Answers
The electric field produced by the two particles is equal to zero at a coordinate on the x-axis of 41.1 cm.
The electric field produced by the two particles can be found using the equation E = kq/r^2, where k is the Coulomb constant, q is the charge of the particle, and r is the distance from the particle. At a point where the electric fields produced by the two particles are equal in magnitude and opposite in direction, the net electric field will be zero.
Using this information, we can set the electric fields produced by each particle equal to each other and solve for the position where they cancel out. This gives us:
k(2.03 x 10⁸)/[(x - 0.22)²] = -k(4.0091)/[(x - 0.71)²]
Simplifying and solving for x gives:
x = 0.411 m or 41.1 cm
As a result, the electric field generated by the two particles is equal to zero at 41.1 cm on the x-axis.
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Related Questions
What is the primary difference between outlaw motorcycle gangs and social motorcycle groups?
O A.
OB.
O C.
O D.
being a structured group with roles
having a group leader
their group activities and behavior
having group rules
Answers
Answer:
The primary difference between outlaw motorcycle gangs and social motorcycle groups is their group activities and behavior. Outlaw motorcycle gangs are typically involved in criminal activities, such as drug trafficking, extortion, and violence. They often have a hierarchical structure and strict rules for membership and behavior. In contrast, social motorcycle groups are primarily focused on riding motorcycles and socializing with other riders. They do not engage in criminal activities and do not have a strict hierarchy or rules for membership. While both types of groups may have some level of structure, such as having a group leader or group rules, the main difference lies in their group activities and behavior.
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
Answers
a) A + B: 3.9 cm, 0°
b) A - B: 0.9 cm, 60°
c) B - A: 0.9 cm, 240°
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.
Answers
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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A voltage of 32 V generates a work done of 2.10x10^-7 J. Calculate the charge.
Answers
Rearranging the formula gives q = W/V.
Substituting the given values, we get:
q = (2.10 x 10^-7 J) / (32 V)
q = 6.56 x 10^-9 C
Therefore, the charge is 6.56 x 10^-9 C.
3
Extremist groups typically mix radical beliefs or values with anger over some aspect of society.
OA. True
OB. False
Answers
Extremist groups typically mix radical beliefs or values with anger over some aspect of society"
Because Extremist groups often mix radical beliefs or values with anger over some aspect of society. They may believe that their group or ideology is under threat, and they may use violence or other extreme measures to defend their beliefs or advance their cause. Extremist groups can be found on the far right, far left, or in religious or cultural movements, and their tactics can range from peaceful protests to terrorism.
A man is in a helicopter ascending vertically at constant rate of 24.5m/s accidentally drops a toy out the window when the helicopter is 120.0m above the ground. (g = 9.8m / s)
a. How long will it take the toy to reach the ground
b. What will its speed be when it hits the ground?
Answers
It will take the toy 5.02 seconds to reach the ground, The speed at which the toy hits the ground is 49.0 m/s.
Free fall is the motion of an object falling solely under the influence of gravity. In free fall, the object experiences an acceleration of 9.8 m/s^2 downwards towards the ground (assuming no air resistance), regardless of its mass or size.
a. To determine the time it takes for the toy to reach the ground, we can use the formula for the height of an object in free fall:
h = (1/2)gt^2
Where h is the initial height, g is the acceleration due to gravity, and t is time.
At the instant the toy is dropped, its initial height above the ground is h = 120.0 m, and the acceleration due to gravity is g = 9.8 m/s^2. Thus, we can rearrange the formula to solve for time:
t = sqrt(2h/g)
t = sqrt(2(120.0 m)/(9.8 m/s^2)) = 5.02 s
So, it will take the toy approximately 5.02 seconds to reach the ground.
b. To find the speed at which the toy hits the ground, we can use the formula for final velocity in free fall:
v = sqrt(2gh)
Where v is the final velocity, g is the acceleration due to gravity, and h is the initial height. At impact, the initial height of the toy is 0 m. Therefore:
v = sqrt(2gh)
v = sqrt(2(9.8 m/s^2)(120.0 m))
v = 49.0 m/s
So, the speed at which the toy hits the ground is approximately 49.0 m/s.
Hence, The toy will fall to the earth in 5.02 seconds, hitting the ground at a speed of 49.0 m/s.
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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)
Answers
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
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?
Answers
At the highest point of the swing, the child has maximum potential energy and zero kinetic energy. At the lowest point of the swing, the child has maximum kinetic energy and zero potential energy. Therefore, the total energy of the system remains constant, and we can write:
PE = KE
where PE is the potential energy and KE is the kinetic energy.
The potential energy of the child on the swing can be calculated as:
PE = mgh
where m is the mass of the child, g is the acceleration due to gravity, and h is the height of the swing at the highest point. Since the swing hangs from 2.6-m-long chains, the height of the swing at the highest point is:
h = 2.6 m - 2.6 m cos(50°) = 1.32 m
Substituting the values, we get:
PE = (20 kg)(9.81 m/s^2)(1.32 m) = 258.2 J
At the lowest point of the swing, all the potential energy is converted to kinetic energy. The kinetic energy of the child on the swing can be calculated as:
KE = (1/2)mv^2
where v is the speed of the child at the lowest point. Substituting the values, we get:
KE = (1/2)(20 kg)v^2
Equating the potential and kinetic energies, we get:
PE = KE
mgh = (1/2)mv^2
2gh = v^2
v = sqrt(2gh)
Substituting the values, we get:
v = sqrt(2 × 9.81 m/s^2 × 1.32 m) = 4.06 m/s
Therefore, the maximum speed of the child on the swing is 4.06 m/s.
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.
Answers
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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What two things can be considered to be substances?
Answers
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:
please I need answer
Answers
The coefficient of friction between the two surfaces is tan α.
option B.
What is coefficient of friction?The coefficient of friction between two surfaces that are in contact is the ratio of the force of friction to normal reaction.
Mathematically, the formula for coefficient of friction is given as;
μ = Ff/Fn
where;
Ff is the force of frictionFn is the normal forceFor the given diagram,
Ff = mg sinα
Fn = mg cosα
The coefficient of friction;
μ = mg sinα/mg cosα
μ = sinα/cosα = tan α
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An electron is accelerated by a constant electric field of magnitude 403 N/C.
(a) Find the acceleration of the electron.
(b) Find the electron's speed after 1.41 ✕ 10-8 s, assuming it starts from rest.
Answers
An electron is accelerated by a constant electric field of magnitude 403 N/C. The acceleration of the electron is 7 × 10¹³ m/s². electron's speed after 1.41 ✕ 10-8 s is 987000 m/s.
Electric field is field around electrically charged particle where columbic force of attraction or repulsion can be experienced by other charged particles. It is denoted by letter E and it's SI unit is V/m Volt per meter or N/C newton per coulomb.
F = qE where E is electric field, q = 1.60 × 10⁻¹⁹ C is charge on the electron and F is Force on the electron
F = 1.60 × 10⁻¹⁹ C × 403 N/C
F = 644.8 × 10⁻¹⁹ N
F = ma
where m = 9.1 × 10⁻³¹ kg , mass of the electron
a = F/m
a = 644.8 × 10⁻¹⁹ N ÷ 9.1 × 10⁻³¹ kg
a = 7 × 10¹³ m/s²
The acceleration of the electron is 7 × 10¹³ m/s².
The electron's speed after 1.41 ✕ 10⁻⁸ s is,
v = u + at
where u is initial velocity, which is zero.
v = at
v = 7 × 10¹³ m/s² × 1.41 ✕ 10⁻⁸ s
v = 987000 m/s
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In which stage is the individual willing to modify their behavior and their
environment to overcome the problem, as they are ready to change and take
the proper steps to make change happen?
OA. Maintenance
OB. Precontemplation
C. Action
D. Contemplation
SUBMIT
Answers
In C. Action stage is the individual willing to modify their behavior and environment to overcome problem, as they are ready to change and take proper steps to make change happen
Five phases of behaviour modification are identified as per phases of modification model. Precontemplation, Contemplation, Preparation, Action, and Maintenance are the phases. The person has made a commitment to change and is actively making changes to their surroundings and behaviour to address the issue in the Action stage.
In this mode, people have a strategy in place, and are generally moving in the right direction. Since it involves making significant changes to behaviour, attitudes, and lifestyle, the action stage is the most labor-intensive. In addition to having the tools and assistance they require for success, the person must be motivated and dedicated to making the change.
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*Calculation
An intensity level change of 1 dB correspond
s to what percentage change in intensity?
Answers
Answer:
An intensity level change of 1 dB corresponds to a 10% change in intensity.
Ice of mass 14.6 kg at 0°C is placed in an ice chest. The ice chest has 3.5 cm thick walls of thermal conductivity 0.01 W/m x K and a surface area of 1.21 m^2. Express your answers with appropriate mks units.
(a) How much heat must be absorbed by the ice during the melting process?
(b) If the outer surface of the ice chest is at 36° C, how long will it take for the ice to melt?
Answers
The heat absorbed by the melting ice is Q = 4,875,600 J.
How to solvea, Given mass (m) = 14.6 kg, then the heat absorbed by the melting ice is Q = 4,875,600 J.
This can be determined using Q = 14.6 kg × 334,000 J/kg.
b. By utilizing the equation P = (0.01 W/m × K × 1.21 m^2 × 36 K) / 0.035 m, we can determine that P equals 12.396 watts.
To discover how long it will take for the ice to melt, we can use another formula: t = Q / P.
With the given value of Q as 4,875,600 joules and P is equal to 12.396 watts, we find that t evaluates to roughly 393,292 seconds.
In order to transform this result into hours, simply divide by 3600 which leads us to t ≈ 109.25 hours.
Therefore, it is predicted that the ice will melt in approximately 109.25 hours.
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A thermodynamic system consists of an ideal gas at an initial volume of 3.50 L and a pressure of 7.9 × 104 Pa. An external force performs 180 J of work as it compresses the gas at constant pressure. What is the new volume of the gas?
Answers
the new volume of the gas is 3.49 L when An external force performs 180 J of work as it compresses the gas at constant pressure.
An ideal gas is a theoretical gas comprised of numerous randomly moving point particles that do not interact with one another. The ideal gas notion is valuable because it obeys the ideal gas law, which is a simplified equation of state, and is susceptible to statistical mechanics analysis. Work is pressure times change in volume.
Given,
initial Volume V₁ = 3.5 L
initial pressure P = 7.9 × 10⁴ Pa
Work = 180J
Work W = PΔV
180 J = 7.9 × 10⁴ Pa × ( 3.5L - V₂ )
2.27 × 10⁻³ = 0.0035m³ - V₂
3.5 - 2.27 × 10⁻³ = V₂
V₂ = 3.49 L
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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)?
Answers
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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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.
Answers
1. Hooke's Law: F = -kx
2. Energy Conservation: 1/2 kx^2 = mgh = 1/2 mv^2
3. Period of motion: T = 2π√(m/k)
where:
F = force exerted by the spring
k = spring constant
x = displacement from equilibrium
m = mass of the block
g = acceleration due to gravity
h = height of the block above the equilibrium point
v = velocity of the block
T = period of motion
a. When the block is at equilibrium, it is at rest and the net force on it is zero. Therefore, we have:
F = -kx = 0
Solving for x, we get:
x = 0
So the compression of the spring at equilibrium is zero.
b. The maximum compression in the spring occurs when the block is at its maximum displacement from equilibrium. At this point, the block momentarily stops before reversing direction. Using energy conservation, we have:
1/2 kx^2 = 1/2 mv^2
where v = 0 at the maximum compression point. Solving for x, we get:
x = √(2mg/k)
So the maximum compression in the spring is √(2mg/k).
c. The maximum acceleration of the block occurs at the equilibrium point, when the spring is fully compressed and then released. At this point, the net force on the block is equal to the maximum force exerted by the spring. Using Hooke's Law, we have:
F = -kx
At the equilibrium point, x = √(2mg/k), so we have:
F = -2mg
The acceleration of the block is given by:
a = F/m = -2g
So the maximum acceleration of the block is 2g downward.
Which of the following is most likely the caption for the illustration that was scratched out of the textbook?
A. An electrically-charged object can attract an uncharged object with magnetic properties.
B. An electrically-charged object is stronger than a magnet.
C. A dry cell battery has magnetic properties.
D. An electric circuit can only have one dry cell battery.
IMAGE DOWN BELOW OR UP
Answers
The correct statement is " A dry cell battery has magnetic properties.", The correct option is C.
A dry cell battery does generate its own magnetic field due to the flow of electric current through the battery.
The magnetic field is created by the movement of charged particles (electrons) within the battery. This magnetic field is relatively weak and is not typically strong enough to be used for practical applications outside of the battery itself.
So, the magnetic properties of the dry cell battery are important for understanding its behavior within an electrical circuit.
Therefore, The correct answer is option C.
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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?
Answers
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 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.
Answers
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
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?
Answers
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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A 250 kg cart starts from rest and rolls down an inclined plane from a height of 550 m. Determine its speed at a height of 125 m above the bottom of the incline. Please round to two decimal places.
Answers
Answer:
24.85 m/s.
Explanation:
PE = mgh = 250 kg x 9.81 m/s^2 x 550 m = 1,358,725 J
PE' = mgh' = 250 kg x 9.81 m/s^2 x 125 m = 308,062.5 J
PE = KE
1,358,725 J = 0.5mv^2
Solving for v, we get:
v = sqrt(2PE/m) = sqrt(2 x 1,358,725 J / 250 kg) = 59.15 m/s (rounded to two decimal places)
PE' + KE' = PE + KE
Since the cart starts from rest at the top of the incline, KE = 0. Therefore:
PE' = KE'
mgh' = 0.5mv'^2
Solving for v', we get:
v' = sqrt(2gh') = sqrt(2 x 9.81 m/s^2 x 125 m) = 24.85 m/s (rounded to two decimal places)
Therefore, the speed of the cart at a height of 125 m above the bottom of the incline is 24.85 m/s.
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.
Answers
F = k * (q1 * q2) / r^2
where F is the force, k is Coulomb's constant (9 x 10^9 N*m^2/C^2), q1 and q2 are the charges of the two objects, and r is the distance between them.
In this case, we have two balloons with charges of 8.37 µC and q2 (unknown), separated by a distance of 30 mm, and experiencing a repulsive force of 0.5 N.
We can plug in the given values and solve for q2:
0.5 N = (9 x 10^9 N*m^2/C^2) * (8.37 µC * q2) / (0.03 m)^2
Simplifying:
q2 = (0.5 N * 0.03 m^2) / (9 x 10^9 N*m^2/C^2 * 8.37 µC)
q2 = 2.05 µC
Therefore, the unknown charge is 2.05 µC.
A 150kg diver jumps off a diving board and hits the water at 40 m/s
What is the kinetic energy of the diver entering the water?
Answers
This is an exercise in kinetic energy, which is a form of energy associated with the movement of an object and its speed. It is important in many areas of physics, from classical mechanics to modern physics. This form of energy can be transformed into other forms of energy, such as thermal energy, sound energy or electrical energy. The formula for calculating kinetic energy is KE = m * v^2/2, where m is the mass of the object and v is its speed.
Kinetic energy is a fundamental concept in classical mechanics. It is used to analyze the movement of objects and calculate the amount of work required to stop them. When an object is in motion, it has kinetic energy, which is equal to half its mass times its speed squared. If the object collides with another object, some of its kinetic energy is transferred to the second object in the form of work or heat.
Kinetic energy is also important in modern physics. In Einstein's theory of special relativity, the mass of a moving object increases with its speed, which means that its kinetic energy also increases. In fact, the kinetic energy of a moving object is a form of energy that is included in Einstein's famous equation E=mc^2, where E is the energy, m is the mass of the object, and c is the speed of light. . This equation shows how the mass of an object and its energy are related.
Kinetic energy is also important in quantum physics. In quantum mechanics, particles have a property called momentum, which is a measure of their motion. Momentum and kinetic energy are related, and experiments in quantum physics often measure the momentum and kinetic energy of particles.
It tells us that the diver has a mass of 150 kg, and that he jumps from a diving board into the water at a speed of 40 m/s.
They ask us what is the kinetic energy of the diver who enters the water?We know that the formula for kinetic energy is:
KE = m * v^2/2. We should not do the formula clearance, because we are going to calculate the kinetic energy.
We already know our data from the formula, now we substitute and solve, then
KE = (m × v²)/2
KE = (150 kg × (40 m/s)²)/2
KE = (150 kg × 1600 m²/s²)/2
KE = 120000 J
When the diver enters the water, the kinetic energy is 120,000 J.
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Answer:
The kinetic energy of the diver entering the water is 120,000 Joules.
Explanation:
The kinetic energy (KE) of an object is given by:
[tex]\sf\qquad\dashrightarrow KE = \dfrac{1}{2} * m * v^2[/tex]
where:
m is the mass of the objectv is its velocity.Plugging in the given values, we get:
[tex]\sf\qquad\dashrightarrow KE = \dfrac{1}{2} * 150\: kg * (40\: m/s)^2[/tex]
[tex]\sf\qquad\dashrightarrow KE = \dfrac{1}{2} * 150\: kg * 1600\: m^2/s^2[/tex]
[tex]\sf\qquad\dashrightarrow KE = \boxed{\bold{\:\:120,000\: J\:\:}}[/tex]
Therefore, the kinetic energy of the diver entering the water is 120,000 Joules.
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.
Answers
Two charges of Q coul each are placed at two opposite corners of a square. What additional charges q placed at each of the other two corners will reduce the resultant electric force on each of the charges Q to zero? Is it possible to choose these charges so that the resultant force on all the charges is zero?
Answers
Answer:
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Keyana and Sam are testing the law of conservation of energy. They use the same ball and release it from the same vertical height. Keyana is using a frictionless track, while Sam's track has friction. They discover Keyana's ball had more kinetic energy than Sam's when it reached the bottom. Which statement best explains why this happened if energy is conserved? Sam's ball lost mass as it traveled along the track. Sam's ball interacting with the track converted energy into heat. Keyana's ball was able to gain momentum. Keyana's ball had more potential energy.
Answers
The true statement is "Sam's ball interacting with the track converted energy into heat." The correct option is B.
The law of conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. This means that the total amount of energy in a closed system remains constant.
The friction between Sam's ball and the track caused some of the energy to be lost as heat, while Keyana's ball experienced no such loss due to the absence of friction in her experiment. Therefore, Keyana's ball retained more of its initial potential energy as kinetic energy, resulting in a greater velocity and hence more kinetic energy at the bottom.
Option A (Sam's ball lost mass as it traveled along the track) is not true because it is not possible for the ball to lose mass during the experiment. The mass of the ball is a constant value and is not affected by the experiment.
Option C (Keyana's ball was able to gain momentum) is not the best explanation because momentum is not conserved in this scenario since external forces like friction are acting on the ball. The ball is only gaining kinetic energy.
Option D (Keyana's ball had more potential energy) is not true because both Keyana and Sam released the ball from the same vertical height. Therefore, both balls had the same initial potential energy. The difference in their kinetic energies at the bottom can be explained by the difference in their conservation of energy due to friction.
Therefore, The correct statement that best explains why Keyana's ball had more kinetic energy than Sam's when it reached the bottom, even though energy is conserved, is: Sam's ball interacting with the track converted energy into heat.
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Can positive charges be liberated by the photoelectric effect?
yes
rarely
no
sometimes
Answers
Answer:
No, positive charges cannot be liberated by the photoelectric effect.
Explanation:
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 .
Answers
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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