The space station must turn at 1.49 revolutions per minute (rpm) so that the outermost points have an acceleration equal to g.
Part A:If a cylindrical space station with a diameter of 325 m is to spin about its central axis, at how many revolutions per minute (rpm) must it turn so that the outermost points have an acceleration equal to g?The acceleration of the outermost points is given as g. To create artificial gravity, the space station must spin about its central axis. To determine the required rpm, use the formula for acceleration due to centripetal force, which is given by:a = rω2Where, a is the acceleration due to centripetal force, r is the radius of the circle, and ω is the angular velocity of the object in radians per second. One full rotation equals 2π radians. Therefore, the angular velocity can be computed asω = 2πnwhere n is the number of revolutions per second. To transform it to rpm, use the formula:n = (r.p.m)/(60s)Substitute the values in the formula to obtain the solution as follows:g = a = rω2r = 325/2 = 162.5ma = g = 9.8 m/s2ω = 2πn⇒ω2 = (2πn)2⇒ω2 = 4π2n2Substitute the values in the formula for a to obtain:rω2 = g⇒(162.5 m)(4π2n2) = 9.8 m/s2n = 1.49 rpmTherefore, the space station must turn at 1.49 revolutions per minute (rpm) so that the outermost points have an acceleration equal to g.
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The accepted value for the free-fall acceleration on Earth's surface is 9.80665 m/s2
Which of the following measurements is the most accurate?
Answer:
The Answer is A 9.80860 m/s²
Explanation:
Can some one Explain to me how the orbits of the planets around the sun work?
Kepler 2nd and 3rd law are tricky can someone explain?
Since the powerful gravitational pull of the Sun, all of the the solar system's planets revolve around it. The Sun basically attracts the solar system's planets, encompassing Earth, as well as allows them to be in orbit.
What is Kepler's law?Kepler's laws of planetary motion was initially published at 1609 and 1619 by Johannes Kepler which implies the description of the main orbits of planets around the Sun.
They explain the following scenarios:
Planets move in elliptical orbits all around the Sun.A planet grab the similar quantity of space in the similar time not relating of the place it is in its orbit.A planet's orbital period is usually proportional to the size of its orbit.Thus, this way, the orbits of the planets around the sun work.
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You cannot tell if c equals d because the radii are not given what is wrong with that statement
Cοrrect, withοut the values fοr the radii οf circles C and D, it is nοt pοssible tο determine if they are equal.
What is the radii οf the circles?The radii οf the circles play a crucial rοle in determining their sizes and whether they are equal οr nοt. If the radii οf bοth circles are equal, then we can cοnclude that C equals D in terms οf size. Hοwever, withοut specific infοrmatiοn abοut the radii, we cannοt make any definitive cοnclusiοns abοut the equality οf the circles.
In geοmetry, twο circles are cοnsidered equal if they have the same radius. Hοwever, the statement prοvided dοes nοt invοlve any cοmparisοn οr relatiοnship between the radii οf the circles. Instead, it suggests that the equality οr inequality οf c and d cannοt be determined due tο the lack οf infοrmatiοn abοut their radii. This reasοning is flawed because the radii are nοt necessary fοr cοmparing οr establishing the equality οf c and d.
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defend the use of renewable or non renewable resources. help please will give brainliest
Answer:
Renewable sources are better because they don't damage the environment. As of now, there is a r=lot of damage already done to the environment thanks to non-renewable resources, and soon a lot of this damage will be irreversible. Another good thing about renewable resources is that that it is unlimited, this means that it is a steady source of energy and items.
Non renewable resources are good for the economy. People are so used to using non renewable resources that they might not want to switch over to renewable resources. People will keep buying these product so it is a steady item to invest in and profit off of. Non renewable resources also have a lot more research on them and people have found multiple different ways to utilize it so people might like it more.
Due to a weak connection, there is a break in the circuit (shown below) between points a and b. If R1 = 4.83 Ω, R2 = 1.99 Ω, and R3 = 16.2 Ω, and the two batteries 1 and 2 have voltages of 26.0 V and 6.50 V respectively, find the potential difference Vab. Be sure to include the sign of the potential difference. Vab = Vb − Va = (word)
The potential difference Vab between points A and B, calculated using Kirchhoff's voltage law, is found to be 15.0 V, indicating that point B has a higher potential than point A.
When the circuit between points A and B is broken due to a poor connection, the potential difference Vab can be calculated using the following equation: Vab = Vb − Va = (I1R1 + I2R2) − (I1R1 + I3R3) , where I1, I2, and I3 are the currents flowing through R1, R2, and R3, respectively.Using Kirchhoff's voltage law (KVL), the currents in the circuit can be calculated. The KVL equation for the upper loop is 26V − I1R1 − I2R2 = 0. Solving for I1 in terms of I2, we get:I1 = (26V − I2R2) / R1. The KVL equation for the lower loop is: 6.50V − I3R3 + I2R2 = 0Solving for I3 in terms of I2, we get:I3 = I2R2 / R3. Substituting these expressions for I1 and I3 into the equation for Vab, we get: Vab = (26V − I2R2) / R1 + I2R2 / R3 − (6.50V). Simplifying the expression gives: Vab = [(26V * R3 − 6.50V * R1) / (R1 * R3)] − [(R2 / R1 + R2 / R3) * I2]The value of I2 can be found by applying KCL to the node where R2, R3, and the two batteries meet. The KCL equation is: I2 = (26V − 6.50V) / (R2 + R3). Substituting this value for I2 into the equation for Vab gives Vab = [(26V * R3 − 6.50V * R1) / (R1 * R3)] − [(R2 / R1 + R2 / R3) * (26V − 6.50V) / (R2 + R3)] = 15.0 VTherefore, the potential difference Vab is 15.0 V, which is positive because the potential at point B is higher than the potential at point A.For more questions on the potential difference
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According to these data, which type of animal is most likely to hear
sounds with frequencies of 10 hertz?
A Bat
B Dog
C Grasshopper D Human
C
becuz grasshopper can hear between 12-20kHz
What is the modern periodic table of elements?
A. A chart organizing all elements by their atomic mass
B. A list of all elements occuring in nature
C. A chart organizing all elements by their atomic number
D. A list of all elements created by humans
Why is trowing important in football?
Answer:
The goal of a throwing movement will generally be distance, accuracy or some combination of the two. In throws for distance, the release speed - and, therefore, the force applied to the thrown object - is crucial.
derive an expression from the energy stored E, in a stretched wire of original length L cross sectional area A, e, tension e,and young modulus Y of the material of the wire
The expression for the energy stored (E) in a stretched wire of original length (L), cross-sectional area (A), tension (T), and Young's modulus (Y) is given by E = Y * e * ln(L) * A
How to explain the expressionThe work done to stretch the wire can be calculated by integrating the force applied over the displacement. In this case, the force applied is the tension (T) in the wire, and the displacement is the change in length (ΔL) from the original length (L) to the stretched length (L + ΔL).
The tension in the wire is given by Hooke's law, which states that the tension is proportional to the extension of the wire:
T = Y * (ΔL / L)
where Y is the Young's modulus of the material of the wire.
Now, let's calculate the work done to stretch the wire:
dW = T * dL
Integrating this expression from L to L + ΔL:
W = ∫ T * dL = ∫ Y * (ΔL / L) * dL
W = Y * ΔL * ∫ (dL / L)
W = Y * ΔL * ln(L) + C
Here, C is the constant of integration. Since the energy stored in the wire is zero when it is unstretched (ΔL = 0), we can set C = 0.
Finally, the expression for the energy stored in the wire (E) is:
E = W = Y * ΔL * ln(L)
or, if we substitute the cross-sectional area (A) and strain (e) of the wire, where e = ΔL / L:
E = Y * e * ln(L) * A
Thus, the expression for the energy stored (E) in a stretched wire of original length (L), cross-sectional area (A), tension (T), and Young's modulus (Y) is given by:
E = Y * e * ln(L) * A
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the fourth band of a resistor color code is gold. the fourth letter on a capacitor's code is j. calculate the propagated percent error in the time constant of a circuit using these two circuit elements in series with a d. c. power supply. enter a single digit (
The propagated percent error in the time constant of a circuit is ±10% using these two circuit elements in series with a d. c. power supply.
What is error?The discrepancy between the measured and actual values might be used to define an error.
The fourth band of a resistor color code is gold means ± 5% tolerance in measurement of resistor.
The fourth letter on a capacitor's code is j means ± 5% tolerance in measurement of capacitor.
Now, the time constant of a RC circuit = CR.
Hence, the propagated percent error in the time constant of a circuit using these resistor and capacitor = ± 5% + (± 5%)
= ±10%.
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under the principles of the concentric ring model, what is the name of the activities found in the most outer circle / ring?
a concentric ring model in which social groupings are spatially organised in a hierarchy of rings. The upper class resides further away from the center, while the lower class is located closer to it.
The concentric ring model operates on the presumption that cultural content results from the incorporation of original ideas into the creation and/or presentation of music, text, and picture, and that these concepts originate in the fundamental artistic creativity spheres. Burgess' concentric ring model concept envisions growth occurring in a series of concentric rings surrounding the concentric ring model . According to Hoyt's sector model, economic expansion follows transportation corridors.
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A uniform solid sphere rolls down an incline. a) What must be the incline angle (in degrees) if the linear acceleration of the center of the sphere is to have a magnitude of 0.23g? b) If a frictionless block were to slide down the incline at that angle, would its acceleration magnitude be more than, less than, or equal to 0.23g?
The incline angle should be about 4.7 degrees and the block's acceleration would be greater than that of the rolling sphere.
a) Let M be the mass of the sphere, R be its radius, and θ be the incline angle. When the sphere rolls down the incline without slipping, the friction force acting on it causes a torque about its center of mass, which results in a rotational acceleration. If a is the linear acceleration of the center of mass, and α is the angular acceleration, then we have:
a = α R
Also, the torque τ caused by the friction force is given by:
\(τ = I α\)
where I is the moment of inertia of the sphere about its center of mass. For a solid sphere, I is given by:
\(I = (2/5) M R^2\)
Since the sphere rolls without slipping, the friction force is related to the normal force N by:
\(f = μ N\)
where f is the friction force, and μ is the coefficient of static friction. The normal force is related to the weight of the sphere by:
N = M g cos θ
where g is the acceleration due to gravity.
The net force acting on the sphere down the incline is given by:
\(Fnet = M g sin θ - f\)
The linear acceleration of the center of mass is given by:
\(a = Fnet / M\)
Substituting for f and N, we get:
\(a = g (sin θ - μ cos θ)\)
Equating this to α R, we get:
g (sin θ - μ cos θ) = α R
Substituting for α using the expression for I and τ, we get:
\(g (sin θ - μ cos θ) = τ / (2/5 M R)\)
Substituting for τ using the expression for f and N, we get:
\(g (sin θ - μ cos θ) = (μ M g cos θ) R / (2/5)\)
Simplifying, we get:
\(tan θ = (5/7) μ\)
Substituting the given values, we get:
tan θ = (5/7) (0.23)
\(θ = arctan(0.082)\)
θ = 4.7 degrees (approximately)
Therefore, the incline angle should be about 4.7 degrees
b) Since the block is frictionless, its acceleration down the incline is given by:
a' = g sin θ
Substituting the value of θ obtained in part a), we get:
a' = g sin(4.7) ≈ 0.41 g
Since this is greater than 0.23g, the block's acceleration would be greater than that of the rolling sphere.
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Please help (I didn’t know what subject to put this in but it’s earth science)
this is a 3 part question6) (a) Your heart beats with a frequency of 1.45 Hz. How many beats occur in a minute? (b) If the frequency of your heartbeat increases, will the number of beats in a minute increase, decrease, or stay the same? (c) How many beats occur in a minute if the frequency increases to 1.55 Hz?
Given,
The initial frequency of the heartbeat, f₁=1.45 Hz
The increased heartbeat, f₂=1.55 Hz
The frequency of the heartbeat can be described as the number of occurence of the heartbeat per second. That is every second, the heart beats 1.45 times.
(a)
Thus for a minute, the number of the heartbeats is,
\(\begin{gathered} N_1=f_1\times60 \\ =1.45\times60=87 \end{gathered}\)Thus 87 beats occur for a minute.
(b)The increase in the frequency of the heartbeat implies the increase in the number of the heartbeat for every second. And hence the beats in a minute increase when the frequency of the heartbeat increases.
(c)
The number of the beats per minute after the increase of the frequency is,
\(\begin{gathered} N_2=f_2\times60 \\ =1.55\times60 \\ =93 \end{gathered}\)Thus after the increase in the frequency, 93 beats occur in a minute.
A speech conversation is transmitted by a direct-sequence spread spectrum (DS-SS) system. The speech is converted to pulse code modulation (PCM) using an anti-aliasing filter with a cut-off frequency of 3.4 kHz and using 256 quantization levels. It is anticipated that the processing gain should not be less that 23 dB. A pseudo random sequence is generated using a feedback shift register of length m = 4. The chip rate is 107 chips per second. Calculate the: a) Required chip rate. (7 marks) b) Number of hopping channels if the speech was transmitted by an frequency- hopping spread spectrum (FH-SS) system
a) Required chip rateThe processing gain is given by\[G_p = 10{\log _{10}}\left( {{\rm{\Gamma }}{N_{ch}}/{B_c}} \right)\]where Γ is the number of chips per symbol, Nch is the number of hopping channels, and Bc is the chip rate.To determine the chip rate, we must first determine the symbol rate. In this case, the symbol rate is the same as the sampling rate of the PCM modulator, which is 256 × 3.4 kHz = 870.4 kHz.
Since there are Γ chips per symbol, and the processing gain must be at least 23 dB,\[\begin{gathered}
23{\rm{ dB}} = 10{\log _{10}}\left( {\Gamma {N_{ch}}/{B_c}} \right) \Rightarrow \hfill \\
10^{23/10} = \Gamma {N_{ch}}/{B_c} \Rightarrow \hfill \\
{B_c} = \Gamma {N_{ch}}/{{10}^{23/10}} \hfill \\
\end{gathered} \]Let us suppose that we use a pseudo-random sequence of length m = 4. In this case, the number of chips per symbol is given by\[{\Gamma _{DS-SS}} = {2^m} - 1 = 15\]Thus, substituting into the previous equation, we get\[B_c = \left( {15\, \times \,{N_{ch}}} \right)/{6.309}\]Solving for Bc and substituting the processing gain requirement of 23 dB, we get\[B_c \ge 3.194\,{\rm{MHz}}\]Thus, the required chip rate is at least 3.194 MHz.
b) Number of hopping channels if the speech was transmitted by a frequency-hopping spread spectrum (FH-SS) systemThe number of hopping channels can be determined using the relationship\[N_{ch} \le B_c/W\]where W is the frequency range covered by the frequency-hopping sequence. In a FH-SS system, this frequency range must be larger than the baseband bandwidth of the signal, which in this case is 3.4 kHz. If we choose a frequency range of W = 4 kHz, then we get\[N_{ch} \le B_c/W = 3.194/4 = 798.5\]Since Nch must be an integer, we can choose Nch = 798. Therefore, the number of hopping channels is 798.
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Compare and contrast reproduction and fertilization.
Answer:
ew so the difference is.. Pollination and Fertilization occur in plants during sexual reproduction.
the difference is Pollination occurs from anthers of stamens to stigma of the ovary and It is a physical process.
fertilizateion is It is the fusion of female and male gametes and It is a genetic and biochemical process.
Explanation:
this was so hard to write out
A 14cm diameter champagne bottle rests on its side on top of a frictionless table. Suddenly, the cork pops and the bottle slides backward for a distance of 22.0 cm in 0.44s. If the mass of the bottle is 500 times the mass of the cork, find the distance from the original position the cork will land on the table.
The distance the cork will land on the table is \(d = 30 m\). If the mass of the bottle is 500 times the mass of the cork.
First, we need the initial velocity of the bottle is:
Using \(d = vt\)
\((0.22) = (v)*(0.44)\\v = 0.5\ m/s\)
Then, using the conservation of momentum, we can find the velocity of the cork
\(mv (bottle) = mv (cork)\\(500)*(0.1) = m(v)\\v = 250\ m/s\)
Now, where the cork lands. It starts at a vertical height of 7 cm (the radius of the bottle and will hit the table somewhere, that is what we need to find. Where it bounces first)
Since the cork has no initial y velocity, we can find the time it would take for it to drop 7 cm.
\(d = v_{o}t + 0.5at^{2}\\0.07 = (0) + (0.5)*(9.8)*(t_2)\\t = 0.120 sec\)
Then, using d = vt, we can find the horizontal distance it flies in that amount of time is:
\(d = (250)*(0.12)\\d = 30 m\)
Therefore, the distance the cork will land on the table is \(d = 30 m\).
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is driving with a velocity of 5 m/s and speeds up to a velocity of 10 m/s over 5 seconds. What is Mr. DaCosta's acceleration?
Select all the correct answers.
Which of these factors make hydrogen fuel cells a better option than burning fossil fuels?
Hydrogen fuel cells have a higher energy efficiency.
Hydrogen fuel cells create less pollution.
Burning fossil fuels relies on outdated devices and technology.
Hydrogen is the most abundant element in the universe.
Hydrogen fuel cells are more expensive than fossil fuels.
Hydrogen fuel cells have a higher energy efficiency.
Hydrogen fuel cells create less pollution.
Hydrogen is the most abundant element in the universe.
What is hydrogen fuel cells?Hydrogen fuel cells are devices that generate electrical energy through a chemical reaction between hydrogen and oxygen.
Hydrogen energy, that is energy derived from hydrogen are considered a form of clean and efficient energy technology.
The factors that make hydrogen fuel cells a better option than burning fossil fuels are;
Hydrogen fuel cells have a higher energy efficiency.Hydrogen fuel cells create less pollution.Hydrogen is the most abundant element in the universe.The remaining options are incorrect as they do not portray the advantageas of the hydrogen fuel cells.
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Which of the following conditions must be met to have electric current flow through
a circuit?
The circuit must be a closed loop.
The circuit must have a source of electric charges (energy).
A potential difference through the circuit must exist.
All of the above conditions are necessary for electric current flow.
Answer:
all of the above conditions are necessary for electric current to flow
Explanation:
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two solid spheres of radius r made of the same type of steel are placed in contact, as shown in the figures above. the magnitude of the gravitational force that they exert on each other is f1. when two other solid spheres of radius 3r made of this steel are placed in contact, what is the magnitude of the gravitational force that they exert on each other? responses
If the gravitational force between two spheres of radius r was 10 N, then the gravitational force between two spheres of radius 3r would be: 10/8 = 1.25 N.
The magnitude of the gravitational force that two solid spheres of radius 3r made of the same type of steel will exert on each other when placed in contact is 8 times the magnitude of the gravitational force that two solid spheres of radius r made of the same type of steel would exert on each other when placed in contact.
This is because the gravitational force between two objects is inversely proportional to the square of the distance between them, and since the distance between the two spheres of radius 3r is 8 times the distance between two spheres of radius r, the gravitational force will be 8 times smaller.
The equation for the gravitational force between two objects is given by F = G*m1*m2/r^2, where G is the gravitational constant, m1, and m2 are the masses of the two objects, and r is the distance between the two objects.
Therefore, since the distance between the two spheres of radius 3r is 8 times greater than the distance between the two spheres of radius r, the gravitational force between them will be 8 times smaller than the gravitational force between the two spheres of radius r.
For example, if the gravitational force between two spheres of radius r was 10 N, then the gravitational force between two spheres of radius 3r would be 10/8 = 1.25 N.
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In the figure, an electron accelerated from rest through potential difference V1=0.851 kV enters the gap between two parallel plates having separation d = 27.5 mm and potential difference V2= 72.8 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap?
In unit-vector notation, this magnetic field should have a value of (-1.805, 0, 0) Tesla.
The uniform magnetic field required to make an electron travel in a straight line through the gap between the two parallel plates is given by the equation B = (V1 - V2)/dv.
Plugging in the known values for V1, V2, and d gives us a result of B = 1.805 T. Since the velocity vector of the electron is perpendicular to the electric field between the plates, the magnetic field should be pointing along the direction of the velocity vector.
Therefore, the magnetic field that should be present between the two plates should point along the negative direction of the velocity vector in order to cause the electron to travel in a straight line.
In unit-vector notation, this magnetic field should have a value of (-1.805, 0, 0) Tesla.
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8.4 air at 200 °f flows at standard atmospheric pressure in a pipe at a rate of 0.08 lb/s. determine the minimum diameter allowed if the flow is to be laminar..
The minimum diameter allowed for laminar flow of air is approximately 0.0674 ft or 0.809 inches.
To determine the minimum diameter allowed for laminar flow of air at 200°F and standard atmospheric pressure in a pipe with a flow rate of 0.08 lb/s, we can use the Reynolds Number equation.
Reynolds Number (Re) is a dimensionless number that represents the ratio of inertial forces to viscous forces in a fluid flow.
For laminar flow, the Re value should be less than 2300. The formula to calculate Reynolds Number is:
Re = (density x velocity x diameter) / viscosity.
Given the values, density of air at standard conditions is 0.0765 lb/ft³, viscosity is 1.05 x 10⁻⁵ lb-s/ft², velocity is 0.08 lb/s divided by the cross-sectional area of the pipe (π/4 x diameter²), and diameter is the unknown variable.
Solving for diameter using the Reynolds Number equation, we get the minimum diameter allowed for laminar flow of air is approximately 0.0674 ft or 0.809 inches.
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Which of the following defines a wavelength
Group of answer choices
A. length of time the wave has been in motion
B. distance between trough and trough
C. distance between quiet water level and crest
D. distance between trough and crest
The answer is D. distance between trough and crest. Wavelength is the distance between two consecutive points of the same phase on a wave, such as two adjacent crests, troughs, or zero crossings.
Wavelength is the distance between two consecutive points of the same phase on a wave, such as two adjacent crests, troughs, or zero crossings. So the answer is the distance between the trough and crest.
The other options are incorrect. Option A is the length of time the wave has been in motion, which is not the same as wavelength. Option B is the distance between the trough and the trough, which is half of the wavelength. Option C is the distance between the quiet water level and the crest, which is not a physical measurement of the wave.
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A michelson interferometer is shown at right. The moving mirror is displaced a distance d. During this displacement, 250 interference fringe shifts are counted. The light being used has a wavelength of 632. 8 nm. Determine the mirror displacement d in nm.
The mirror displacement d is 317.12 nm. In a Michelson interferometer, interference fringes are created due to the interference of two beams of light.
A Michelson interferometer is a device used to measure small changes in the distance between two mirrors. It consists of a beam splitter, two mirrors, and a detector. One beam of light is split into two and travels to the mirrors, where they are reflected back towards the beam splitter. The two beams of light then recombine at the detector, creating an interference pattern.
When one of the mirrors is moved, the interference pattern shifts. The amount of shift depends on the distance moved and the wavelength of the light being used. By measuring the shift in the interference pattern, we can determine the displacement of the mirror.
In this problem, we are given that 250 interference fringe shifts were counted when the mirror was moved a distance d. The wavelength of the light being used is 632.8 nm.
Each interference fringe shift corresponds to a change in the path difference between the two beams of light by one wavelength. So, the total change in the path difference is 250 times the wavelength of the light:
250 × 632.8 nm = 158,200 nm
Therefore, the mirror displacement d is 158,200 nm. However, this displacement is in both directions (i.e., the mirror moved back and forth). To find the displacement in just one direction, we divide by 2:
d = 158,200 nm / 2 = 79,100 nm
Therefore, the mirror displacement d is 79,100 nm in one direction.
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Si la rapidez del sonido en el agua es de 1450 m/s. ¿Cuánto tiempo tardará en recorrer 500 m en el fondo del lago?
Answer:
2.9
Explanation:
es 2 minutos con 9 segundos seria algo así (1450)÷(500)
A car has a mass of 1000 kg. It is driving to the right.
Draw a free body diagram showing the forces acting on it.
Find it’s weight on Earth.
How do I even draw a body diagram? Please help.
Answer:
Explanation:
What is a free body diagram?
Answer: a force diagram is a graphical illustration used to visualize the applied forces and resulting reactions on a body in a given condition
Drawing a free-body diagram for this problem
Answer: Look at the attached picture, ask me any questions if you are still confused. It is a little messy since I didn't have my pen.
Find its weight on Earth
Answer: The weight is dependent on the mass of the object and the gravitational constant on the planet. The gravitational constant, in this case, is 9.8.
so the weight = mass * gravitational constant = m * g = 1000 * 9.8
= 9800 N
Hope that helps!
what wavelength em radiation would be emitted most strongly by matter at the temperature of the core of a nuclear explosion, about 10,000,000 k?
The wavelength of electromagnetic radiation that would be emitted most strongly by matter at the temperature of the core of a nuclear explosion of 10,000,000 k will be 2.898 × 10^-10 meters.
Wavelength of electromagnetic radiationThe wavelength of electromagnetic radiation emitted by matter at a certain temperature can be determined using Wien's displacement law, which states that the wavelength of maximum emission (λmax) is inversely proportional to the temperature of the object:
λmax = b / T
where b is a constant known as Wien's displacement constant, equal to 2.898 × 10^-3 m·K.
Substituting the given temperature of 10,000,000 K into this equation, we get:
λmax = (2.898 × 10^-3 m·K) / (10^7 K) = 2.898 × 10^-10 m
Therefore, the wavelength of electromagnetic radiation emitted most strongly by matter at the temperature of the core of a nuclear explosion is approximately 2.898 × 10^-10 meters, which corresponds to the ultraviolet region of the electromagnetic spectrum.
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A spring of spring constant 800 N/m is used to launch a 15.0 g projectile vertically upward. By how much must the spring be compressed in order for the projectile to reach a maximum height of 35.0 m? a. 11.3 cm b. 3.50 m
c. 15.2 cm
d. 18.4 cm
The spring must be compressed by approximately 0.321 meters and 32.1 cm in order for the projectile to reach a maximum height of 35.0 meters. Hence, the correct option is (b).
To determine the amount by which the spring must be compressed, we can use the principle of conservation of mechanical energy.
The potential energy stored in the compressed spring is equal to the gravitational potential energy gained by the projectile as it reaches its maximum height.
The potential energy stored in the spring is given by the equation:
Potential energy (PE) = (1/2) * k * x²
Where:
k is the spring constant (800 N/m)
x is the compression of the spring (unknown)
The gravitational potential energy gained by the projectile at the maximum height is given by:
Potential energy (PE) = m * g * h
Where:
m is the mass of the projectile (15.0 g = 0.015 kg)
g is the acceleration due to gravity (approximately 9.8 m/s²)
h is the maximum height (35.0 m)
Setting the potential energy equations equal to each other:
(1/2) * k * x² = m * g * h
Simplifying the equation:
(1/2) * 800 N/m * x² = 0.015 kg * 9.8 m/s² * 35.0 m
x² = (0.015 kg * 9.8 m/s² * 35.0 m) / (0.5 * 800 N/m)
x² = 0.1029 m²
Taking the square root of both sides to solve for x:
x = √(0.1029 m²)
x ≈ 0.321 m
Therefore, the spring must be compressed by approximately 0.321 meters or 32.1 cm in order for the projectile to reach a maximum height of 35.0 meters.
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two identical positive charges are .6 meters apart. which is true about the electric field and potential at the point which is directly in-between the two?
Option D: two positive charges that are the same 0.6 meters apart Despite the potential being positive, the electric field is zero.
The electric field E caused by a point charge +q at a distance r is given by, E=kq/r².
As both charges are positive and equal in magnitude, the net electric field between them will be zero because both fields are equal and in opposition to one another.
Typically, electric potential V owing to a point charge +q at a distance r is given by,
V=kq/r
the electric potential V owing to a point charge +q at a distance of 0.3 (midpoint) is given by, where V is measured in terms of the sign of the charge q.
V′=kq/0.3
and electric potential V brought on by a second point charge +q located at a distance of 0.3
V′′=kq/0.3
The net potential is consequently located in the middle of the line connecting the two like charges.
V=V′+V′′ =2kq/0.3
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The complete question is:
Two identical positive charges are 0.6 meters apart.
Which is true about the electric field and potential at the point which is directly in between the two?
A. The electric field and potential both equal zero.
B. The electric field and potential are both positive numbers.
C. The electric field is a positive number while the potential is a zero.
D. The electric field is zero while the potential is a positive number.