Answer
a)0.0495 J
b)0.01681 m
c)0.7218 m/s
Explanation:
Given
Mass of the.toy M = 0.190 kg
force constant k = 350 N/m
Displacement from equilibrium x = 0.0140 m
Speed v = 0.400 m/s
a)What is the toy's total energy at any point of its motion?
The total energy at any point of it's motion can be calculated by adding together both the potential and kinetic energy of the toy, since it's posses potential energy when at rest and kinetic energy at motion
Total energy E = kinetic energy + potential energy
E = ¹/₂mv² + ¹/₂kx²
E = ¹/₂ (0.190)(0.4)² + ¹/₂ (350)(0.0140)²
E = 0.0495 J
Hence,the total energy is 0.0495 J
b) the amplitude of the motion can be calculated using below formula
Let amplitude = A
E = ¹/₂KA²
if we make Amplitude A the subject of the formula we have
A=√(2E/k)
But we have calculated our E up there, our K was given in question then if we substitute we have
A= √(2×0.0495)/350
Ans: 0.01681 m
Hence, our Amplitude is 0.01681 m
c) the the toy's maximum speed during its motion can be calculated using the expression below
Let maximum speed = vmax
E = (1/2)M * vmax^2
If we make vmax the subject of the formula we have
vmax =√(2E/m)
vmax= √(2×0.0495)/0.190
vmax=0.7218 m/s
Hence our vmax is 0.7218 m/s
Suppose the moon was twice as a massive as it is. Would the month be Select one: a. half as long bthe same c. twice as long d. 1/4 as long e. 4 times as long
Answer:
The correct answer is B
Explanation:
The lunar month is the time it takes for the moon to go around the Earth, for this we use Newton's second law where the force is the universal force of attraction
F = ma
the universal attractive force is
F = G M_earth m_moon / r²
Accelerations centripetal acceleration
a = w² r
the angular velocity is for the movement is
w = 2π / T
Where T is the period of revolution; let's substitute
G M_eath m_moon / r² = m_moon (2π /T)² r
G M_earth = 4π² / T² r³
T² = (4π² / G M_eart) r³
Let's analyze this equation we see that it does not depend on the mass of the Luma, therefore the period is the same
The correct answer is B
If three forces are equal and their resultant force is zero, then measure of its internal angle is: a)0° b)90° c)60° d)45° Fill in the blanks, tell me which one is right. a or b or c or d
Answer:
edqr3fr =wdmmwfmnl[=kvlfkgvb
Explanation:bcz idk
Me BeLIves iT iS ZeRo So A
What is the maximum number of electrons in an atom that can have the following quantum numbers?
a. n = 3, m1 = -2;
b. n = 4, l = 3;
c. n = 5, l = 3, ml = 2;
d. n = 4, l = 1 ml = 0.
Answer:
Explanation:
a ) n = 3, m1 = -2
when n = 3 , l = 0 , 1 , 2 .
when l = 2 , one electron may have m = -2 .
two electrons with s = + 1/2 and - 1/2 may have m = -2 .
So only two electrons may have the configuration of n = 3 , m = -2 .
b ) n = 4, l = 3
when , n = 4 and l = 3 , m may have values -3 , -2 , -1 , 0 , 1 , 2 , 3 . Each m have two electrons with s = + 1/2 and - 1/2 .
So altogether there are 7 x 2 = 14 electrons that have configuration of n = 4, l = 3 .
c ) n = 5, l = 3, ml = 2
Similar to case of a ) , only two electrons with s = + 1/2 and - 1/2 may have configuration of n = 5, l = 3, ml = 2
d ) n = 4, l = 1 ml = 0.
In this case also only two electrons may have configuration of
n = 4, l = 1 ml = 0. with s = + 1/2 and - 1/2 .
(a) The maximum number of electrons in an atom that have n = 3, ml = -2 is two electrons.
(b) The maximum number of electrons in an atom that have n = 3, ml = -2 is 14 electrons.
(c) The maximum number of electrons in an atom that have n = 5 l = 3, ml = 2 is two electrons.
(d) The maximum number of electrons in an atom that have n = 4 l = 1 , ml = 0 is two electrons.
The given parameters:
n = 3, ml = -2n = 4, l = 3n = 5, I = 3, ml = 2n = 4, I = ml = 0The maximum number of electrons in an atom that have n = 3, ml = -2
the quantum number = 3the maximum number of electron = 2The maximum number of electrons in an atom that have n = 4, l = 3
the quantum number = 4the maximum number of electron = (2 x 3) + 1 = 7The orbital is 7 which corresponds to f-orbital and the maximum number of electrons = 14;
The maximum number of electrons in an atom that have n = 5 l = 3, ml = 2
the quantum number = 5the maximum number of electrons = 2The maximum number of electrons in an atom that have n = 4 l = 1 , ml = 0
the quantum number = 4the maximum number of electrons = 2Learn more about quantum number of electrons here: https://brainly.com/question/11575590
Select the correct answer.
A car traveling south is 200 kilometers from its starting point after 2 hours. What is the average velocity of the car?
OA. 100 kilometers/hour south
OB.
200 kilometers/hour
OC.
200 kilometers/hour north
OD 100 kilometers/hour
A car traveling south is 200 kilometers from its starting point after 2 hours. What is the average velocity of the car?
Choose: 100 kilometers/hour south
Answer:
100 kilometers/hour its d
The magnetic flux through a certain coil is given by φm = (1/50π) cos 100πt
where the units are SI. The coil has 100 turns. The magnitude of the induced EMF when t = 1/200 s is:_______.
A. 1/50π V
B. 2/π V
C. 100 V
D. zero
E. 200 V
Answer:
A. 1/50π V
Explanation:
Given;
magnetic flux through the coil, φm = (1/50π) cos 100πt
t = 1/200 s
The magnitude of the induced EMF is given by;
[tex]EMF = \frac{d \phi_m}{dt} \\\\EMF =\frac{d}{dt} (1/50 \pi)cos \ 100\pi t)\\\\EMF = (1/50 \pi)cos \ 100\pi \\\\EMF =(1/50 \pi)cos \ 100 *180\\\\ EMF =(1/50 \pi)cos \ 18000\\\\ EMF =(1/50 \pi) (1)\\\\EMF =(1/50 \pi) \ V[/tex]
Therefore, the magnitude of the induced EMF is 1/50π V
The correct option is "A. 1/50π V"
A refracting telescope has a 1.48 m diameter objective lens with focal length 15.4 m and an eyepiece with focal length 3.28 cm. What is the angular magnification of the telescope
Answer:
m = 469.51
Explanation:
Given that,
The diameter of a refracting telescope is 1.48 m
Focal length of the objective lens is 15.4 m
Focal length of an eyepiece is 3.28 cm
We need to find the angular magnification of the telescope. The ratio of focal length of objective lens to the focal length of the eye piece is called angular magnification of the telescope. So,
[tex]m=\dfrac{f_o}{f_e}\\\\m=\dfrac{15.4}{3.28\times 10^{-2}}\\\\m=469.51[/tex]
So, the angular magnification of the telescope is 469.51.
A cylindrical container of water has a height of 12 in and opens to atmosphere it squirts horizontally from a hole near the bottom. (Assume for parts a and b that the cross sectional area of this cylinder is much larger than the cross sectional area of the hole).
a) What are the values of the pressure at
1. The surface of water
2. Just outside the hole
3. At the bottom of the container, ignoring the velocity at which the water level moving. I
b) Determine the speed at which the water leaves the hole when the water level is 6 cm above the hole.of
c) Now assume that the ratios of the cross sectional areas of the cylinder to that of the hole is 10 times, calculate the velocity at which the surface of water dropping down, when the water level is 6 cm above the hole.
Answer:
a) 1 & 2The pressure at the surface of water and just outside the hole are both atmospheric pressure. { mean value of 101,325 pascals (roughly 14.6959 pounds per square inch).}
3. P(bottom) = 2987.04 Pa
b) v = 1.0844 m/s
c) v₁ = 0.11 m/s
Explanation:
a)
1) The pressure at the surface of water is same as the atmospheric pressure { mean value of 101,325 pascals (roughly 14.6959 pounds per square inch).}
2) The pressure at just outside the hole is also same as the atmospheric pressure. { mean value of 101,325 pascals (roughly 14.6959 pounds per square inch).}
3) At the bottom of the container, the gauge pressure is given by:
P(bottom) = pgh
where h = 12in = 0.3084m
P(bottom) = 1000 kg/m³ × 9.8 m/s² × 0.3084m
P(bottom) = 2987.04 Pa
b)
The velocity at which the water leaves the hole can be obtained from Bernouilli's equation. Point 1 is at the surface of water, point 2 is just outside the hole;
p₁ + 1/2pv₁² + pgh₁ = p² + 1/2pv₂² + pgh₂
Pressures on both sides are the same and the velocity of the water at the surface is approximately zero (since the hole's cross sectional area is much smaller than the container's). The difference in depths h1 - h2 is just the height of the water level
so
pgh = 1/2pv₂²
v = √(2gh)
we substitute
v = √( 2 × 9.8 m/s² × 0.06 m
v = 1.0844 m/s
c)
Now the velocity of the water level can't be neglected, we can use the continuity equation:
v₂ = (A₁/A²)V₁
so Back to Bernouilli's:
1/2pv₁² + pgh₁ = 1/2 (10v₁)² + pgh₂
phg = 99/2pv₁²
v₁ = √(2/99gh)
v₁ = √(2/99 × 9.8 m/s² × 0.06 m)
v₁ = 0.11 m/s
Where did the gold of the Inca civilization come from?
Answer:
ocean-continental convergence
What amount of heat is required to increase the temperature of 75.0 grams of gold from 150°C to 250°C? The specific heat of gold is 0.13 J/g°C.A. 750 joulesB. 980 joulesC. 1300 joulesD. 1500 joulesE. 2500 joules
Answer:
980 J, B
Explanation:
Given that.
mass of substance, m = 75 g
initial temperature of system, θ1 = 150° C
final temperature of system, θ2 = 250° C
specific heat capacity, c = 0.13 J/gC
Q = mcΔθ, where
Q = quantity of heat required in J
m = mass of substance in G
c = specific heat capacity of substance in J/gC
Δθ = change in temperature °C
Δθ = θ2 - θ1
Δθ = 250° C - 150° C
Δθ = 100° C
now that we have all our values, what we do next is to substitute and apply all in the initial formula given
Q = mcΔθ
Q = 75 * 0.13 * 100
Q = 7500 * 0.13
Q = 975 J
Thus, we can say they amount of heat required to increase the temperature of 75g of gold, from 150° - 250° is 975 J, which is approximately, 980 J.
Option B
Answer:
980 B for plato
Explanation:
The magnetic field perpendicular to a single 16.7-cm-diameter circular loop of copper wire decreases uniformly from 0.750 T to zero.
If the wire is 2.25 mm in diameter, how much charge moves past a point in the coil during this operation? The resistivity of copper is 1.68Ã10â8Ωâm.
Express your answer to three significant figures and include the appropriate units.
Answer:
1.24 C
Explanation:
We know that the magnitude of the induced emf, ε = -ΔΦ/Δt where Φ = magnetic flux and t = time. Now ΔΦ = Δ(AB) = AΔB where A = area of coil and change in magnetic flux = Now ΔB = 0 - 0.750 T = -0.750 T, since the magnetic field changes from 0.750 T to 0 T.
The are , A of the circular loop is πD²/4 where D = diameter of circular loop = 16.7 cm = 16.7 × 10⁻²m
So, ε = -ΔΦ/Δt = -AΔB/Δt= -πD²/4 × -0.750 T/Δt = 0.750πD²/4Δt.
Also, the induced emf ε = iR where i = current in the coil and R = resistance of wire = ρl/A where ρ = resistivity of copper wire =1.68 × 10⁻⁸ Ωm, l = length of wire = πD and A = cross-sectional area of wire = πd²/4 where d = diameter of wire = 2.25 mm = 2.25 × 10⁻³ m.
So, ε = iR = iρl/A = iρπD/πd²/4 = 4iρD/d²
So, 4iρD/d² = 0.750πD²/4Δt.
iΔt = 0.750πD²/4 ÷ 4iρD/d²
iΔt = 0.750πD²d²/16ρ.
So the charge Q = iΔt
= 0.750π(Dd)²/16ρ
= 0.750π(16.7 × 10⁻²m 2.25 × 10⁻³ m)²/16(1.68 × 10⁻⁸ Ωm)
= 123.76 × 10⁻² C
= 1.2376 C
≅ 1.24 C
Both the x and y coordinates of a point execute simple harmonic motion. The frequencies are the same but the amplitudes are different. The resulting orbit might be:
Answer:
the orbit resulting an ELIPSE
Explanation:
Harmonic motion is described by the expression
x = A cos (wt +Ф₁)
In this exercise it is established that in the y axis there is also a harmonic movement with the same frequency, so its equation is
y = B cos (wt + Ф₂)
the combined motion of the two bodies can be found using the Pythagorean theorem
R² = x² + y²
R² = [A² cos² (wt + Ф₁) + B² cos² (wt + Ф₂)]
to simplify we can assume that the phase in the two movements are equal
R = √(A² + B²) cos (wt + Ф)
If the two amplitudes are equal we have a circular motion, if the two amplitudes are different in elliptical motion, the amplitudes of the two motions are
circular R² = (A² + A²)
elliptical R² = (A² + B²)
We see from the last expression that the broadly the two axes is different, so the amplitude is an ellipse.
By which the orbit resulting an ELIPSE
A 90 kg man lying on a surface of negligible friction shoves a 63 g stone away from himself, giving it a speed of 4.4 m/s. What speed does the man acquire as a result
Answer:
the speed acquired by the man is: [tex]0.00308\,\,\frac{m}{s}[/tex]
Explanation:
Use conservation of linear momentum to solve this problem, and make sure you start by converting the 63 g stone mass into kilograms = 0.063 kg.
Now from conservation of linear momentum, the momentum imparted to the stone (which is the product of the stone's mass time its speed) must equal in magnitude that of the 90 kg man. Then we need to find the unknown speed of the man:
[tex]m_1\.v_1=m_2\,v_2\\0.063\,(4.4)\,\frac{kg\,m}{s} =v_2\,(90\,\,kg)\\0.2772\,\frac{kg\,m}{s}=v_2\,(90\,\,kg)\\v_2=\frac{0.2772}{90} \,\frac{m}{s} \\v_2=0.00308\,\,\frac{m}{s}[/tex]
therefore the speed acquired by the man is: [tex]0.00308\,\,\frac{m}{s}[/tex]
A uniform disk a uniform hoop and a uniform sphere are released at the same time at the top of an inclined ramp. They all roll without slipping in what order do they reach the bottom of the ramp?
a. disk hoop, sphere
b. sphere, hoop, disk
c. hoop, sphere, disk
d. sphere, disk, hoop
e. hoop, disk, sphere
Answer:
D. The sphere the disk and the hoop
Explanation:
This is because the sphere has inertial of
2/5mR²
Disk 1/2mR²
Hope mR²
So these are moment of inertial which is resistance or opposition to rotation so since the sphere has a smaller moment to inertial it will move faster and reach the ground first then the disk then the hoop in that order
A toy uses a spring to shoot an arrow with a suction cup on the end. The toy shoots a 34.2 g arrow and gives it a speed of 5.50 m/s. If the efficiency of the toy is 69.0%, how much elastic potential energy was stored in the spring? Show all your work.
Answer:
0.750 J
Explanation:
69% of the elastic energy is converted to kinetic energy.
0.69 EE = KE
0.69 EE = ½ mv²
EE = mv² / 1.38
EE = (0.0342 kg) (5.50 m/s)² / 1.38
EE = 0.750 J
Find the angle between two polarizers that will result in one-eighth of the light incident on the second polarizer passing through.
Answer:
The angle is [tex]\theta = 6.93 *10^{1}[/tex]
Explanation:
From the question we are told that
The intensity of light emerging from the second polarizer is [tex]I_2 = \frac{1}{8} * I_1[/tex]
Now the light emerging from the first polarizer is [tex]I_1 = \frac{I_o}{2}[/tex]
Where [tex]I_o[/tex] is the intensity of the unpolarized light
Now according to Malus law the intensity of light emerging from the second polarizer is mathematically represented as
[tex]I_2 = \frac{I_1}{8} = I_1 cos^2(\theta )[/tex]
=> [tex]I_2 = \frac{I_1}{8} = I_1 cos^2(\theta )[/tex]
=> [tex]\theta = cos^{-1}[0.3536][/tex]
=> [tex]\theta = 69.3^o[/tex]
=> [tex]\theta = 6.93 *10^{1}[/tex]
Firecrackers A and B are 600 m apart. You are standing exactly halfway between them. Your lab partner is 300 m on the other side of firecracker A. You see two flashes of light, from the two explosions, at exactly the same instant of time. Define event 1 to be firecracker A explodes and event 2 to be firecracker B explodes. According to your lab partner, based on measurements he or she makes, does event 1 occur before, after, or at the same time as event 2? Explain
Answer:
Explanation:
A and B are 600 m apart . firecrackers explodes and make two waves , sound waves and light waves . they spread out on all sides . The person sitting in the middle , observes two lights simultaneously and after some time hears two sound simultaneously . It is so because waves coming from A and B covers equal distance to reach the middle point . Same will be the case for sound waves .
But for observer sitting on the other side of A , both light and sound wave will not reach simultaneously . Light wave coming from A will reach earlier because distance covered by light will be less . Similarly sound coming from A will reach earlier . So he / she will observe cracker at A to have exploded earlier than that at B .
A large rock that weighs 164.0 N is suspended from the lower end of a thin wire that is 3.00 m long. The density of the rock is 3200kg/m3. The mass of the wire is small enough that its effect on the tension in the wire can be ignored. The upper end of the wire is held fixed. When the rock is in air, the fundamental frequency for transverse standing waves on the wire is 42.0 Hz. When the rock is totally submerged in a liquid, with the top of the rock just below the surface, the fundamental frequency for the wire is 28.0 Hz. What is the density of the liquid?
Answer:
ρ_liquid = 1,778 10³ kg/m³
Explanation:
In a wire the speed of the wave produced is
v = √T/μ
wave speed is also related to frequency and wavelength
v = λ f
as they indicate that the frequency is the fundamental, there must be a single antinode in the center
L = 2λ
λ = 2L
Using the translational equilibrium equation
T -W = 0
T = W
let's substitute
2L f = √ W /μ
μ = W / 4 L² f²
μ = 164 / (4 3² 42²)
μ = 2.5825 10⁻³ kg / m
this is the linear density of the wire
Now let's analyze when the rock is submerged in a liquid, the thrust acts on the rock
B = ρ g V
when writing the equilibrium equation we have
T + B -W = 0
T = W - B
T = W - ρ_liquid g V (1)
to find the volume of the rock we use the concept of density
ρ_body = M / V
V = M /ρ_body
W = M g
V = W / g ρ_body
V = 164 / (9.8 3200)
V = 0.00523 m³
V = 5.23 10⁻³ m³
The speed of a wave on a string is
v = √ T /μ
speed is also related to wavelength and frequency
v = λ f
indicate that the frequency formed is the fundamental one, therefore it has a single antinode in the center and two nodes at the fixed points
L = λ/ 2
λ= 2L
we substitute and look for tension
2L f = √T /μ
T = 4L² f² μ
T = 4 3² 28² 2.5825 10⁻³
T = 72.888 N
We already have the volume of the rock and the tension on the rope, we can substitute in equation 1 and find the density of the liquid
T= W – ρ_liquid g V
ρ_liquid = (W -T) / gV
ρ_liquid = ( 164 – 72,888) / ( 9,8 5,23 10⁻³)
ρ_liquid = 1,778 10³ kg/m³
Explanation:
When Ina wire the speed of the wave produced isThen v = √T/μAfter that, the wave speed is also related to the frequency and also wavelengthThen v = λ fAlso, as they indicate that the frequency is fundamental, then there must be a single antinode in the centerAfter that L = 2λThen λ = 2LNow we are Using the translational equilibrium equation is T -W = 0 T = WThen let's substitute 2L f = √ W /μ μ = W / 4 L² f² μ = 164 / (4 3² 42²) μ = 2.5825 10⁻³ kg / m this is the linear density of the wireThen Now let's analyze when the rock is submerged in a liquid, the thrust acts on the rock B = ρ g VAfter that when writing the equilibrium equation we have T + B -W = 0 T = W - B T = W - ρ_liquid g V (1)then to find the volume of the rock we use the concept of density is ρ_body = M / V V = M /ρ_body W = M g V = W / g ρ_body V = 164 / (9.8 3200) V = 0.00523 m³ V = 5.23 10⁻³ m³Then The speed of a wave on a string is v = √ T /μWhen the speed is also related to wavelength and frequency v = λ fThen indicate that the frequency formed is the fundamental one, also, therefore, it has a single antinode in the center and also that two nodes at the fixed points L = λ/ 2 λ= 2LThen we substitute and also look for tension 2L f = √T /μ T = 4L² f² μ T = 4 3² 28² 2.5825 10⁻³ T = 72.888 NThen We already have the volume of the rock and also the tension on the rope, we can substitute in equation 1 and also that find the density of the liquid T= W – ρ_liquid g V ρ_liquid = (W -T) / gV ρ_liquid = ( 164 – 72,888) / ( 9,8 5,23 10⁻³) ρ_liquid = 1,778 10³ kg/m³
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Calderas and craters are similar because they are both landforms that show the removal of land at the surface above an area due to volcanic activity.a) trueb) false
Answer:
True
Explanation: A calderas is a large volcanic crater, especially one formed by a major eruption leading to the collapse of the mouth of the volcano.
A Crater is a volcanic crater is an approximately circular depression in the ground caused by volcanic activity. It is typically a bowl-shaped feature within which occurs a vent or vents.
A 0.250 kgkg toy is undergoing SHM on the end of a horizontal spring with force constant 300 N/mN/m. When the toy is 0.0120 mm from its equilibrium position, it is observed to have a speed of 0.400 m/s.Find
(a) the total energy of the object at any point in its motion,
(b) the amplitude of the motion, and (c) the maximum speed attained by the object during its motion.
Answer:
(a) The total energy of the object at any point in its motion is 0.0416 J
(b) The amplitude of the motion is 0.0167 m
(c) The maximum speed attained by the object during its motion is 0.577 m/s
Explanation:
Given;
mass of the toy, m = 0.25 kg
force constant of the spring, k = 300 N/m
displacement of the toy, x = 0.012 m
speed of the toy, v = 0.4 m/s
(a) The total energy of the object at any point in its motion
E = ¹/₂mv² + ¹/₂kx²
E = ¹/₂ (0.25)(0.4)² + ¹/₂ (300)(0.012)²
E = 0.0416 J
(b) the amplitude of the motion
E = ¹/₂KA²
[tex]A = \sqrt{\frac{2E}{K} } \\\\A = \sqrt{\frac{2*0.0416}{300} } \\\\A = 0.0167 \ m[/tex]
(c) the maximum speed attained by the object during its motion
[tex]E = \frac{1}{2} mv_{max}^2\\\\v_{max} = \sqrt{\frac{2E}{m} } \\\\v_{max} = \sqrt{\frac{2*0.0416}{0.25} } \\\\v_{max} = 0.577 \ m/s[/tex]
a. The total energy of the toy at any point in its motion is 0.0416 Joules.
b. The amplitude of the motion is equal to 0.0167 meter.
c. The maximum speed attained by the toy during its motion is 0.577 m/s.
Given the following data:
Mass of toy = 0.250 kgSpring constant = 300 N/mDistance = 0.0120 mSpeed = 0.400 m/sa. To find the total energy of the toy at any point in its motion:
Mathematically, the total energy of an object undergoing simple harmonic motion (SHM) is given by:
[tex]E = \frac{1}{2} MV^2 + \frac{1}{2} kx^2[/tex]
Where:
k is the spring constant.x is the distance.M is the mass of an object.V is the speed of an object.Substituting the given parameters into the formula, we have;
[tex]E = \frac{1}{2} \times 0.25 \times 0.400^2 + \frac{1}{2} \times 300 \times 0.0120^2\\\\E = 0.125 \times 0.16 + 150 \times 0.000144\\\\E=0.02+0.0216[/tex]
E = 0.0416 Joules.
b. To find the amplitude of the motion, we would use this formula:
[tex]A = \sqrt{\frac{2E}{k} } \\\\A = \sqrt{\frac{2 \times 0.0416}{300} } \\\\A = \sqrt{2.77 \times 10^{-4}}[/tex]
A = 0.0167 meter.
c. To find the maximum speed attained by the object during its motion:
[tex]V_{max} = \sqrt{\frac{2E}{M} } \\\\V_{max} = \sqrt{\frac{2 \times 0.0416}{0.25} } \\\\V_{max} = \sqrt{2.77 \times 10^{-4}}[/tex]
Maximum speed = 0.577 m/s
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A hollow, thick-walled, conducting cylinder carries a current of 11.2 A and has an inner radius ri = r and outer radius ro = 3r/2, where r = 4.90 mm. Determine the magnitude of the magnetic field at the following distances from the center of the cylinder.
(a) ra = r/2 T
(b) rb = 5r/4 T
(c) rc = 2r T
Answer:
a. 0 T b. 1.03 × 10⁻⁴ T c. 2.29 × 10⁻⁴ T
Explanation:
a. Using ampere's law ∫B.ds = μ₀i
for ra = r/2, i = 0 (since no current is enclosed) and
∫B.ds = B∫ds = B(2πr/2) = Bπr
So, Bπr = 0
B = 0 T
b. rb = 5r/4
WE find the current enclosed between r = r and r = 5r/4. The total current density in the holow thick-walled conducting cylinder is J = i/[π(3r/2)² - πr²] = i/[9πr²/4 - πr²] = i/8πr²/4 = i/2πr².
Since the current density is constant, we find the current, i' enclosed between r = r and r = 5r/4. J = i'//[π(5r/4)² - πr²] = i'/[25πr²/16 - πr²] = i'/9πr²/16 = 16i'/9πr²
So, i/2πr² = 16i'/9πr²
i' = 9i/32
Using ampere's law ∫B.ds = μ₀i'
∫B.ds = = B∫ds = B × 2π(5r/4) = 5Bπr/2
5Bπr/2 = μ₀(9i/32)
B = 9μ₀i/32πr × 2/5
B = 9μ₀i/80πr
Substituting r = 4.90 mm = 4.90 × 10⁻³ m and i = 11.2 A, we have
B = 9μ₀i/80πr
= 9 × 4π × 10⁻⁷ H/m × 11.2 A/80π(4.90 × 10⁻³ m)
= 403.2/392 × 10⁻⁴ T
= 1.029 × 10⁻⁴ T
≅ 1.03 × 10⁻⁴ T
c. rc = 2r
Using ampere's law ∫B.ds = μ₀i
∫B.ds = = B∫ds = B × 2π(2r) = 4Bπr
4Bπr = μ₀i (since i = current enclosed = 11.2 A)
B = μ₀i/4πr
= 4π × 10⁻⁷ H/m × 11.2 A/4π(4.90 × 10⁻³ m)
= 2.286 × 10⁻⁴ T
≅ 2.29 × 10⁻⁴ T
A cheetah can accelerate from rest to a speed of 27.0 m/s in 6.75 s. What is its acceleration (in m/s2)?
Explanation:
we use the formula, Vf=Vi+at
since the cheetah accelerated from rest, it's initial speed is 0, 27=0+a (6.75), a=4 m/s2
An unmanned spacecraft has been sent to another planet to detect other life forms that might be quite different from those on Earth. If the probe could only send back one still picture, which property or properties of life would be observable in a picture?
Answer:
The presence of water
Explanation:
Any evidence of water that might appear on the still photo would be a clear indication of life on the planet. This is because scientists believe that for life to thrive elsewhere as it has done here on Earth, it needs water. Water is necessary for fertilization of reproductive cells for some organism, and for others it is where their developing young starts life from. For most, all life biochemical system needs a certain level of moisture to function properly.
determine the maximum angle theta for which the light rays incident on the end of the optical fiber of radius 1 mm are subhect to the total internal reflection along the walls of the fiber. assume that the fiber has an index of refraction od 1.2 and that the outside medium is air. note that the rays refracts when entering the fiber g
Answer:
Explanation:
Let the critical angle be C .
sinC = 1 / μ where μ is index of refraction .
sinC = 1 /1.2
= .833
C = 56°
Then angle of refraction r = 90 - 56 = 34 ( see the image in attached file )
sin i / sinr = 1.2 , i is angle of incidence
sini = 1.2 x sinr = 1.2 x sin 34 = .67
i = 42°.
What is the emf of a cell consisting of a Pb2 / Pb half-cell and a Pt / H / H2 half-cell if [Pb2 ]
Answer:
0.083 V
Explanation:
The equation of the reaction is;
Pb(s) + 2H^+(aq) -------> Pb^2+(aq) + H2(g)
E°cell = E°cathode - E°anode
E°cathode = 0.00 V
E°anode = -0.13 V
E°cell = 0.00-(-0.13)
E°cell = 0.13 V
Q= [Pb^2+] pH2/[H^+]^2
Q= 0.1 × 1/[0.05]^2
Q= 0.1/0.0025
Q= 40
From Nernst's equation;
Ecell= E°cell- 0.0592/n log Q
Ecell= 0.13 - 0.0592/2 log (40)
Ecell = 0.13 - 0.047
Ecell= 0.083 V
If the speed of a car is 20m/s .How long does it take to cover a distance of 1km?
Answer: 50 seconds
Explanation:
1km=1000m
Distance/speed=time
1000/20=50
50 seconds
Explanation:
Hey, there!!
Here,
speed (s)= 20m/s
distance (d)= 1km
= 1000m
now,
we have formula,
[tex]t = \frac{d}{s} [/tex]
putting value,
[tex]t = \frac{1000m}{20m/ s } [/tex]
cancelling the like terms,
[tex]t = 50s[/tex]
Therefore, the time is 50s.
Hope it helps...
what will you use to measure the length of a copper wire of 50cm long?
Answer:
BS33
Explanation:
its a cable length meter used for measuring length of all kinds of wires.
English units of distance include the
Answer:mile
Explanation: heres a hint think aboyt the distance between your house to school
Suppose you place your face in front of a concave mirror. Which one of the following statements is correct? A) If you position yourself between the center of curvature and the focal point of the mirror, you will see an enlarged image of your face. B) No matter where you place yourself, a real image will be formed. C) Your image will always be inverted. D) Your image will be diminished in size. E) None of these statements are true.
Answer:
If you position yourself between the center of curvature and the focal point of the mirror, you will see an enlarged image of your face.
Explanation:
A concave mirror is a curved mirror. The position of an object placed at any point in front of the mirror and the corresponding image formed by the concave mirror are depicted in appropriate ray diagrams.
If I place my face between the centre of curvature and the principal focus of the concave mirror, the image formed will be enlarged, real and inverted.
A red laser from the physics lab is marked as producing 632.8-nm light. When light from this laser falls on two closely spaced slits, an interference pattern formed on a wall several meters away has bright red fringes spaced 6.00 mm apart near the center of the pattern. When the laser is replaced by a small laser pointer, the fringes are 6.19 mm apart. What is the wavelength of light produced by the pointer?
Answer:
The wavelength is [tex]\lambda_R = 649 *10^{-9}\ m[/tex]
Explanation:
From the question we are told that
The wavelength of the red laser is [tex]\lambda_r = 632.8 \ nm = 632.8 *10^{-9}\ m[/tex]
The spacing between the fringe is [tex]y_r = 6.00\ mm = 6.00*10^{-3} \ m[/tex]
The spacing between the fringe for smaller laser point is [tex]y_R = 6.19 \ mm = 6.19 *10^{-3} \ m[/tex]
Generally the spacing between the fringe is mathematically represented as
[tex]y = \frac{D * \lambda }{d}[/tex]
Here [tex]D[/tex] is the distance to the screen
and d is the distance of the slit separation
Now for both laser red light light and small laser point D and d are same for this experiment
So
[tex]\frac{y_r}{\lambda_r} = \frac{D}{d}[/tex]
=> [tex]\frac{y_r}{\lambda_r} = \frac{y_R}{\lambda_R}[/tex]
Where [tex]\lambda_R[/tex] is the wavelength produced by the small laser pointer
So
[tex]\frac{6.0 *10^{-3}}{ 632.8*10^{-9}} = \frac{ 6.15 *10^{-9}}{\lambda_R}[/tex]
=> [tex]\lambda_R = 649 *10^{-9}\ m[/tex]
Question : Is it possible for heat to transfer from T3 to T1 and why?
Answer:
no its a negative
Explanation:
because they both are positive