In the figure particle 1 (of charge +8.45 mC), particle 2 (of charge +8.45 mC), and particle 3 (of charge Q) form an equilateral triangle of edge length a. For what value of Q (both sign and magnitude) does the net electric field produced by the particles at the center of the triangle vanish?
Answers
The value of Q for which the net electric field produced by the particles at the center of the triangle vanishes is, Q = −5.63 × 10⁻³ C, with a negative sign indicating that the charge is negative.
Let's choose a coordinate system where the center of the equilateral triangle is at the origin, and the particles are located at the vertices of an equilateral triangle of edge length a. Then, the electric field produced by each particle at the center is:
E₁ = k * q₁ / r₁², where q₁ = +8.45 mC, r₁ = a / √3
E₂ = k * q₂ / r₂², where q₂ = +8.45 mC, r₂ = a / √3
E₃ = k * Q / r₃², where r₃ = a
Here, k is Coulomb's constant, which is approximately equal to 9 × 10⁹ N⋅m²/C².
Since the three particles are equally distant from the center of the triangle, the magnitude of the net electric field at the center is:
|E_net| = |E₁ + E₂ + E₃|
Using the above equations for E₁, E₂, and E₃, we can substitute the values and simplify the expression:
|E_net| = k * (q₁ / r₁² + q₂ / r₂² + Q / r₃²)
= k * [8.45 × 10⁻³ C / (a² / 3) + 8.45 × 10⁻³ C / (a² / 3) + Q / a²]
= k * [(16.9 × 10⁻³ C) / (a² / 3) + Q / a²]
For the net electric field to be zero, we need:
|E_net| = k * [(16.9 × 10⁻³ C) / (a² / 3) + Q / a²] = 0
This implies:
(16.9 × 10⁻³ C) / (a² / 3) + Q / a² = 0
Solving for Q, we get:
Q / a² = −(16.9 × 10⁻³ C) / (a² / 3)
Q = −16.9 × 10⁻³ C / 3
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Related Questions
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.
A radioactive source has decayed to 1/10 of 1% of its initial activity in 100 days. What is its half life period?
Answers
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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A portable power source is available for travelers who need electricity for
appliances. The power scurce provides 54 W of power to operate an air
compressor for inflating tires. This compressor draws 4.5 A of current when
connected to the power supply. What is the voltage across the compressor?
Answers
The voltage across the compressor is 12 V.
Power of the power source, P = 54 W
Current utilized, I = 4.5 A
The equation for power of a circuit is given by,
P = VI
Therefore, voltage across the compressor,
V = P/I
V = 54/4.5
V = 12 V
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1. A neutron has a neutral charge because:
a. it is composed of positive quarks and negative electrons
b. it is composed of an equal number of protons and electrons
c. it is composed of an equal number of positive and negative electrons
d. it contains a specific combination of quarks
Answers
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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What is the process where light bounces back from an object at the same angle and intensity as it. is received by the object?
Answers
Answer: It is Reflection
Explanation: Reflection occurs when incoming solar radiation bounces back from an object or surface that it strikes in the atmosphere, on land, or water, and is not transformed into heat.
Speed velocity and acceleration puzzle level 2
Answers
When describing motion, speed indicates the pace at which an object is travelling. It has one scalar component identifying its magnitude, irrespective of direction.
How to explain the informationThe unit for measuring speed can be either meters per second (m/s) or miles per hour (mph). For velocity, it's a different story. Its definition encompasses both speed and direction since it's a vector quantity. Measureable just like speed using m/s or mph.
In plain physic terms, acceleration reveals how much speed changes over time; hence it is also a vector quantity with not only size but also direction. Depending on whether a physical item is increasing in momentum, slowing down or static, the value could be positive, negative, or zero. Acceleration is calculated using units metres per second squared (m/s2).
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Which two factors affect the amount of thermal energy an object has?
A. The amount of motion its particles have
B. The mass of the object
c. The directions in which its particles are moving
D. The amount of space between its particles
Answers
The two factors that affect the amount of thermal energy an object has are;
A. The amount of motion its particles haveD. The amount of space between its particlesWhat is thermal energy?Thermal energy can be regarded as the energy which is been contained within a system it can be considered as the one that is responsible for its temperature.
It should be noted that the Heat is the flow of thermal energy and it can be seen as opne that deals with how heat is transferred between different systems .
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Which item is a piece of golf equipment that supports the ball so the player can strike it?
O fairway
O divot
O par
O tee
Answers
Which of the following is NOT an interaction among body systems?
A. The circulatory system works with the digestive system to deliver digested nutrients to cells.
B. The nervous system send signals to the musculoskeletal system to cause movement.
C. The excretory system works with the circulatory system to remove toxic carbon dioxide from cells.
D. The immune system gathers information for the respiratory system to aid in white blood cell production.
Answers
Option C, "The excretory system works with the circulatory system to remove toxic carbon dioxide from cells," is NOT an interaction among body systems.
Carbon dioxide is a waste product of cellular respiration, and it is removed from the body by the respiratory system, not the excretory system. The circulatory system plays a role in transporting carbon dioxide from the body's tissues to the lungs, where it can be exhaled.
Answer:
C: The excretory system works with the circulatory system to remove toxic carbon dioxide from cells.
Explanation:
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
Answers
Answer:
Explanation:
Something that cannot be broken down into simpler substances through chemical reactions
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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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.
Answers
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 toy racing car moves with constant speed around the circle shown below. When it is at point A its coordinates are x = 0, y = 3 m and its velocity is (6 m/s)ˆi. When it is at point B its velocity and acceleration are
Answers
The speed of the car is 6 m/s. The acceleration vector at point B has a direction of (-1, -1) and a magnitude of approximately 16.97 m/s².
We can start by finding the speed of the toy car. Since it is moving with constant speed around the circle, its speed is the same at points A and B. To find the speed, we can use the fact that the velocity vector has a magnitude equal to the speed:
|v| = √((6 m/s)²) = 6 m/s
So the speed of the car is 6 m/s.
Next, we can find the direction of the velocity vector at point B. We know that the car is moving around a circle centered at the origin, and that point B is on the circle. Therefore, the velocity vector at point B is tangent to the circle and perpendicular to the line connecting the origin to point B.
The line connecting the origin to point B is given by:
y = (0 - 3)/(0 - (-3)) * (x - (-3)) + 0
y = -x + 3
The velocity vector at point B is therefore perpendicular to this line, which means it has a direction given by the vector (1, -1).
Finally, we can find the acceleration vector at point B. Since the car is moving with constant speed around a circle, it is undergoing uniform circular motion, which means it is accelerating towards the center of the circle. The magnitude of the acceleration is given by:
a = v² / r
where v is the speed and r is the radius of the circle. We don't know the radius of the circle, but we can find it using the fact that point B lies on the circle. The distance from the origin to point B is:
d = √((-3 - 0)² + (0 - 3)²) = 3√(2) m
Therefore, the radius of the circle is:
r = d / 2 = (3√(2)) / 2 m
Substituting in the values for v and r, we get:
a = (6 m/s)² / ((3√(2)) / 2 m) ≈ 16.97 m/s²
To find the direction of the acceleration vector, we can use the fact that it is pointing towards the center of the circle. The center of the circle is at the origin, so the acceleration vector at point B is given by the vector (-3, 0) minus the vector (0, 3), which is:
(-3, 0) - (0, 3) = (-3, -3)
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calculate the potential energy of a 11kg object that is 11m off the ground
Answers
The potential energy of an 11kg object that is 11m off the ground is 1199.8J.
The potential energy of the body is defined as the energy which is possessed by the body when the position of the body is at rest. When the object is at rest the potential energy is possessed by the body and then when the body starts moving the potential energy is converted into kinetic energy.
The potential energy of a body is given by the expression:
P.E=mgh;
where 'm' is the mass of the body which is given as 11kg given in the question, and 'g' is the acceleration due to gravity which is equal to (9.8 m/s^2).
So the potential energy here is:
P.E = (11kg)*(9.8 m/s^2)*(11m)
P.E = 1199.8 Joules.
Therefore, the potential energy of an 11kg object that is 11m off the ground is 1199.8J.
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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?
Answers
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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As explained by the second law of thermodynamics, which example of energy transformation could never occur?
A.**The 400 J of heat added to the operating gas of a heat engine is transformed into 400 J of work.
B.The 400 J of kinetic energy of a rolling ball is transformed into 400 J of heat.
C.A refrigerator removes 100 cal of heat from a bottle of milk while using 75 cal of electrical energy.
D.A heat engine does 25 J of work while expelling 10 J of heat to the cold reservoir.
Answers
The example of energy transformation that could never occur, as explained by the second law of thermodynamics, is the 400 J of heat added to the operating gas of a heat engine is transformed into 400 J of work. Option A is correct.
The second law of thermodynamics states that in any energy transformation, the total entropy (measure of disorder) of a closed system will always increase or remain constant. It means that some energy will always be wasted as heat and cannot be completely converted into useful work. The second law of thermodynamics is a fundamental law of nature that governs energy transformations.
It states that in any energy transformation process, the total entropy (measure of disorder) of a closed system will always increase or remain constant. Entropy can be thought of as a measure of the amount of energy that is unavailable to do useful work. It is impossible to transform all 400 J of heat into work without generating any waste heat. This is because the heat engine must expel some heat to the cold reservoir to comply with the second law. Option A is correct.
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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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help
1. Calculate the Energy of skater at all the positions shown. Position C is the highest point the skater reaches
Answers
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 rectangle loop with a length of 3 mm and width of 6 mm is positioned in a uniform magnetic field of magnitude 0.5 N/C so that the plane of the loop makes an angle of 75° with the magnetic field. Find the flux passing through the rectangle loop.
Answers
flux = 2.34 x 10^-6 Wb
Explanation:
The magnetic flux through a loop is given by the product of the magnetic field and the area of the loop, multiplied by the cosine of the angle between the normal to the plane of the loop and the magnetic field.
In this case, the magnitude of the magnetic field is given as 0.5 N/C. However, we assume that this value refers to the electric field (which is measured in newtons per coulomb), instead of the magnetic field. Therefore, we will assume that the magnitude of the magnetic field is actually 0.5 T.
The area of the rectangle loop is given by the product of its length and width, i.e.,
A = (3 mm) x (6 mm) = 18 mm^2
Converting this to SI units, we get:
A = 18 x 10^-6 m^2
The angle between the plane of the loop and the magnetic field is given as 75°. Therefore, the cosine of this angle is:
cos(75°) = 0.259
Putting all these values together, we get:
flux = B * A * cos(75°)
flux = (0.5 T) * (18 x 10^-6 m^2) * 0.259
flux = 2.34 x 10^-6 Wb
Therefore, the magnetic flux passing through the rectangle loop is 2.34 x 10^-6 Weber (Wb).
2. Single Choice
In a transverse wave, the individual particle of the medium ( )
A: moves in a circle.
B: moves in ellipses.
C: move parallel to the direction of the wave's travel.
D: move perpendicular to the direction in which the waves travel.