Answer:
a. 3π/2 b. 0.36 m c. 0.234 m/s d. 42.55 m/s²
Explanation:
Here is the complete question
A mass m = 1.1 kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. The spring has spring constant k = 130 N/m and negligible mass. The mass undergoes simple harmonic motion when placed in vertical motion, with its position given as a function of time by y ( t ) = A c o s ( ω t − ϕ ) , with the positive y-axis pointing upward. At time t = 0 the mass is observed to be passing through its equilibrium height with an upward speed of v 0 = 3.9 m/s.
A. Find the smallest positive value of ϕ , in radians.
B. Calculate the value of A in meters.
C. What is the mass's velocity along the y-axis in meters per second, at the time t = 0.15 s?
D. What is the magnitude of the mass's maximum acceleration, in meters per second squared?
Solution
a. Since y ( t ) = A c o s ( ω t − ϕ ), the smallest possible value for ϕ is gotten when c o s ( ω t − ϕ ) = 0 ⇒ ω t − ϕ = cos⁻¹ 0 = π/2
ω t − ϕ = π/2.
At t = 0, ω t − ϕ = ω 0 − ϕ = 0 − ϕ = π/2
− ϕ = π/2
ϕ = -'π/2
Since this is a negative angle, we add 2π to the right side.
So, ϕ = -'π/2 + 2π = 3π/2
ϕ = 3π/2
b. Since v = Aω = A√(k/m) where v = maximum velocity at time t = 0 = 3.9 m/s. A = amplitude, k = spring constant = 130 N/m and m = mass = 1.1 kg
A = v/√(k/m) = 3.9 m/s/√(130 N/m/1.1 kg) = 3.9/√118.18 = 3.9/10.87 = 0.36 m
c. To find its velocity, we differentiate y(t)
So, v = dy(t)/dt = dA c o s ( ω t − ϕ )/dt = -'ωAsin( ω t − ϕ ) = v₀sin( ω t − ϕ )
v = v₀sin( ω t − ϕ ) = v₀sin( ω t − ϕ)
Substituting the value of the variables,
v = 3.9sin( 10.87 t − 3π/2)
At t = 0.15 s,
v = 3.9sin( 10.87 × 0.15 − 3π/2)
v = 3.9sin( 1.6305 − 4.7124)
v = -'3.9sin( -3.0819)
v = -'3.9 × - 0.06
v = 0.234 m/s
d. The maximum acceleration, a
a = Aω² = Ak/m = 0.36 × 130/1.1 = 42.55 m/s²
Answer:
a) F = 10.4 rad/s
b) A = 0.375 m
c) ϕ = 3π/2
d) V(t) = -ωAsin( ω t - 3π/2 )
e) V = 0.144 m/s
f) a = 40.625 m/s²
Explanation: Given that
mass m = 1.2 kg
The spring constant k = 130 N/m Time t = 0
Distance d = 0.35 m
y( t ) = A c o s ( ω t − ϕ )
At time t = 0
Speed of Vo = 3.9 m/s.
a) Find the angular frequency of oscillations in radians per second
W = √(k/m)
2πF = √(k/m)
F = 1/2π√(k/m)
F = 1/2π √(130/1.2)
F = 1.66Hz
1 Henz = 6.28 rad/s therefore,
F = 1.66 × 6.28
F = 10.4 rad/s
b) Calculate the value of A in meters.
V = Aω = A√(k/m)
where V = 3.9 m/s the maximum velocity at time t = 0
A = amplitude
A = v/√(k/m)
A = 3.9/√(130/1.2)
A = 3.9/10.4
A = 0.375 m
c. Determine the value of ϕ in radians
If y( t ) = A c o s ( ω t − ϕ ) We can obtain the smallest possible value of ϕ when c o s ( ω t − ϕ ) = 0
ω t − ϕ = cos⁻¹ 0 = π/2
ω t − ϕ = π/2.
At t = 0,
ω(0) − ϕ = π/2
− ϕ = π/2
ϕ = -'π/2
This is a negative angle, let us add 2π to the right side. So,
ϕ = -'π/2 + 2π = 3π/2
ϕ = 3π/2
d. Enter an expression for velocity along y axis as function of time in terms of A, ϕ and t using the value of ϕ from part c.
To find expression for velocity, we differentiate y(t) with respect to time t So,
V = dy/dt = dA c o s ( ω t − ϕ )/dt
V = -ωAsin( ω t − ϕ )
Therefore
V(t) = -ωAsin( ω t + π/2 )
Or
V(t) = -ωAsin( ω t - 3π/2 ) ...... (1)
e. What is the velocity of mass at time t = 0.25 s?
From equation (1)
V(t) = V₀sin( ω t − ϕ )
Substituting the value of the variables,
V = 3.9sin( 10.4t − 3π/2)
At t = 0.25 s,
V = 3.9sin( 10.4 × 0.25 − 3π/2)
V = 3.9sin( 2.6 − 4.7124)
V= -3.9sin( -2.1124)
V= -3.9 × - 0.037
V = 0.144 m/s
f. What is the magnitude of mass's maximum acceleration?
The maximum acceleration a = Aω²
a = Aω² =
a = Ak/m
a = 0.375 × 130/1.2
a = 40.625 m/s²
In the picture, what can you say about the indices of refraction n1 and n2? (1 point)
n1 < n2
n1 > n2
n1 = n2
Not enough information to tell
Answer:
(c) n1 = n2
Explanation:
You want to know what can be said about the indices of refraction when a light ray continues on a straight path from one medium to another.
RefractionWhen a wave passes through media where the index of refraction changes, its path will be bent in accordance with Snell's law. When the index of refraction does not change, the path will remain unbent.
The figure shows the path of the ray is a straight line, so we can conclude ...
n1 = n2 . . . . . choice C
__
Additional comment
Even if the indices are different, the path will remain straight if the angle of incidence is 0—the path is normal to the interface between media. Here, the path is not shown as normal to the interface.
A liquid of density 830 kg/m3 flows through a horizontal pipe that has a cross-sectional area of 1.20 x 10-2 m2 in region A and a cross-sectional area of 9.40 x 10-2 m2 in region B. The pressure difference between the two regions is 6.50 x 103 Pa. What are (a) the volume flow rate and (b) the mass flow rate?
Answer:
A) volume flow rate = 0.047 m3/s
B) mass flow rate = 39.01 kg/s
Explanation:
Detailed explanation and calculation is shown in the image below
Compute the quantity of heat released by 25.0 g of steam initially at 100.0oC, when it is cooled to 34.0°C and by 25.0 g of water initially at 100.0 oC, when it is cooled to 34.0°C.
Answer:
For steam, heat released E = 15.26KJ
For water, heat released E2 = 6.91KJ
Explanation:
Given;
Mass(steam) ms = 25g
Mass (water) mw = 25g
Change in temperature of both steam and water ∆T = 100-34= 66°C
Specific heat of water C = 4.186 J/g.°C
Specific Latent heat L = 334J/g
For steam;
Heat released E = msL + msC∆T
E = (25×334) + (25×4.186×66)
E = 15256.9J
E = 15.26KJ
For water;
Heat released E2 = mwC∆T
E2 = 25×4.186×66
E2 = 6906.9J
E2 = 6.91KJ
A glass flask whose volume is 1000 cm3 at a temperature of 1.00 ∘C is completely filled with mercury at the same temperature. When the flask and mercury are warmed together to a temperature of 52.0 ∘C , a volume of 8.25 cm3 of mercury overflows the flask.If the coefficient of volume expansion of mercury is 18.0×10−5K−118.0×10 compute the coefficient of volume expansion of the glass.
Answer:
[tex]1.8\times 10^{-5}/K[/tex]
Explanation:
Volume of glass flask,[tex]V_0=1000 cm^3[/tex]
[tex]T_1=1.00^{\circ} C[/tex]
[tex]T_2=52.0^{\circ} C[/tex]
Over flow[tex]\Delta V=8.25 cm^3[/tex]
Coefficient of mercury=[tex]\beta_{Hg}=18.0\times 10^{-5}/K[/tex]
[tex]\Delta V_{Hg}=\beta_{Hg}V_0(T_2-T_1)=18\times 10^{-5}\times 1000\times (52-1)[/tex]
[tex]\Delta V_{Hg}=9.18 cm^3[/tex]
[tex]\Delta_{gass}=\Delta V-\Delta_{Hg}=9.18-8.25=0.93 cm^3[/tex]
[tex]\beta_{gass}=\frac{\Delta V_{gass}}{V_0(T_2-T_1)}[/tex]
[tex]\beta_{gass}=\frac{0.93}{1000\times (52-1)}[/tex]
[tex]\beta_{gass}=1.8\times 10^{-5}/K[/tex]
Hence, the coefficient of volume expansion of the glass=[tex]1.8\times 10^{-5}/^{\circ} C[/tex]
The coefficient of volume expansion of the glass [tex]\bold { 1.8 x 10^-^5\ K^-^ 1}[/tex]
Given here,
Volume of the glass flask = 1000[tex]\bold {cm^3}[/tex]
Initial temperature = 1[tex]\bold{^oC}[/tex]
Final temperature = 52 [tex]\bold{^oC}[/tex]
[tex]\bold{ \Delta V = V_0 \beta \Delta T}[/tex]
Where,
[tex]\bold {\Delta V}[/tex] - Change in volume
[tex]\bold{V_0}[/tex] - initial volume = 1000cm
[tex]\bold {\beta }[/tex] - coefficient of volume expansion
[tex]\bold{\Delta T }[/tex] - temperature [tex]\bold { = T_2- T_1}[/tex]
Put the values in the formula
[tex]\bold {\Delta V_H_g = 18\times 10^-^5 \times 1000\times 51}\\\\\bold {\Delta V_H_g = 9.18 cm^3}[/tex]
[tex]\bold {\Delta Vglass = \Delta V_H_g - \Delta _H_g}\\\\\bold {\Delta Vglass = 9.18 -8.25 }\\\\\bold {\Delta Vglass = 0.93 cm^3}[/tex]
So, coefficient of volume expansion for gas,
[tex]\bold {\beta glass = \dfrac {0.93 }{1000 \times 51}}\\\\\bold {\beta glass = 1.8 x 10^-^5\ K^-^ 1}[/tex]
The coefficient of volume expansion of the glass [tex]\bold { 1.8 x 10^-^5\ K^-^ 1}[/tex]
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Suppose you are 3.3km away from a rifle range where someone is practicing shooting. How long would it take you to hear the sound of a shot fired by him?
Can you guys answer quickly, its urgent.
Answer:9.5 seconds(approx.)
Explanation:time=distance/speed
here,
distance=3.3 km= 3300 m
standard speed of sound=344 m/s
so, time=3300/344
time=9.5(approx.)
Final answer:
It would take approximately 9.71 seconds for the sound of a shot to travel 3.3 km and reach you, using the speed of sound of 340 m/s.
Explanation:
To calculate how long it would take for you to hear the sound of a shot fired from 3.3 km away, we need to use the speed of sound. In general, the speed of sound is approximately 340 meters per second (m/s) at sea level under normal conditions. Therefore, we can use the formula:
Time = Distance / Speed of Sound.
Now we simply plugin the values to get:
Time = 3300 meters / 340 m/s = 9.71 seconds
Therefore, it would take approximately 9.71 seconds for the sound of the shot to travel 3.3 km and reach you.
Why do you think the combined wave is more powerful than either the transverse or longitudinal wave with the same amplitude
Answer:
Explanation:
The combined wave only end up been more powerful than the Longitudinal wave. This means, the transverse wave is more powerful than the combined wave. In transverse wave, the oscillation is perpendicular to the direction of the wave, while in longitudinal wave, the motion of the movement of the object is parallel to the movement of the wave. And in combined wave, the movement of the medium is in a circular manner,
Tarzan, whose mass is 94 kg, is hanging at rest from a tree limb. Then he lets go and falls to the ground. Just before he lets go, his center of mass is at a height 2.8 m above the ground and the bottom of his dangling feet are at a height 2.0 above the ground. When he first hits the ground he has dropped a distance 2.0, so his center of mass is (2.8 - 2.0) above the ground. Then his knees bend and he ends up at rest in a crouched position with his center of mass a height 0.5 above the ground.(a) Consider the point particle system. What is the speed v at the instant just before Tarzan's feet touch the ground? v = _______ m/s. (b) Consider the extended system. What is the net change in internal energy for Tarzan from just before his feet touch the ground to when he is in the crouched position?
Tarzan's speed just before his feet touch the ground is 7.4 m/s, calculated using conservation of energy. The net change in internal energy as he bends his knees and stops is 2603.4 J, equivalent to the loss of kinetic energy.
Part (a): Speed of Tarzan Before Touchdown
To find the speed of Tarzan just before his feet touch the ground, we can use the principle of conservation of energy. Initially, Tarzan has gravitational potential energy due to being at a height of 2.8 m above the ground. When he lets go, this potential energy converts to kinetic energy as he falls. At the instant before his feet touch the ground, he is at a height of 0.8 m (2.8 m - 2 m), and the gravitational potential energy at this point converts into kinetic energy. Using the conservation of energy:
Initial Potential Energy = Final Kinetic Energy
mghinitial = 1/2*mv^2
Plugging in the values:
94 kg × 9.8 m/s2 × 2.8 m = (1/2) × 94 kg × v2
After solving the equation, we find:
v = 7.4 m/s
Part (b): Net Change in Internal Energy
The net change in internal energy is the difference between the kinetic energy just before the feet touch the ground and the energy when Tarzan is crouched. Assuming no losses, all the kinetic energy converts into internal energy. Without specific details on work done by Tarzan to flex his muscles or any other form of energy conversion, the kinetic energy that is no longer present in the motion would be assumed to convert fully to internal energy (such as heat). The net change in internal energy equates to the kinetic energy which is lost:
Change in Internal Energy = 1/2*mv^2 - 0 J, since he is at rest.
Using the speed found in part (a) and Tarzan's mass: 1/2*× 94 kg × (7.4 m/s)2
This calculation results in a net change in internal energy of: 2603.4 J
In an ac induction motor, the stator produces a rotating magnetic field that induces current in the rotor windings. The rotor current generates a magnetic field in opposition to the magnetic field of the stator, thereby causing the rotor to turn.A. TrueB. False
A. True
According to the Faraday-Lenz law, the current in the rotor is generated by the change in the magnetic flux due to the rotating stator, the polarity of the induced current is such that it produces a magnetic field that opposes the change in magnetic flux that produced it. Which causes the rotor to turn
What is the equivalent resistance in this circuit?
Ω
What is the current in this circuit?
A
Answer:
6.0?
Explanation:
What is the current in this circuit?
A
Hold on, our servers are swamped. Wait for your answer to fully load.
Answer:
The first one is 15.
The second one is 3.0.
Explanation:
You add up all the sides accept the voltage. 2+3+4+6= 15
For the second one you divide the voltage by all the resisters. 45/15=3
Kinetic energy varies jointly as the mass and the square of the velocity. A mass of 1515 grams and velocity of 77 centimeters per second has a kinetic energy of 147147 ergs. Find the kinetic energy for a mass of 1010 grams and velocity of 99 centimeters per second?
Answer:
The second kinetic energy is 162 J.
Explanation:
Given that,
Mass, [tex]m_1=15\ g[/tex]
Velocity, [tex]v_1=7\ cm/s[/tex]
Kinetic energy, [tex]K_1=147\ ergs[/tex]
Mass, [tex]m_2=10\ g[/tex]
Velocity, [tex]v_2=9\ cm/s[/tex]
We need to find kinetic energy [tex]K_2[/tex]. Kinetic energy is given by :
[tex]K=\dfrac{1}{2}mv^2[/tex]
So,
[tex]\dfrac{K_1}{K_2}=\dfrac{m_1}{m_2}\times \dfrac{v_1^2}{v_2^2}\\\\K_2=\dfrac{K_1}{\dfrac{m_1}{m_2}\times \dfrac{v_1^2}{v_2^2}}\\\\K_2=\dfrac{147}{\dfrac{15}{10}\times \dfrac{7^2}{9^2}}\\\\K_2=162\ J[/tex]
So, the second kinetic energy is 162 J.
A ski lift has a one-way length of 1 km and a vertical rise of 200 m. The chairs are spaced 20 m apart, and each chair can seat three people. The lift is operating a a steady speed of 10 km/h. Neglecting friction and air drag and assuming the average mass of each loaded chair is 250 kg, determine the power required to operate this ski lift. Also estimate the power required to accelerate this ski lift in 5 s to its operating speed when it is first turned on. (steady power = 68.1 kW; start-up = 43.7 kW)
Answer:
P = 68.125 kW
P startup = 43.05 kW
Explanation:
The power required to operate this ski lift is 43.05 KW.
What is power?The quantity of energy moved or converted per unit of time is known as power in physics. The watt, or one joule per second, is the unit of power in the International System of Units. A scalar quantity is power.
The lift is operating a a steady speed of 10 km/h = 10×(1000/3600) m/s = 25/9 m/s.
Average mass of the chair= 250 kg.
Acceleration of the chair = 25/9 /5 m/s² = 5/9 m/s².
Vertical component of this acceleration is = (5/9) ×{200/√(200²+1000²)} m/s²
= 0.1089 m/s²
Hence, the required height = 1/2 × 0.1089 ×5² m = 1.362 m.
So, the total work done = mgh +1/2mv²
= 250×9.8×1.362 + 1/2× 250 × (25/9)² joule
= 215240.56 joule
So, the power required to operate this ski lift = 215240.56 /5 watt = 43048.112 W = 43.05 KW.
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Kinect energy is expressed using the unit
Answer:
joule
Explanation:
every unit for Energy is joule J
On a merry-go-round, animals at the edge are located 4 times farther from the axis of rotation than the animals near the center. The animals near the center has a rotational speed of 3 RPM and a tangential speed of 2 m/sec.
What is the rotational speed of the animals near the edge?
a 3 RPM
b 12 RPM
c 2 RPM
d 6 RPM
Answer:
12 RPM
Explanation:
I would calculate the distance from the edge to the center, and then multiple that by 3RPM with 2 m/sec
Technician A says that to perform a maximum output test on a typical heavy-duty truck charging circuit, the engine should be run at 1500 rpm. Technician B says that alternator rpm is typically at least three times engine rpm. Who is correct?
Answer:
Both Technicaian A and B is correct
Explanation:
An alternator is a device that converts mechanical energy into electrical energy. In every alternator, there is unavoidable power losses. Such losses could be mechanical,drive belt or getting the alternator's bearing heated and electrical loss.more also changing magnetic field also causes some losses in an alternator. The diodes of an alternator get hot when there is drop in votage.At reasonable maximum engine speeds, For instance when it read 1500 RPM to redline and there is heavy loads, starting from the idle through the red line with light electrical accessory loads, Nothing will happen to battery, it will just goes along for the ride. Unless it wait for the alternator to fall below operating speeds.
Therefore, when technician A says that to perform a maximum output test on a typical heavy-duty truck charging circuit, the engine should be run at 1500 rpm, and Technician B says that alternator rpm is typically at least three times engine rpm. Both of them is is correct.
Light refracts when traveling from air into glass because light
Answer:
Speed of light changes
Explanation:
Since glass is denser than air so the speed of light in glass is less than in air so light rays bend i.e. refract.
Light refracts when traveling from air into glass due to a change in speed caused by differences in optical density. The process, governed by Snell's Law, results in the bending of light towards the normal line as it enters the denser medium.
Explanation:Light refracts when traveling from air into glass because light waves undergo a change in speed when they pass from one medium to another. This process is known as refraction. Refraction occurs because there is a change in light's propagation speed due to the difference in optical density between air and glass. When light rays propagate from air (less optically dense) into glass (more optically dense), they bend towards the normal line—a line perpendicular to the boundary between the two media. This bending happens according to Snell's Law, which relates the angle of incidence to the angle of refraction, taking into account the refractive indices of the two media.
Degeneracy pressure stops the crush of gravity in all the following except
Answer:
A very massive main- sequence star
Explanation:
Degeneracy pressure refers to pressure expend by dense material , which is composed of fermions, which is an example of electrons in a white dwarf star. According to Pauli exclusion principle, which states that no two fermions can exist in the same quantum state, actually give details about the pressure.
When there is stellar masses that is less than about 1.44 of that of solar masses, there will be gravitational fall in the energy , and the energy will not be sufficient to produce the neutrons of a neutron star, therefore, the fall is abstruptly stopped through the electron degeneracy to form white dwarfs.this result to the creation of an effective pressure that further prevents gravitational fall.
A force F acts in the forward direction on a cart of mass m. A friction force ff opposes this motion. Part A Use Newton's second law and express the acceleration of the cart. Express your answer in terms of the variables F, f, and m.
The acceleration of the cart can be calculated using the equation a = (F - f) / m, where F is the applied force, f is the friction force, and m is the mass of the cart.
Explanation:The acceleration of the cart can be expressed using Newton's second law, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Therefore, the acceleration (a) of the cart can be calculated using the equation:
a = (F - f) / m
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what will happen and give a reason
1 - Don't put the coat on the snowman - it will melt him
2 - I don't think the coat will make any difference
3 - I think it will keep him cold and stop him from melting.
Answer:
1 or 2 or 3
Explanation:
it depends whether the coat is a light or dark colour. if it is lighly coloured it will not absorb heat from the sun and wont melt the snowman. if it is darkly coloured it will be number 1
the coat wont make a difference if the temperature of the snowman is the same and the temperature outside the snoman and the sun isnt shining. the coat would just make him look smart - so number 2
it coul keep in the cold and block out the warmth so number 3
How does atmospheric pressure affect the boiling point of a liquid
Answer:
The atmospheric pressure and boiling point are directly proportional
Increasing atmospheric pressure increases the boiling point also
Explanation:
The atmosphere contain molecules that are in constant motion. They exert a downward force on a liquid’s surface. The higher the air pressure, the harder it is for the liquid to evaporate. Therefore, the boiling point of a solvent or liquid is affected by the atmospheric pressure and boiling point is raised.
A liquid in a high pressure environment boils at a higher temperature.
When placed in a lower pressure environment it boils at a lower temperature.
What is the energy source that heats a contracting protostar?
A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 290 N applied to its edge causes the wheel to have an angular acceleration of 0.814 rad/s2.What is the mass of the wheel?
Answer:
The mass of the wheel is 2159.045 kg
Explanation:
Given:
Radius [tex]r = 0.330[/tex]
m
Force [tex]F = 290[/tex] N
Angular acceleration [tex]\alpha = 0.814 \frac{rad}{s^{2} }[/tex]
From the formula of torque,
Γ [tex]= I\alpha[/tex] (1)
Γ [tex]= rF[/tex] (2)
[tex]rF = I \alpha[/tex]
Find momentum of inertia [tex]I[/tex] from above equation,
[tex]I = \frac{rF}{\alpha }[/tex]
[tex]I = \frac{0.330 \times 290}{0.814}[/tex]
[tex]I = 117.56[/tex] [tex]Kg. m^{2}[/tex]
Find the momentum inertia of disk,
[tex]I = \frac{1}{2} Mr^{2}[/tex]
[tex]M = \frac{2I}{r^{2} }[/tex]
[tex]M = \frac{2 \times 117.56}{(0.330)^{2} }[/tex]
[tex]M = 2159.045[/tex] Kg
Therefore, the mass of the wheel is 2159.045 kg
The incoming infrared radiation from the Sun as it travels towards Earth is _____. mostly reflected back out into space mostly absorbed and transmitted toward Earth's surface equally absorbed and reflected completely blocked and reflected by the upper atmosphere
Answer:
Mostly absorbed and transmitted toward Earth's surface
Explanation:
Infrared radiation from the sun reaches the Earth's surface and warms the Earth's surface. It emits some infrared radiation, some absorbed by gases such as carbon dioxide in the atmosphere. This is known as the greenhouse effect. and If it don't, radiation from the earth is powerful enough to burn the skin.
so correct answer is Mostly absorbed and transmitted toward Earth's surface
Answer:
mostly absorbed and transmitted toward Earth's surface
Explanation:
) Diameter of a star: Assume that the temperature of the Sun is 5800K and the temperature of Sirius A is 10,000K. If the luminosity of Sirius A is 23 times that of the Sun, calculate the radius of Sirius A relative to the Sun. Sirius A is ______ times the size of the Sun. Your answer should be a number in the format (x.x).
Answer:
Sirius A is 1.608 times the size of the Sun.
Explanation:
The radiant flux establishes how much energy an observer or a detector can get from a luminous source per unit time and per unit surface area.
[tex]R_{p} = \frac{L}{4\pi r^2}[/tex] (1)
Where [tex]R_{p}[/tex] is the radiant power received from the source, L is its intrinsic luminosity and r is the distance.
The Stefan-Boltzmann law is defined as:
[tex]R_{p} = \sigma \cdot T^{4}[/tex] (2)
Where [tex]R_{p}[/tex] is the radiant power, [tex]\sigma[/tex] is the Stefan-Boltzmann constant and T is the temperature.
Then, equation 2 can be replaced in equation 1
[tex]\sigma \cdot T^{4} = \frac{L}{4\pi r^2}[/tex] (3)
Notice that L is the energy emitted per second by the source.
Therefore, r can be isolated from equation 3.
[tex] r^2 = \frac{L}{4\pi \sigma\cdot T^{4}}[/tex]
[tex] r = \sqrt{\frac{L}{4\pi \sigma\cdot T^{4}}}[/tex] (4)
The luminosity of the Sun can be estimated isolating L from equation 3.
[tex]L = (4\pi r^2)(\sigma \cdot T^{4}) [/tex]
but, [tex]r = 696.34x10^{6}m[/tex] and [tex]T = 5800K[/tex]
[tex]L_{Sun} = 4\pi (696.34x10^{6}m)^2(5.67x10^{-8} W/m^{2} K^{4} )(5800K)^{4}) [/tex]
[tex]L = 3.90x10^{26} W[/tex]
To find the luminosity of Sirius A, the following can be used:
[tex]\frac{L_{SiriusA}}{L_{sun}} = 23[/tex]
[tex]{L_{SiriusA}} = (3.90x10^{26} W)(23)[/tex]
[tex]{L_{SiriusA}} = 8.97x10^{27}W[/tex]
Finally, equation 4 can be used to determine the radius of Sirius A.
[tex] r = \sqrt{\frac{8.97x10^{27}W}{4\pi (5.67x10^{-8} W/m^{2} K^{4})(10000K)^{4}}}[/tex]
[tex]r = 1.12x10^{9}m[/tex]
So, Sirius A has a radius of [tex]1.12x10^{9}m[/tex]
[tex]\frac{1.12x10^{9}m}{696.34x10^{6}m} = 1608[/tex]
Hence, Sirius A is 1.608 times the size of the Sun.
A thin rod of length 0.79 m and mass 130 g is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with angular speed 3.61 rad/s. Neglecting friction and air resistance, find (a) the rod's kinetic energy at its lowest position and (b) how far above that position the center of mass rises.
Answer:
a) 0.3965 j
b) 0.3112 m
Explanation:
The picture attached explains it all. Thank you
A current carrying gold wire has diameter 0.84 mm. The electric field in the wire is 0.49 V/m. What are (a) the current carried by the wire; (b) the potential difference between two points in the wire 6.4 m apart; (c) the resistance of a 6.4-m length of this wire
Explanation:
Given that,
Diameter of the gold wire, d = 0.84 mm
Radius, r = 0.42 mm
Electric field in the wire, E = 0.49 V/m
(a) Electric current density is given by :
[tex]J=\dfrac{I}{A}[/tex]
And electric field is :
[tex]E=\rho J[/tex]
[tex]\rho[/tex] is resistivity of Gold wire
So,
[tex]E=\dfrac{\rhi I}{A}\\\\I=\dfrac{EA}{\rho}\\\\I=\dfrac{0.49\times \pi (0.42\times 10^{-3})^2}{2.44\times 10^{-8}}\\\\I=11.12\ A[/tex]
(b) The potential difference between two points in the wire is given by :
[tex]V=E\times l\\\\V=0.49 \times 6.4\\\\V=3.136\ V[/tex]
(c) Resistance of a wire is given by :
[tex]R=\rho \dfrac{l}{A}\\\\R=2.44\times 10^{-8}\times \dfrac{6.4}{\pi (0.42\times 10^{-3})^2}\\\\R=0.281\ \Omega[/tex]
Hence, this is the required solution.
Final answer:
To find the current carried by the gold wire, use Ohm's law. To find the potential difference between two points in the wire 6.4 m apart, multiply the electric field by the distance. To find the resistance of a 6.4-m length of the wire, use the formula R = ρL/A.
Explanation:
To find the current carried by the gold wire, we can use Ohm's law which states that the electric field (E) is equal to the product of the current (I) and the resistance (R) of the wire. Rearranging the equation, we can solve for the current: I = E/R. Given that the diameter of the wire is 0.84 mm, we can calculate the cross-sectional area using the formula for the area of a circle (A = πr^2). With the cross-sectional area, we can find the resistance by using the formula R = ρL/A, where ρ is the resistivity of gold and L is the length of the wire. Finally, we can substitute the values into the equation to find the current carried by the wire.
(b) To find the potential difference between two points in the wire 6.4 m apart, we can multiply the electric field by the distance between the two points: V = E × d.
(c) The resistance of a 6.4-m length of this wire can be found using the formula R = ρL/A, where ρ is the resistivity of gold, L is the length of the wire, and A is the cross-sectional area of the wire.
Ultrasound with a frequency of 4.257 MHz can be used to produce images of the human body. If the speed of sound in the body is the same (1.06 km/s) as in salt water, what is the wavelength in the body? Answer in units of m.
The wavelength of an ultrasound with a frequency of 4.257 MHz in the human body is approximately 0.000249 meters or 0.249 mm, calculated using the formula
λ = v/f with the given speed of sound (1060 m/s) and the frequency.
The question is asking to calculate the wavelength of an ultrasound with a frequency of 4.257 MHz in the human body, given the speed of sound in the body is 1.06 km/s. To find the wavelength, we use the formula λ = v/f, where λ is the wavelength, v is the speed of sound, and f is the frequency.
First, we convert the speed of sound from km/s to m/s: 1.06 km/s = 1060 m/s. Then we use the given frequency (f) of 4.257 MHz, which we also convert to Hz: 4.257 MHz = 4.257 x 106 Hz. Now we can calculate the wavelength:
λ = v/f
λ = 1060 m/s / 4.257 x 106 Hz
λ ≈ 0.000249 m
Therefore, the wavelength of the ultrasound in the body is approximately 0.000249 meters or 0.249 mm.
The wavelength of 4.257 MHz ultrasound in the human body, using the speed of sound of 1.06 km/s, is approximately 0.249 mm.
To determine the wavelength of ultrasound in the body given the frequency and the speed of sound, we can use the formula:
lambda = v / f, where
lambda is the wavelength,
v is the speed of sound, and
f is the frequency of the ultrasound wave. The speed of sound in the body is given as 1.06 km/s, which is equivalent to 1060 m/s. The frequency of the ultrasound is 4.257 MHz, or 4.257 x 106 Hz. Plugging these values into the formula:
lambda = 1060 m/s / 4.257 x 106 Hz
The result will yield the wavelength of ultrasound in the human body, measured in meters.
Performing the calculation:
lambda = 1060 / 4.257 x 106
lambda = 0.000249 m or approximately 0.249 mm
The wavelength of 4.257 MHz ultrasound in the human body is therefore about 0.249 mm.
The electric power consumed by a circuit with one light bulb is 24 W. The voltage of the battery is 3 V. What is the current in the circuit?
Answer:
8 ampere
Explanation:
P= V x I
so
I = P/V
I= 24 /3
I = 8 A
veronicas velocity was measured as 4.3 m/s. She displaced 20 meters in 4.7 seconds. Which piece of information is missing for the correct calculation of velocity?
Answer: B
Explanation:
The top and bottom surfaces of a metal block each have an area of A = 0.030 m 2, and the height of the block is d = 0.11 m. At the top surface of the block, a force F1 is applied to the right, while at the bottom surface of the block, a force F2 is applied to the left, causing a shear in the metal block. If F1 = F2 = 30 ⨯ 106 N and the displacement between the two edges due to the shear is 1.12 10-3 m, what is the shear modulus of the metal
Answer:
Shear modulus is equal to [tex]9.82\times 10^{10}N/m^2[/tex]
Explanation:
We have given area [tex]A=0.030m^2[/tex]
Force is given [tex]F_1=F_2=30\times 10^6N[/tex]
Height of the block d = 0.11 m
Change in height of the block [tex]\Delta d=1.12\times 10^{-3}m[/tex]
Stress is given by
[tex]stress=\frac{force}{area}[/tex]
[tex]stress=\frac{30\times 10^6}{0.030}=10^9N/m^2[/tex]
Strain is equal to
[tex]strain=\frac{\Delta d}{d}[/tex]
[tex]strain=\frac{1.12\times 10^{-3}}{0.11}=10.18\times 10^{-3}[/tex]
Shear modulus is equal to
Shear modulus [tex]=\frac{stress}{strain}[/tex]
[tex]=\frac{10^9}{10.18\times 10^{-3}}=9.82\times 10^{10}N/m^2[/tex]
Convection
A) is energy similar to radiant heat from the sun.
B) is the result of conductive heat loss to the air that overlies the surface of the body.
C) is the direct transfer of energy through physical contact.
D) changes a liquid to a vapor.
Answer:
A) energy similar to radiant heat from the sun