Since the refractive index of the core is higher than that of the cladding, light in the core striking the cladding boundary at an angle steeper than the critical angle is reflected back into the core by total internal reflection.
What is refractive index?The numerical aperture (n12 - n22 = NA2) can be provided to find the refractive index of the cladding. The formula for determining the number of reflections in an optical fiber is: Number of reflections =lx=l3d= 2203106=57735 57000.Due to the helical nature of the optical path, this type of optical fiber works only if the wavelength is significantly smaller than the core radius. This means that the core of a step-index fiber has a constant refractive index.Since the refractive index of the core is higher than that of the cladding, light in the core striking the cladding boundary at an angle steeper than the critical angle is reflected back into the core by total internal reflection.to learn more about refractive index from the given link:
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What is the magnitude of the electric field at a point 2.0m from a point charge q=4.0nC? A.9N/CB.90N/CC.0.9N/CD.900N/C
The electric field has a 9 N/C magnitude.
In this case, we must find the size of an electric field resulting from a specific charge.
The idea of an electric field is taken from the reformulated version of Coulomb's law.
We'll employ the following formula:
E = 9 x 10 9 Nm2/C2 (q/r2), where q is the charge and C r is the charge's distance from the electric field, both expressed in coulombs.
R = 2 m for the information provided.
q = 4.0 nc = 4 x 10⁻⁹ C
E = ?
the problem's resolution
Use the following information to replace the formula for the electric field:
E=9x10-9 Nm2/C2 (q/r2)
E = 4 x 109 C / (2m)2 (4 x 109 N / m2)2
E = 9 N/C
As a result, the electric field's strength is 9 N/C in the direction of the charge.
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two identical spheres with mass are hung from silk threads of length (fig. p21.60). the spheres have the same charge, so the radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. show that if the angle is small, the equilibrium separation between the spheres is (hint: if is small, then )
The equilibrium distance between the centers of the balls will be
x =[tex](2q1q2lmg)^{\frac{1}{3} }[/tex].
What are the main forces acting on each balll?To find the equilibrium distance between the two balls, we need to consider the forces acting on each ball. The main forces acting on each ball are the gravitational force and the electrostatic force between the two balls.
The gravitational force on each ball is given by:
Fg = mg (where g is the acceleration due to gravity)
The electrostatic force between the two balls is given by:
Fe = kq1q2/x² (where k is Coulomb's constant, and x is the distance between the centers of the two balls)
For equilibrium to occur, the net force on each ball must be zero. Therefore, we can set up the following equation:
Fg - Fe = 0
Substituting in the values for Fg and Fe, we get:
mg - (kq1q2/x²) = 0
Solving for x, we get:
x =[tex](2q1q2lmg)^{\frac{1}{3} }[/tex].
where l is the length of the silk threads.
So, the equilibrium distance between the centers of the balls will be:
x =[tex](2q1q2lmg)^{\frac{1}{3} }[/tex].
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A net force is required to stop a 100 kg car , traveling at 3 m.s -1 . By what factor would the NT force acting on the car change if
a) the car was stopped in double time
b) the car was stopped in 1 tenth of the time
c) the car was traveling at double the velocity and it's stopped in the same time ?
You must add up all of the forces operating on a certain object in order to calculate the net force acting on that object.
How are net forces calculated?These interactions can be summed up by Newton's second law of motion. Net Force = Mass Acceleration, or F = m a, is how the preceding equation for acceleration may be expressed to solve for net force.For the 1000kg automobile to accelerate by 3m/s2, 3000N of force is required.Numerous additional forces, such as gravitational force Fg, frictional force Ff, and the normal force, act on the body when a force is applied to it. These additional forces serve to balance the original force. FNet = Fa + Fg + Ff + FN is the result, and it represents the net force formula.To learn more about net force refer to:
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Part A
Consider each of the following statements that you might hear in everyday life. Classify each statement as either an observation or an explanation.
[Observations]
- James is wearing a yellow shirt
- The defendant's DNA was found at the crime scene
- The plastic melted when I held it near the light bulb
- The defendant's calendar says he was at lunch when the crime occurred
[Explanations]
- James wears a yellow shirt when his other shirts are dirty
- Plastic melts when it reaches a temperature that breaks bonds that hold its structure intact
- The defendant only intended to scare the victim
Understanding the difference between an explanation and an observation is crucial for success in science (essentially a hypothesis that seeks to explain what we observe).
How do observation and explanation differ from one another?Understanding the difference between an explanation and an observation is crucial for success in science (essentially a hypothesis that seeks to explain what we observe).Generally speaking, galaxies are getting farther apart over time.Due to the expanding universe, we can see objects that are up to 46.1 billion light-years away. The items we can perceive and the objects we may someday be able to reach will always be constrained, no matter how much time passes.The five senses of sight, hearing, smell, touch, and taste can all be used to create observations. Use your sense of smell instead of taste when observing the world outside today.To learn more about observation refer to:
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A 75.2 kg base runner begins his slide into second base while moving at a speed of 4.17 m/s. He slides so that his speed is zero just as he reaches the base. The acceleration of gravity is 9.8 m/s². What is the magnitude of the mechanical energy lost due to friction acting on the run- ner? Answer in units of J.
The mechanical energy loss magnitude due to friction acting on the slider.
What is the mechanical energy loss due to rotor friction?To calculate mechanical energy use the following formula: Mechanical energy = ½ mv2 + mgh. h is the height from the floor. From this formula we can see that the only variables are mass, altitude and velocity. Power = power x speed. Friction force multiplied by constant velocity tells you how much energy is "lost" in one second. If you know the length of the lamp, you can combine that with a constant velocity to find out how many seconds it took to dissipate the amount of energy.Mechanical energy is the ratio of the speed at which the force is applied to the machine to the speed at which the load moves. Mechanical energy is also defined as the ratio of force displacement to load displacement.To learn more about Mechanical energy from the given link:
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In which of the following situations is the velocity constant, but the acceleration is not zero? In no situation can velocity be constant at the same time there is non-zero acceleration A car drives at constant speed along a winding road. A sprinter runs a 100-meter dash along a straight track.A train moves along a straight track at constant speed
In no case can velocity be constant while there is non-zero acceleration.
What is the relation between velocity and acceleration?During uniformly accelerated, straight-line motion, the relationship between velocity and time is straightforward. The greater the change in velocity, the longer the acceleration. When the acceleration is constant, the change in velocity is directly proportional to time.This is also the case in uniform motion, where the object moves at a constant speed. Because acceleration implies a non-zero change in velocity with respect to time, a particle can have zero acceleration if the velocity is constant but non-zero.When the magnitude and direction of a velocity do not change over time, it is said to be constant. In other words, this is when the rate of change of an object's position remains constant over time.To learn more about acceleration refer to :
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1. What is the volume of a solid aluminum sphere with a diameter of 5 inches? Report in cubic meters.
a. If the density of aluminum is 2,700 kg/m3 what is the mass of the aluminum?
b. How many aluminum atoms are in the sphere?( the stable aluminum isotope is 27Al.)
c. Now suppose we give our aluminum sphere a potential of +100 Volts, this corresponds to a charge of about . How many electrons have been gained/lost?
The volume of solid aluminum sphere is 0.00858 cubic meters and mass is 23.16 kg.
The atomic mass is the mass of an atom. The atomic mass or relative isotopic mass refers to the mass of a single particle, and therefore is tied to a certain specific isotope of an element. The atomic mass is carried by the atomic nucleus, which occupies only about 10-12 of the total volume of the atom or less, but it contains all the positive charge and at least 99.95% of the total mass of the atom. Note that, each element may contain more isotopes, therefore this resulting atomic mass is calculated from naturally-occuring isotopes and their abundance.The volume of sphere is given by formula : [tex]\frac{4}{3} \pi r^{3}[/tex]
Where,
r = radius of sphere
Given, r = 5 inches = 0.127 meters
Putting this value in above equation we get, Volume= 0.00858 cubic meters.
Given density of aluminum is 2700 kg/m^3
We know that:
Density = Mass / Volume
i.e. Mass = Density * Volume
= 2700 kg/m^3 * 0.00858 m^3
= 23.16 kg
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an athlete suspected of using steroids is given two tests that operate independently of each other. test a has probability 0.9 of being positive if steroids have been used. test b has probability 0.8 of being positive if steroids have been used.
P(Event) is a probability that an event will occur, and conditional probability may be used to compute it. Given that an athlete has taken steroids, the likelihood that they will test positive for steroid usage is 0.72, or 72%.
If steroids have been used, Test A has a 0.9 chance of being positive, hence P(Test A Positive | Steroids Used) = 0.9
If steroids have been used, there is a 0.8 likelihood that Test B will be positive, hence P(Test B Positive | Steroids Used) = 0.8
The likelihood that a sportsperson will use steroids is denoted by P. (Steroids Used).
The probability that an athlete will test positive for steroid use can be determined using the conditional probability formula, which is as follows: P(Test Positive | Steroids Used) = P(Test A Positive and Test B Positive | Steroids Used) = P(Test A Positive | Steroids Used) * P(Test B Positive | Steroids Used).
= 0.9 * 0.8 = 0.72
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A capacitor has an initial charge of 10 µC. It is observed that after discharging for 2ms through a resistor of 8.7 kn, the charge of the capacitor is now only 8.1 μС. What is the capacitance of the capacitor? Express your answer in micro Farad, and keep three significant digits.
The capacitance on the capacitor with initial charge of 10µC is 1.094 μF.
What is Capacitance?Capacitance can be defined as the capability of a material object or any device to store the electric charge. Capacitance is measured by the change in charge in response to the difference in electric potential of an object, it is expressed as the ratio of the quantities.
Initial charge, Q₀ = 10μC
Time, t = 2 ms
1ms = 10⁻³s
t = 2 × 10⁻³s
Resistance, R = 8.7K Ω
1ΚΩ = 10³Ω
R = 8.7 × 10³ Ω
Charge, Q = 8.1 μC
For a discharging RC circuit
Q = Q₀ × [tex]e^{-t/RC}[/tex]
(Q/Q₀) = [tex]e^{-t/RC}[/tex]
8.1/Q = [tex]e^{-0.002/8.7.10^{3}.C }[/tex]
Apply In on both sides,
In(8.1/10) = ln(e⁻2×10⁻³/8.7 × 10³ × C)
ln(0.81) = 2 × 10⁻³/ 8.7 × 10³ × C
-0.210 = 2 × 10⁻³/ 8.7 × 10³ × C
C = 2 × 10⁻³/8.7 × 10³ × 0.210
C = 2 × 10⁻³/ 1.827 × 10³F
C = 1.094 μF
Therefore, the capacitance of the capacitor is 1.094 μF.
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Compare accuracy and precision.
Answer:
Accuracy refers to how close a measurement is to the true or accepted value. Precision refers to how close measurements of the same item are to each other. Precision is independent of accuracy.
Answer:
Accuracy refers to how close a measurement is to the true or accepted value. Precision refers to how close measurements of the same item are to each other.
Explanation:
Precision is independent of accuracy.
alice and bob are strangers. alice wants bob to send her a private message a and be able to verify the integrity of the message. what should bob do? (h() is a hash function and assume both alice and bob knows h()). bob generates an encryption key k and relies on pki to send alice x, y, h where y
Bob should use Public Key Infrastructure (PKI) to encrypt the message using his private key and a symmetric encryption key, which he then encrypts using Alice's public key.
To ensure Bob can securely send Alice a private message and Alice can verify the integrity of the message, Bob should use a combination of public-key encryption and a hash function.
Bob should first generate an encryption key k, which he will use to encrypt the message A. Then, he should use public-key encryption to generate two values: Y, which is PubE(bob-pri,k), and H, which is PubE(Alice-pub, h(A)). Y is the encryption key Bob will share with Alice, and H is a hash of the message A which Alice can use to verify the integrity of the message.
Finally, Bob should use symmetric encryption to generate X, which is SymE(k, A). This will be the encrypted version of message A that Bob can send to Alice.
By combining public-key encryption and a hash function, Bob can securely send Alice a private message and Alice can verify the integrity of the message.
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The question is -
Alice and Bob are strangers. Alice wants Bob to send her a private message A and be able to verify the integrity of the message. What should Bob do? (h() is a hash function and assume both Alice and Bob know h()). Bob generates an encryption key k and relies on PKI to send Alice X, Y, H where Y=PubE(bob- pri,k), X=SymE(k, A), H=PubE(Alice-pub, h(A)). This works. This does not work because this message can be read by anyone. This does not work because Alice cannot verify Bob's public key This does not work because Alice cannot have access to the encryption key k
A stone is thrown downwards with a speed of 5ms, from the top of a building of height 180 m. Take point of projection as the origin and vertical downward direction as negative. Determine
a. the velocity of stone at the end of 3 s.
b. the displacement of stone at the end of 3 s.
c. the time taken by the stone to travel a distance of 150 m.
Explanation:
open the image for detailed solution
Blake and Drew are playing horseshoes. Blake takes the first turn, and his horseshoe lands three-fourths of the way to the target. Drew takes the next turn, and his horseshoe lands past the target. Which statement best explains the results?(1 point)
The horseshoes have the same mass, but Drew threw with less force than Blake.
Drew used a horseshoe with more mass and threw with the same force as Blake.
The horseshoes have the same mass, but Drew threw with more force than Blake.
Drew used a horseshoe with more mass and threw with less force than Blake.
The statement that best explains the result is The horseshoes have the same mass, but Drew threw with more force than Blake.
The most likely explanation is that Drew threw the horseshoes harder than Blake, despite the fact that they have the same mass.
A force is an input that can change an object's motion according to physics. An object with mass might travel faster or at a different speed as a result of a force. Forces can also be conceptualized as a push or a pull. A force has strength and direction since it is a vector quantity. It is calculated using the metric newton, a SI unit (N). Newton's second law's original formulation read: "The net force of an item is equal to the rate of change of its momentum over time."
Once Blake leaves when Drew and I play horseshoes, his first horseshoe lands about three-fourths of the way to the target. The next time Drew turns, his horseshoe is off-target. Because of this, even though the two horseshoes have equivalent masses, horseshoe Drew experiences greater force and misses the target.
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A 2.4 kg block of wood sits on a frictionless table. A 3.0 g bullet, fired horizontally at a speed of 510 m/s , goes completely through the block, emerging at a speed of 180 m/s .
Part A What is the speed of the block immediately after the bullet exits?
The velocity of the block immediately after the bullet exits is 0.413 m/s in the direction of the bullet, if the weight of the block is 2.4 kg.
The mass of the bullet, m₁ = 3 g = 0.003 kg
The mass of the block, m₂ = 2.4 kg
Initial speed of the bullet, v₁ = 510 m/sec
Initial speed of the block, v₂ = 0 (at rest)
Emerging velocity of the bullet, v₃ = 180 m/s
Let the final velocity of the block, = v₄
By the law of conservation of momentum,
m₁v₁ + m₂v₂ = m₁v₃ + m₂v₄
0.003 × 510 + 2.4 × 0 = 0.003 × 180 + 2.4 × v₄
1.53 - 0.54 = 2.4 × v₄
v₄ = 0.99/2.4
v₄ = 0.413 m/s
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a 2.3 g plastic bead charged to -4.3 nc and a 3.8 g glass bead charged to 17.5 nc are 2.1 cm apart (center to center). part a what are the magnitudes of the accelerations of the plastic bead and the glass bead? express your answers using two significant figures. enter your answers numerically separated by a comma.
The answer will be in N/kg, you can use the conversion factor 1 N/kg = 10^5 m/s^2 to get the answer in m/s^2
The magnitudes of the accelerations of the plastic bead and the glass bead can be calculated using Coulomb's law, which states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. The formula for the force between two charges is:
F = (k * q1 * q2) / r^2
where F is the force, k is the Coulomb constant, q1 and q2 are the charges, and r is the distance between the charges.
Since the acceleration is the force divided by the mass, we can use the formula:
a = F / m
where a is the acceleration, F is the force, and m is the mass.
To find the acceleration of the plastic bead, we can substitute the known values into the formula:
a = (k * (-4.3 nC) * 17.5 nC) / (2.1 cm)^2 / 2.3 g
To find the acceleration of the glass bead, we can substitute the known values into the formula:
a = (k * (-4.3 nC) * 17.5 nC) / (2.1 cm)^2 / 3.8 g
Note that the k constant is not provided in the problem statement and can be considered as 1/4πε0.
The answer will be in N/kg, you can use the conversion factor 1 N/kg = 10^5 m/s^2 to get the answer in m/s^2
Acceleration cannot be provided as k is not given and the values of the constant may change.
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A surface on which all points are at the same potential is referred to as
A a constant electric force surface
B a constant electric field surface
C an equipotential surface
D an equivoltage surface
A surface on which all points are at the same potential is referred to as equipotential surface.
When all of the points on a surface have the same electric potential, the surface is said to have an equipotential potential.
An equipotential surface is a surface on which all points are at the same potential. It is a surface of constant potential and a surface where the electric field is always perpendicular to it. It does not necessarily imply a constant electric field, just a constant potential.
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what are the strength and direction of the electric field at the position indicated by the dot in (figure 1)? assume that x -axis is horisontal and points to the right, and y -axis points upward.
Velocity in x direction remains constant i.e, vx = 10 m/s Now acceleration is 0.
what are the strength and direction of the electric field at the position indicated by the dot in (figure 1)?
The electric field generated by the positive charge at the dot is directed away from the positive charge. The electric field generated by the negative charge at the dot is directed towards the negative charge.The direction of the electric field due to positive point charge is always acts away from the point charge and electric field due to the negative charge acts towards the negative charge.Because an electric field has both magnitude and direction, the direction of the force on a positive charge is chosen arbitrarily as the direction of the electric field. Because positive charges repel each other, the electric field around an isolated positive charge is oriented radially outward.To learn more about direction refers to:
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select all that apply which of the following values are needed to solve for the heat capacity of a heated unknown solid when it is placed in a coffee cup calorimeter? select all that apply. multiple select question. the final temperature of the system the initial temperature of the water the mass of the solid the initial temperature of the solid the mass of the water in the cup the pressure of the system
Following values are needed to solve for the heat capacity of a heated unknown solid when it is placed in a coffee cup calorimeter: initial temperature of the water, initial temperature of the solid, mass of the solid mass of water in the cup and final temperature of the system.
What is calorimeter?Calorimeters are used to measure volume and heat produced during certain time period.
Object used for calorimetry, or the process of measuring the heat of chemical reactions or physical changes as well as heat capacity is called calorimeter. Differential scanning calorimeters, isothermal micro calorimeters, titration calorimeters and accelerated rate calorimeters are the common types.
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An airfoil has upper and lower surfaces defined by the equations: 1. For 0 < (x/c) < 0.6 Y upper = 0.4(x/c), Y lower = 0.2(x/c) 2. For 0.6 < (x/c) < 1.0
Y upper = 0.6(1 - x/c), Y lower = 0.3(1 - x/c) Note you need to do the analysis of over each segment separately. Analyze this using the thin airfoil theory, 1. Show that the equations for the camber and half thickness distributions are A. For 0 < (x/c) < 0.6 n = 0.3(x/c), n = 0.1(x/c) B. For 0.6 < (x/c) < 1.0
n = 0.45 (1 - x/c), n = 0.15 (1 - x/c)
The equations for the camber and half thickness distributions are:
A. For 0 < (x/c) < 0.6 n = 0.3(x/c), t = 0.1(x/c)
B. For 0.6 < (x/c) < 1.0 n = 0.45 (1 - x/c), t = 0.15 (1 - x/c)
The camber and half thickness distributions can be found using the thin airfoil theory. According to this theory, the camber and half thickness distributions are given by:
n = (Y upper - Y lower ) / 2 (for camber)
t = (Y upper + Y lower ) / 2 (for half thickness)
For the given airfoil, we can find the camber and half thickness distributions by applying the above equations to each segment separately.
The theory simply states that flow around an airfoil is described as two-dimensional flow around a thin airfoil. It is possible to imagine it addressing an airfoil with zero thickness and infinite wingspan.
For 0 < (x/c) < 0.6
Y upper = 0.4(x/c), Y lower = 0.2(x/c)
Therefore,
n = (0.4(x/c) - 0.2(x/c)) / 2 = 0.3(x/c)
t = (0.4(x/c) + 0.2(x/c)) / 2 = 0.1(x/c)
For 0.6 < (x/c) < 1.0
Y upper = 0.6(1 - x/c), Y lower = 0.3(1 - x/c)
Therefore,
n = (0.6(1 - x/c) - 0.3(1 - x/c)) / 2 = 0.45 (1 - x/c)
t = (0.6(1 - x/c) + 0.3(1 - x/c)) / 2 = 0.15 (1 - x/c)
So, the equations for the camber and half thickness distributions are:
A. For 0 < (x/c) < 0.6 n = 0.3(x/c), t = 0.1(x/c)
B. For 0.6 < (x/c) < 1.0 n = 0.45 (1 - x/c), t = 0.15 (1 - x/c)
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How are Newton’s Laws used to describe the motion of planets? Justify your response in two or more complete sentences in the essay box below.
Newton's laws of motion can be used to explain the motion of planets through their orbital paths, as well as their gravitational attraction to each other.
How are Newton's Laws applied to planet motion?
Planetary motion is described by Newton's laws of motion. According to Newton's first law, unless acted upon by an outside force, an object will remain at rest or move in a straight line.
Planets are subject to this law in that they stay in their orbits unless perturbed by a force acting from outside their solar system, such as another planet's gravitational pull.
The rate of a body's change in momentum is inversely proportional to the force acting on it, according to Newton's second law. According to this law, a planet's acceleration is proportional to the net force acting on it, which is the result of the combined gravitational effects of other bodies.
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A skydiver is falling at terminal velocity before opening her parachute. After opening her parachute, she falls at
a much smaller terminal velocity. How does the total upward force before she opens her parachute compare to
the total upward force after she opens her parachute?
(A) The ratio of the forces is equal to the ratio of the velocities.
(B) The upward force with the parachute will depend on the size of the parachute.
(C) The upward force before the parachute will be greater because of the greater velocity.
(D) The upward force in both cases must be the same.
In both scenarios, the upward force must be the same. Regardless of the speed, the force of air resistance equals your weight when you are falling with terminal velocity.
The drag force is inversely related to both the effective area of the falling object and the speed squared. The forces of gravity and drag are equal at terminal velocity. The effective area of the parachute substantially expands when it opens, greatly increasing the drag force. The stronger drag force causes the speed to decrease, which in turn causes the drag force to decrease until it and the force of gravity are once again in balance since the drag and gravity forces are no longer in balance.
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a particle of uniform mass m is locaed inside a uniform solid sphere of radius r and mass m at a distance r from its center (a) sho that the gravitational potential energy of the system is U=GMmr^2 /2R^3 - 3GmM/2R ?
(a) The gravitational potential energy of the system is [tex]\frac{GmM}{2R^3}r^2 - \frac{3GmM}{2R}[/tex] (Proved), and (b) the amount of work done by the gravitational force in bringing the particle from the surface of the sphere to its center will [tex]-\frac{GMm}{2R}[/tex].
Assuming that a concentric spherical surface passes through where a particle of mass m resides.
so from that imaginary boundary
The mass of the inner part is
M' = [tex]\frac{M}{\frac{4\pi r^3}{3} } . \frac{4}{3} \pi r^3[/tex]= Mr³/r³
The potential at P due to this inner part is
V₁ = -GM'/r
or V₁ = -GMr²/R³
Now, to find the potential at P due to the outer part of the sphere, we will divide this by concentric shells.
so, dm = [tex]\frac{M}{\frac{4\pi r^3}{3} } . \frac{4}{3} \pi x^2 dx[/tex] = 3Mx²dx/R³
by further solving,
[tex]-\frac{Gdm}{x} = -3\frac{GM}{R^3}xdx[/tex]
so by integrating,
V₂ = [tex]\int\limits^R_r -3\frac{GM}{R^3}xdx[/tex]
or V₂ = [tex]-\frac{3GM}{2R^3} (R^2-r^2)[/tex]
So, the total potential at P will be
V = V₁ + V₂ = -GMr²/R³ [tex]-\frac{3GM}{2R^3} (R^2-r^2)[/tex]
or V = [tex]-\frac{GM}{2R^3}(3R^2-r^2)[/tex]
and we know that potential energy U = mV = [tex]\frac{GmM}{2R^3}r^2 - \frac{3GmM}{2R}[/tex] {Hence Proved}
(b) we know that potential energy at the center is Uc = [tex]-\frac{3GmM}{2R}[/tex] {r=0}
At surface {r+R} Us = [tex]-\frac{GMm}{R}[/tex]
hence, work done W = Uc - Us = [tex]-\frac{GMm}{2R}[/tex]
Therefore, (a) The gravitational potential energy of the system is [tex]\frac{GmM}{2R^3}r^2 - \frac{3GmM}{2R}[/tex] (Proved), and (b) the amount of work done by the gravitational force in bringing the particle from the surface of the sphere to its center will be [tex]-\frac{GMm}{2R}[/tex].
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The complete question is:
a particle of uniform mass m is located inside a uniform solid sphere of radius r and mass m at a distance r from its center (a) sho that the gravitational potential energy of the system is U=GMmr^2 /2R^3 - 3GmM/2R ? (b) Write an expression for the amount of work done by the gravitational force in bringing the particle from the surface of the sphere to its center.
during and after eyewall replacement, which of the following is true about the hurricane's strength?
Since a tropical cyclone's eyewall has the greatest winds, the storm often weakens during this time when the inner wall is "choked" by the outer wall.
A ring of tall thunderstorms that form the eyewall produce intense rains and typically have the greatest winds. Wind speed, a measure of the storm's strength, can alter due to changes in the eye and eyewall's structure. The cycle of eyewall replacement is one characteristic of major hurricanes. To put it simply, a new eye starts to form around the old one. The old eye is replaced with the new one, whose diameter gradually shrinks.
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A fireman d = 39.0 m away from a burning building directs a stream of water from a ground-level fire hose at an angle of i = 31.0° above the horizontal as shown in the figure. If the speed of the stream as it leaves the hose is vi = 40.0 m/s, at what height will the stream of water strike the building?
The height will be 11.4m
The height at which the stream of water strikes the building can be found by solving for h in the equation:
h = viy * t - (1/2)gt^2
Where:
viy (vertical component of velocity) = vi * sin(i) = 40.0 m/s * sin(31.0°)
t = d / vix = 39.0 m / (40.0 m/s * cos(31.0°))
g = 9.8 m/s^2
By substituting the values, we can find that the height of the stream strikes the building is approximately:
h = (40.0 m/s * sin(31.0°)) * (39.0 m / (40.0 m/s * cos(31.0°))) - (1/2)(9.8 m/s^2)((39.0 m / (40.0 m/s * cos(31.0°)))^2
Therefore, h = 11.4 m
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To determine the height at which the stream of water will strike the building, we can calculate the horizontal distance and vertical component of the stream's velocity. By using the formulas for horizontal distance, vertical component, time, and height, we can solve for the height at which the stream will strike the building. In this case, the height is approximately 19.9 meters.
Explanation:To determine the height at which the stream of water will strike the building, we need to consider the vertical and horizontal components of the stream's velocity. We can calculate the horizontal distance the water travels using the formula d = vit. In this case, d = 39.0 m (the distance from the fireman to the building), vi = 40.0 m/s (the speed of the stream), and t is the time it takes for the water to reach the building. Since the water is fired at an angle of 31.0° above the horizontal, the vertical component of its velocity can be found using the formula vfy = visin(i). Once we have the vertical component of the stream's velocity, we can calculate the time it takes for the water to reach the building using the formula t = d/vix. Finally, we can use the time and the vertical component of the stream's velocity to find the height at which the stream will strike the building using the formula y = vfy × t - 0.5gt², where g is the acceleration due to gravity (approximately 9.8 m/s²).
Plugging in the values, we get:
d = 39.0 m
vi = 40.0 m/s
i = 31.0°
vfy = vi × sin(i)
t = d/vix
y = vfy × t - 0.5gt²
After calculating all the values, the height at which the stream of water will strike the building is approximately 19.9 meters.
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for this trajectory, what would the vertical component of acceleration for the module be at time tm
The vertical component of acceleration at time tm can be determined by taking the second derivative of the vertical position vector with respect to time.
What is velocity?
Velocity is a vector quantity that measures the rate and direction of change in an object's position. It is typically expressed in units of meters per second (m/s). Velocity is equal to the distance traveled divided by the time it takes to travel that distance. Velocity is also related to acceleration, which is the rate of change of velocity.
At time tm, the vertical component of acceleration for the module would be the derivative of the vertical velocity vector with respect to time, which is the change in vertical velocity over time. This can be calculated by taking the second derivative of the vertical position vector with respect to time. Since the position vector is a function of time, the acceleration can be determined by taking the second derivative of the position vector with respect to time, which is defined as the rate of change of the velocity with respect to time. Therefore, the vertical component of acceleration at time tm can be determined by taking the second derivative of the vertical position vector with respect to time.
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You have 125 g
of a certain seasoning and are told that it contains 26.0 g
of salt. What is the percentage of salt by mass in this seasoning?
The percentage of salt by mass in this seasoning is 20.80%.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
You have 125 g of seasoning.
Amount of salt = 26.0 g
So, the percentage of salt by mass in this seasoning is = Amount of salt/total amount of seasoning× 100%
= 26.0 g / 125 g × 100%
= 20.80 %.
Hence, the percentage of salt by mass in this seasoning is 20.80%.
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when these two freight cars of diffrent mass collide and couple what will be their resultant velocity
It is possible to use the idea of momentum conservation. combined mass's velocity is v. As a result, the combined masses will move at a speed of 1 m/s following the collision.
What occurs when two vehicles with different mass collision?The occupants of the lighter automobile would endure significantly higher accelerations and, consequently, much higher forces than the occupants of the heavier car in a collision between two vehicles of unequal mass. Potential energy is the term for this.It is possible to use the idea of momentum conservation. combined mass's velocity is v. As a result, the combined masses will move at a speed of 1 m/s following the collision.If there is no net loss of kinetic energy in the system as a result of the collision, the collision is said to be elastic. In elastic collisions, both kinetic and momentum energy are conserved.To learn more about velocity refer to:
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he cable ade is tied at a and e, and loops through the frictionless loop on the 10 kg mass as shown. cables ab and ac are in the x and z directions, respectively.
The cables AB and AC are in the X and Z directions (See Picture), respectively. Tension in cable ADE will be 98 N.
In physics, tension is defined as the pulling force that is transmitted axially through the use of a string, rope, chain, or similar object, or by the ends of a rod, truss member, or other similar three-dimensional object. Tension can also be defined as the action-reaction pair of forces acting at the ends of the aforementioned elements.
Let us consider the Free body Diagram(See picture).
According to the Free body Diagram, the Point D is in equilibrium.
We know, at Equilibrium condition,
[tex]T-mg=0[/tex]
[tex]T=mg[/tex]
Now, given mass(m) = 10kg, and we know [tex]g=9.8m/sec^{2}[/tex]
[tex]T=10*9.8[/tex]
[tex]T=98N[/tex]
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The complete question is:
The cable ADE is tied at A and E, and loops through the frictionless loop on the 10 kg mass as shown. Cables AB and AC are in the y and x directions, respectively. Use a free body diagram of point D to determine the tension T in cable ADE
TRUE OR FALSE when the bob of a simple pendulum is straight down during a cycle, the potential energy will be at maximum since its mass is traveling at a maximum velocity.
The given statement "When the bob of a simple pendulum is straight down during a cycle, the potential energy will be at maximum since its mass is traveling at a maximum velocity" is FALSE. It is because
The potential energy will be zero as the height reaches the lowest. Its mass is travelling at a maximum velocity so that it makes the kinetic energy at maximum.How to determine the potential energy on a pendulum?On a moving pendulum bob, there will be kinetic and potential energy. The kinetic energy is dependent on the velocity, while the potential energy is dependent on the height of object.
However, the sum of the two forms of energy is conserved. This is based on the Conservation of Mechanical Energy. It states that the total mechanical energy of a system is conserved. It can be expressed as
E initial = E final
KE₁ + U₁ = KE₂ + U₂
½mv₁ + mgh₁ = ½mv₂ + mgh₂
Where
E = mechanical energyKE = kinetic energyU = potential energym = mass of an objectv = speed of objecth = height of objectThe index 1 and 2 shows at point 1 (initial) and 2 (final).
Bob of a simple pendulum.
At the maximum velocity, the height is at the lowest, straight down during a cycle. It is at mean position. The potential energy is close to zero because the height is also close to zero.
Meanwhile, at the minimum velocity (close to zero), the height of a pendulum is at the highest. The potential energy is at the highest and the kinetic energy is zero.
Hence, when the bob of a simple pendulum is straight down during a cycle, the potential energy will be zero and the kinetic energy is at maximum. The statement is false.
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A rabbit escaping a fox runs across level ground, zipping north for 3.04 m, darting exactly northwest for 2.56 m, and then dropping 0.6 m straight down underground into the safety of its burrow.How far, d, does the rabbit end up from its starting point?
Zipping 3.04 metres distance in north, precisely 2.56 metres northwest, and finally plunging 0.6 metres straight down into the security of its burrow 4.59 m later, the rabbit has travelled from its starting place.
The rabbit initially travels 3.04 metres north, then 2.56 metres northwest. The Pythagorean theorem may be used to determine the hypotenuse of a right triangle with 3.04 m and 2.56 m-long legs in order to determine the total distance the rabbit has travelled in a north-westerly direction:
d = sqrt(3.04^2 + 2.56^2)
sqrt(15.984), sqrt(9.4304 + 6.5536), and d = 3.99 m
The vertical component of the rabbit's distance travelled must now be included. The rabbit descended 0.6 metres below earth. The rabbit travels a total distance of d = sqrt(15.984) + 0.6 m d = 3.99 m + 0.6 m = 4.59 m from its starting place.
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