the amplitude of the motion and φ is the phase angle.
To find A and φ, we need to use the initial conditions. We know that at t=0, the rodent is at its maximum displacement, so x(0) = A. We also know that at t=0, the velocity of the rodent is zero, so vx(0) = -Aωsin(φ) = 0. This means that either A=0 (the rodent is not moving) or sin(φ) = 0 (the rodent is moving with maximum velocity). We will assume that the latter is true, so sin(φ) = 0 and cos(φ) = 1.
Now we can write:
x(t) = A*cos(ωt)
To find A, we use the fact that the rodent has a mass of 0.400 kg and is moving on a spring with force constant 3.50 N/m. The force on the rodent is given by:
F = -kx = -3.50 N/m * A*cos(ωt)
At maximum displacement, the force is equal to the weight of the rodent:
mg = 0.400 kg * 9.81 m/s^2 = 3.92 N
So we can write:
3.92 N = -3.50 N/m * A
A = -1.12 m
Therefore, the equation of motion for the rodent is:
x(t) = -1.12cos(3.20t)
To find the velocity and acceleration of the rodent, we take the derivative of the displacement with respect to time:
vx(t) = dx/dt = 3.58sin(3.20t)
ax(t) = d^2x/dt^2 = -11.46cos(3.20t)
To find the damping force, we use the equation:
Fd = -bv = -bdx/dt = -b3.58sin(3.20t)
We don't know the value of b, so we can't solve for it directly. However, we can use the fact that the damping force is equal to the work done by the damping force over one cycle of motion. This work is equal to the energy lost by the system due to damping. Since the system is losing energy at a rate proportional to its velocity, we can write:
Energy lost per cycle = Average damping force * Distance traveled per cycle
The distance traveled per cycle is equal to 2piA = 7.04 m, since the rodent moves from its maximum displacement to its minimum displacement and back again in one cycle.
The average damping force over one cycle is equal to the time average of the damping force:
<Fd> = (1/T)∫[0,T] -bdx/dt dt
where T = 2*pi/ω is the period of the motion. Evaluating the integral gives:
<Fd> = (1/T)∫[0,T] -b(-1.12)3.20sin(3.20*t) dt
<Fd> = 3.58*b
Since the energy lost per cycle is also equal to (1/2)kA^2, we can write:
(1/2)kA^2 = <Fd>2pi*A
Solving for b, we get:
b = (kA)/(2pi)
Substituting the given values, we get:
b = (3.50 N/m * 1.12 m)/(2*pi) = 0.62 Ns/m
Therefore, the equation of motion for the rodent is:
x(t) = -1.12cos(3.20t)
vx(t) = 3.58sin(3.20t)
ax(t) = -11.46cos(3.20t)
and the damping force is given by:
Fd = -0.62*vx(t)
Note that the negative sign indicates that the damping force acts in the opposite direction to the velocity of the rodent. This means that the damping force will cause the amplitude of the motion to decrease over time, and the rodent will eventually come to rest at the equilibrium position.
Therefore,The equation of motion for the rodent is x(t) = -1.12cos(3.20t), and the damping force is Fd = -0.62*vx(t).
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