A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.2 m*N. If the mass of the rotor is 4.8 kg and it can be approximated as a solid cylinder of radius .0710 m, through how many revolutions will the rotor turn before coming to rest, and how long will it take?
Answers
Upon calculations, the solution was found to be that the centrifuge rotor will make approximately 5,579 revolutions before coming to rest, and it will take about 32.4 seconds for it to do so.
The centrifuge rotor, with a mass of 4.8 kg and approximated as a solid cylinder of radius 0.0710 m, is initially rotating at 10,300 rpm. It comes to rest due to a frictional torque of 1.2 m*N acting on it.
To determine the number of revolutions the rotor will make before coming to rest and the time it will take, we can use the principles of rotational dynamics.
The initial angular velocity of the rotor can be calculated by converting the given 10,300 rpm to rad/s: 10,300 rpm = (10,300 rev/min) * (2π rad/rev) * (1 min/60 s) ≈ 1,080 rad/s.
The frictional torque acting on the rotor can be related to the angular acceleration through the equation τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration.
In this case, the torque is 1.2 m*N, and the moment of inertia for a solid cylinder is given by I = ½ * m * r^2, where m is the mass and r is the radius.
Rearranging the equation τ = Iα, we can solve for α: α = τ / I. Substituting the given values, we find α = 1.2 m*N / (½ * 4.8 kg * (0.0710 m)^2) ≈ 33.3 rad/s^2.
The final angular velocity of the rotor is zero since it comes to rest.
Using the equation ω = ω₀ + αt, where ω is the final angular velocity, ω₀ is the initial angular velocity, α is the angular acceleration, and t is the time, we can solve for t: 0 = 1,080 rad/s + (-33.3 rad/s^2) * t.
Rearranging the equation, we find t ≈ 32.4 s.
The number of revolutions can be calculated by dividing the initial angular displacement by 2π.
The initial angular displacement can be obtained by multiplying the initial angular velocity by the time: θ = ω₀ * t. Substituting the given values, we have θ = 1,080 rad/s * 32.4 s ≈ 35,088 rad.
Finally, the number of revolutions is given by the equation N = θ / (2π), where N is the number of revolutions: N ≈ 35,088 rad / (2π rad/rev) ≈ 5,579 revolutions.
Therefore, the centrifuge rotor will make approximately 5,579 revolutions before coming to rest, and it will take about 32.4 seconds for it to do so.
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Related Questions
Since monsoons are storms that usually occur during a specific time of year in certain regions, you could not compare them to thunderstorms. please select the best answer from the choices provided t f
Answers
The statement "Since monsoons are storms that usually occur during a specific time of year in certain regions, you could not compare them to thunderstorms" is absolutely false.
What is monsoon?Monsoon may be characterized as a seasonal transformation in the direction of the predominant, most potent, currents of a region. It blows from cold to warmer regions of the geographical locations.
Thunderstorms basically originated identically with monsoons more frequently. Monsoon involves sudden and gradual rainfall, extreme wind, and a drop-down in temperature.
The occurrence of monsoon is fixed at different geographical locations, but the occurrence of thunderstorms will not be definite or predominantly known.
Thus, the statement "Since monsoons are storms that usually occur during a specific time of year in certain regions, you could not compare them to thunderstorms" is absolutely false.
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Answer:
False
Explanation:
a person riding in an elevator stands on a metric scale. if the mass of the person is 60.0 kg and the elevator accelerates upward with an acceleration of 4.90 m/s2, what is the reading on the scale?
Answers
The reading on the scale is 882.6 N when the elevator accelerates upwards with an acceleration of 4.90 m/s².
Given that the mass of a person is 60.0 kg and the elevator accelerates upwards with an acceleration of 4.90 m/s², we have to determine the reading on the scale.
Let F be the force exerted by the scale on the person. Then, by Newton's second law of motion, the net force acting on the person is Fnet= m * a
where m = 60.0 kg is the mass of the person and a = 4.90 m/s² is the acceleration of the elevator. Hence, the net force acting on the person is given by;
Fnet = 60.0 kg * 4.90 m/s²
Fnet = 294.0 N
Therefore, the scale reading is equal to the force exerted by the scale on the person. Since the elevator is accelerating upwards, the force exerted by the scale on the person is greater than the weight of the person, which is the force of gravity acting on the person.
The force of gravity acting on the person is given by;
Fg = m * g, where g = 9.81 m/s² is the acceleration due to gravity. Hence, the force of gravity acting on the person is given by;
Fg = 60.0 kg * 9.81 m/s²Fg = 588.6 N
Therefore, the scale reading is given by the sum of the force of gravity acting on the person and the net force acting on the person;
F = Fg + Fnet
F = 588.6 N + 294.0 N
F = 882.6 N
Thus, the reading on the scale is 882.6 N when the elevator accelerates upwards with an acceleration of 4.90 m/s².
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find ways you can change the total energy
Answers
Answer:
The ways to change the total energy are to either make the hill taller to increase it or make the hill lower to decrease the total energy.
Explanation:
The total mechanical energy of a system is the sum of the total kinetic energy and total potential energy.
what is a Rube Goldberg machine and show me a pic? PLEASE.
Answers
Answer:
This picture is just one example of a Rube Goldberg machine. It's sort of like a chain reaction. There are a lot of cool videos you could look up on you tube that demonstrate what they are.
Explanation:
complete the following sentence. an activity that is relatively short in time (< 10 seconds) and has few repetitions predominately uses the _____________ energy system.
Answers
An activity that is relatively short in time (< 10 seconds) and has few repetitions predominately uses the Phosphagen energy system. The Phosphagen energy system is also known as the ATP-CP (adenosine triphosphate and creatine phosphate) system.
It is said that energy is produced through three systems in our body, i.e., ATP-CP system, lactic acid system, and aerobic system. The ATP-CP system is the first system, and it provides the quickest energy and is of the shortest duration. When an activity that is relatively short in time and has few repetitions, predominately uses the Phosphagen energy system, it gets its energy from the ATP-CP system.
When we perform an intense physical activity like a short sprint or jumping, it's all about the ATP-CP system. The ATP-CP system produces energy rapidly through the use of stored ATP (adenosine triphosphate) and CP (creatine phosphate).ATP (adenosine triphosphate) is the source of energy for muscle contractions. It is produced through the breakdown of foods we eat and stored in our muscle tissues. However, the ATP reserves are limited and only provide energy for about 3-5 seconds of intense activity.
CP (creatine phosphate), on the other hand, is a high-energy molecule stored in our muscles. It helps to quickly regenerate ATP when the muscles require energy, which allows the muscles to work longer. However, CP stores are also limited and provide energy for only 8-10 seconds of intense activity.
The Phosphagen energy system is used when the body performs an intense physical activity that lasts for a short duration and has few repetitions, like sprinting or jumping. The ATP-CP system is the first system that provides the quickest energy and is of the shortest duration.
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A ball hits a wall horizontally at 6m/s and rebounces at 4.4m/s the ball is in contact with wall for 0.04 sec. what is the acceleration.
Answers
Answer:
Acceleration (a) = 40 m/s²
Explanation:
Given:
Initial velocity (u) = 6 m/s
Final velocity (v) = 4.4 m/s
Time taken (t) = 0.04sec
Find:
Acceleration (a) = ?
Computation:
We know that,
⇒ v = u + at
⇒ a = (v - u) / t
⇒ Acceleration (a) = (4.4 - 6) / 0.04
⇒ Acceleration (a) = (-1.6) / 0.04
Acceleration (a) = 40 m/s²
Which are internal adaptations? Select ALL that apply.
A hollow bones in birds
B gills in fish
C hard turtle shell
D warm-blooded mammals
E camouflage
Answers
Hollow bones in birds, gills in fish and warm-blooded mammals are internal adaptations.
What is adaptation?There are three similar definitions of adaptation in biology. First, the dynamic evolutionary process of natural selection improves the evolutionary fitness of organisms by adapting them to their environments. Second, it's a state that the populace reaches during that process.
Various strategies can be used by organisms to adapt to their surroundings. They are capable of biological adaptation, which entails changing how the body works. The bodies of people who reside in high altitudes are an illustration of biological adaptability which is essential for survival.
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What is the observation and what is the inference in the following text. Explain.
The chimpanzee climbed the tall tree. The chimpanzee must be very strong,
Answers
Observation: The chimpanzee climbed the tall tree.
Inference: The chimpanzee must be very strong,
Explanation:
An inference differs from an observation because an inference is a guess or possible explanation about a phenomenon. On the other hand, an observation is a statement based on evidence gathered through the senses. In this context, the sentence that is an observation is "The chimpanzee climbed the tall tree" because this statement is based on visual evidence. Moreover, the inference is "The chimpanzee must be very strong" because this is just a guess to explain how the chimpanzee climbed up the tree.
14. If 100 grams of sodium nitrate are dissolved in 100 grams of water
at 60 degrees C, is the solution formed saturated, unsaturated, or
supersaturated?
Answers
Answer:
Unsaturated
Explanation:
the solubility of sodium nitrate is at 60 C is 124g/ml therefore, putting 100 grams will not saturate fully.
The hockey player is moving at a speed of 9. 5 m/s. if it takes him 2 seconds to come to a stop under constant acceleration, how far does he travel while stopping?
Answers
Answer:
\(9.5\; {\rm m}\).
Explanation:
Let \(u\) and \(v\) denote the velocity of this hockey player before and after stopping, respectively. The question states that \(u = 9.5\; {\rm m\cdot s^{-1}}\) and implies that \(v = 0\; {\rm m\cdot s^{-1}\) since the hockey player has come to a stop.
The duration of this acceleration is \(t = 2\; {\rm s}\).
Since the acceleration of this hockey player was constant, SUVAT equation would apply. In particular, the SUVAT equation \(x = (1/2)\, (v + u) \, (t)\) gives the displacement \(x\) of this hockey player during that \(2\; {\rm s}\) of acceleration:
\(\begin{aligned} x &= \frac{1}{2}\, (9.5\; {\rm m\cdot s^{-1}} + 0\; {\rm m\cdot s^{-1}})\, (2\; {\rm s}) = 9.5\; {\rm m} \end{aligned}\).
In other words, this hockey player would have travelled \(9.5\; {\rm m}\) while stopping.
List 1 advantage and 1 disadvantage of a series circuit.
Answers
Explanation:
advantage: Easy to design and build the circuit
disadvantage: if one component in a series circuit fails, then all the components in the circuit fail because the circuit has been broken.
hope it helps!
Impulse can be defined as
The frequency at which something occurs
The change in velocity
The change in momentum from an force within the system
The change in momentum from a force outside of the system
Answers
Explanation:
The change in momentum from an force within the system.
A sprinter had the following speeds at different times during a race: 0 m/s at 0 s, 4 m/s at 2 s, 7 m/s at 4 s, 10 m/s at 6 s, 12 m/s at 8 s, and 10 m/s at 10 s. Plot these data on a speed-time graph. During what time intervals is the acceleration positive? Negative? Is the acceleration ever zero?
Answers
Answer:
Explanation:
We build graphs of speed and acceleration.
Acceleration is positive in the interval (0 - 8) s.
Acceleration is negative in the interval (8-10) s.
a) Write down the full set of equations for a time series (Xt)tez following an AR(1) model with non-zero mean and ARCH(1) errors. b) Give a formula for value-at-risk calculated at time t, that is for the conditional quantile of Xt+1 in terms of previous values of the process and quantiles of the innovation distribution.
Answers
The AR(1) model with non-zero mean and ARCH(1) errors can be expressed as X_t = μ + φX_{t-1} + ε_t. The value-at-risk (VaR) calculated at time t, representing the conditional quantile of X_{t+1}, can be expressed as VaR_t(X_{t+1}, q) = μ + φX_t + σ_tq
a) The AR(1) model with non-zero mean and ARCH(1) errors can be expressed as follows:
X_t = μ + φX_{t-1} + ε_t
ε_t = σ_tZ_t
σ_t^2 = α_0 + α_1ε_{t-1}^2
Where:
X_t is the time series at time t.
μ is the non-zero mean.
φ is the autoregressive coefficient.
ε_t is the error term at time t.
σ_t is the conditional standard deviation of the error term at time t.
Z_t is a standard normal random variable.
α_0 and α_1 are the parameters of the ARCH(1) model.
b) The value-at-risk (VaR) calculated at time t, representing the conditional quantile of X_{t+1}, can be expressed using the previous values of the process and quantiles of the innovation distribution.
VaR_t(X_{t+1}, q) = μ + φX_t + σ_tq
Where:
VaR_t(X_{t+1}, q) is the value-at-risk at time t for X_{t+1} at quantile q.
μ and φ are as defined in part (a).
X_t is the value of the time series at time t.
σ_t is the conditional standard deviation of the error term at time t.
q is the desired quantile of the innovation distribution.
To calculate the value-at-risk at time t, you need to know the current value of X_t and the conditional standard deviation σ_t. Additionally, you need to specify the desired quantile q, which represents the tail probability associated with the risk measure.
The formula above combines the mean, autoregressive component, and the quantile of the innovation distribution to estimate the potential loss or downside risk at time t+1 based on the observed data and model parameters.
The AR(1) model with non-zero mean and ARCH(1) errors provides a way to capture the dynamics of a time series while accounting for heteroscedasticity. By incorporating the conditional standard deviation into the value-at-risk calculation, one can estimate the potential losses at a specified quantile, taking into account the previous values of the process and the distribution of the innovation term.
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The kinematic equations are only
valid if which of the following is
constant?
A) a
C) Δx
B) Vf
D) t
Answers
Answer:
a
Explanation:
kinematical equations are only valid for motion with constant acceleration (uniformly accelerated motion).
Hopefully this answer helped you!!!
A 1400 kg car traveling at 17.0 m/s to the south collides with a 4700 kg truck that is at rest. The car and truck stick together and move together after collision. What is the final velocity of the two-vehicle mass? If Kinetic Energy = 0.5 * m * v^2, calculate the KE before the crash and the KE of the combined vehicles after the crash.
Answers
Answer:
Final velocity = 7.677 m/s
KE before crash = 202300 J
KE after crash = 182,702.62 J
Explanation:
We are given;
m1 = 1400 kg
m2 = 4700 kg
u1 = 17 m/s
u2 = 0 m/s
Using formula for inelastic collision, we have;
m1•u1 + m2•u2 = (m1 + m2)v
Where v is final velocity after collision.
Plugging in the relevant values;
(1400 × 17) + (4700 × 0) = (1400 + 1700)v
23800 = 3100v
v = 23800/3100
v = 7.677 m/s
Kinetic energy before crash = ½ × 1400 × 17² = 202300 J
Kinetic energy after crash = ½(1400 + 1700) × 7.677² = 182,702.62 J
A 25.2 kg gazelle moving 2.33 m/s
sees a lion, and exerts a 113 N
force to accelerate. How fast is
it moving 2.00 s later?
Answers
113N = 25.2a
a = 4.48 m/s^2
Vf = Vi + at
Vf = 2.33 + 4.48(2) = 11.3 m/s
The velocity of the gazelle after 2 seconds is equal to 11.3 m/s.
What is the equation of motion?The equations of motion have described the relationship between the time, velocity, acceleration, and displacement of a moving object.
The equations of motions can be described as shown below:
\(v = u + at\\S = ut +\frac{1}{2}at^2 \\ v^2-u^2 = 2aS\)
Given the mass of the gazelle, m = 25.2 Kg
The force acting to accelerate, F = 113N
The acceleration in the speed of gazelle is given by: a = F/m
a = 113/ 25.2
a = 4.48 m/s²
The initial speed of the gazelle, u = 2.33 m/s
From the first equation of motion we can calculate the final velocity of the gazelle:
v = u + at
v = 2.33 + (4.48) (2)
v = 11.3 m/s
Therefore, the velocity of the gazelle 2 seconds later is 11.3 m/s.
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if you take a picture of your friend, who is standing 3.90 m from the lens, using a camera with a lens with an 85 mm focal length, how far from the sensor is the lens?
Answers
If you take a picture of your friend, who is standing 3.90 m from the lens, using a camera with a lens with an 85 mm focal length, the sensor is 1.087 m from the lens.
1 / f = 1 / v + 1 / u
f = Focal length
v = Image distance
u = Object distance
u = 3.9 m
f = 85 mm
f = 0.85 m
1 / v = 1 / f - 1 / u
1 / v = 1 / 0.85 - 1 / 3.9
1 / v = 3.05 / 3.315
v = 1.087 m
The sign convention for this formula is:
When the object is on the same side of the refracting surface as the incoming light, the value of u is taken as positive else taken as negative.When the image is on the same side of the refracting surface as the incoming light, the value of v is taken as positive else taken as negative.Therefore, the sensor is 1.087 m from the lens.
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You leave Chicago, Illinois at 8am and fly to Portland, Oregon. Your flight takes 2.5 hours. What time do you arrive in Portland?
Answers
Answer:
10:30am ........................
Answer:
maybe around 10:30 I would say
1. two protons are held a distance d apart. the electrostatic force and the gravitational force that one proton exerts on the other are fe and fg, respectively. compare the magnitudes and directions of these forces using calculations to support your answer.
Answers
The electrostatic force between like charges (such as two protons) is repulsive, meaning it acts in the opposite direction to the displacement.
By calculating the magnitudes and considering the direction of the forces, you can compare Fe and Fg and determine their relationship.
To compare the magnitudes and directions of the electrostatic force (Fe) and the gravitational force (Fg) between two protons, we can use the equations for these forces and apply the appropriate values.
The electrostatic force between two charged particles is given by Coulomb's Law:
Fe = k * (q1 * q2) / r^2
where k is the electrostatic constant (k ≈ 9 × 10^9 N·m^2/C^2), q1 and q2 are the charges , and r is the distance between the particles.
The gravitational force between two objects is given by Newton's Law of Universal Gravitation:
Fg = G * (m1 * m2) / r^2
where G is the gravitational constant (G ≈ 6.67 × 10^-11 N·m^2/kg^2), m1 and m2 are the masses and r is the distance between the particles.
Comparing the magnitudes: The masses and charges of the protons are the same, the magnitudes of Fe and Fg will depend on the respective constants and the distance between the protons.
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As a woman walks, her entire weight is momentarily placed on one heel of her high-heeled shoes. this creates quite a large pressure on the ground; in fact, in the early days of commercial flight, women were not allowed to wear high-heeled shoes because aircraft floors were too thin to withstand such large pressures. Calculate the pressure, in pounds per square inch, exered on the floor by the heel if it has an area of 1.45 cm2 and the woman's mass is 635 kg
Answers
The pressure exerted on the floor by the woman's heel is approximately 6243.76 pounds per square inch. This is a very high pressure and could cause damage to thin or fragile surfaces.
To calculate the pressure exerted on the floor by the woman's heel, we can use the formula:
pressure = force / area
We can calculate the force exerted by the woman's heel by multiplying her weight by the acceleration due to gravity:
force = mass * acceleration due to gravity
force = 635 kg * 9.81 m/s^2
force = 6232.35 N
We can convert the area of the heel from square centimeters to square meters:
area =\(1.45 cm^2 / (100 cm/m)^2\)
area = \(0.000145 m^2\)
Now we can substitute the values into the formula for pressure:
pressure = force / area
pressure = \(6232.35 N / 0.000145 m^2\)
pressure = 4.298 × \(10^7\) Pa
To convert this to pounds per square inch (psi), we can use the conversion factor:
1 Pa = 0.000145038 psi
pressure = 4.298 × \(10^7\) Pa * 0.000145038 psi/Pa
pressure = 6243.76 psi
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When a car speeds up when rounding a curve, what happens to its centripetal
acceleration?
A.) It decreases
B.) It increases
C.) It remains constant.
D.) It is zero.
Answers
Science
Write two examples of heating appliances
Answers
Answer:
a} Infrared radiant heaters.
b} Fan heaters.
Explanation:
I hope this is okay, should I give more.
Suppose Person A runs off the edge of the cliff at 2 m/s and Person B runs off the edge at 1 m/s. Which will hit the ground farther from the base of the cliff?
Answers
Answer:
Person A will hit a distance fatherExplanation:
Based on the fact that the velocity of person A is more than that of person B, that is from the question, person A has a velocity of 2m/s and person B has a velocity of 1m/s, this clearly shows that person A has the tendency to hit a distance farther from the cliff than person B.
2 questions, brainliest if you get them correct! please only answer if you really know you are right.
thanks! :)
Answers
Answer:
1. C2. ABrainliest please thanks
Answer:
Number 1 is c and number 2 is a
When a photon of light scatters off of a free stationary electron, the wavelength of the photon.
Answers
Wavelength of the incident photon = \(\lambda = 0.025nm = 0.025 \times 10^{-9}m\)
\(\lambda ^{'}-\lambda = \frac{h}{m_{e}c} \times (1- cos\theta )\)
Using the above formula we get Shifting wavelength \(\lambda = 0.027 \times 10^{-9}m\)
What is wavelength?In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns.The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ).The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to frequency of the wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.To learn more about Wavelength with the given link
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Question:
A photon moving in the +x-direction, scatters off a free stationary electron. The wavelength of the incident photon is 0.0250 nm. After the collision, the electron moves at an angle α below the +x-axis, while the photon moves at an angle θ = 83.3° above the +x-axis. (Assume that the electron is traveling slow enough that the non-relativistic relationship between momentum and velocity can be used.)
(a) Find the shifting Wavelength of the incident photon
5. Your riding a skateboard that is 1.4 kg and goingnortheast with a velocity of 19 m/s. You weigh about 52kg. What is the total momentum of you and theskateboard.What is the mass of the the skateboard.Find the combined mass.Find the velocity of you and the skateboard.
Answers
Answer:
Explanation:
Here is the information we have.
Skateboard: 1.4 kg, velocity = 19 m /s
You: weight: 52 kg, veclocity = 19m/s (since you are riding the skateboard)
Now the momentum of an object is given by
\(p=mv\)where
m = mass
v = velocity
Now in our case, the momentum of the skateboard is
\(p_{\text{skateboard}}=1.4\operatorname{kg}\cdot19m/s=26.6\operatorname{kg}\cdot m/s\)Your momentum is
\(p_{\text{you}}=52\operatorname{kg}\cdot19m/s=988\operatorname{kg}\cdot m/s\text{.}\)Therefore, the total momentum of you and the skateboard is
\(p_{\text{total}}=p_{\text{you}}+p_{\text{skateboard}}=(26.6+988)kg\cdot m/s\)\(\Rightarrow\boxed{p_{\text{total}}=1014.6\operatorname{kg}\cdot m/s\text{.}}\)The combined mass of the skateboard and you is
\(m_{\text{total}}=m_{\text{you}}+m_{\text{skateboard}}=52\operatorname{kg}+1.4\operatorname{kg}\)\(\Rightarrow\boxed{m_{\text{total}}=53.4\operatorname{kg}\text{.}}\)Hence, to summerise
total momentum = 1014.6 kg * m/s
combined mass = 53.4 kg.
Does water go down the drain counterclockwise in the northern hemisphere and clockwise in the southern hemisphere?
Answers
The direction in which water flows down a drain is not affected by whether you are in the northern or southern hemisphere.
What is the movement of water in hemispheres?
The idea that water drains counterclockwise in the northern hemisphere and clockwise in the southern hemisphere is a popular myth.
The direction in which water flows down a drain is actually determined by a combination of factors such as the shape of the basin or container, the location of the drain, and any other forces acting on the water, such as the Coriolis force.
The Coriolis force is a real phenomenon that affects the movement of objects in the atmosphere and oceans, but its effect on the flow of water down a drain is generally too weak to be noticeable. In fact, the direction of rotation of the Earth has very little impact on the direction in which water flows down a drain.
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What is the correct rule-of-thumb for estimating mean wind and storm motion when the hodograph is relatively straight
Answers
When the hodograph is relatively straight, the rule-of-thumb for estimating mean wind and storm motion is to use the 1-2-3 rule.
This rule states that for every 1 knot of wind speed at the surface, the wind speed increases by 2 knots for every 1000 feet of height, and the direction turns to the right by 30 degrees.
Using this rule, the mean wind can be estimated by measuring the wind speed and direction at the surface and then adding the appropriate amount of speed and direction for each additional 1000 feet of height.
The storm motion can be estimated by applying the 1-2-3 rule to the wind direction at various heights in the atmosphere and then averaging the resulting vectors.
It is important to note that the 1-2-3 rule is a rough estimate and should not be relied on as the sole source of information for predicting severe weather events.
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in eq. (10.1) in the lab manual, the constant is 41.1 gmcm-2sec-1 in air. a piece of paper has a mass per unit area of approximately 7x10-3gm/cm2. if the frequency is 4.6 khz, what does theory predict for the ratio of the transmitted amplitude to the incident amplitude of the sound wave? (a sound wave is a pressure wave.)
Answers
Sound wave in air can be considered as a pressure wave. The mass per unit area of a piece of paper is about 7×10−3 gm/cm².
The constant in air is 41.1 gm/cm².sec. With a frequency of 4.6 kHz, The transmitted amplitude to the incident amplitude of the sound wave is given by equation 10.1 in the lab manual as:\($$\frac{A_t}{A_i} = \frac{2Z_2}{Z_1+Z_2}$$\)where, Z is the acoustic impedance and is given by:\($$Z = \rho c$$\)
where, ρ is the density of the medium and c is the speed of sound in the medium.
Now, the impedance in air, Z1 is given by:\($$Z_1 = \rho_1c_1 = 1.29\times 10^{-3} kg/m^3\times 343 m/s = 442.47 Ns/m^3$$\)The impedance in paper, Z2 is given by:\($$Z_2 = \rho_2c_2 = 7\times 10^{-3} kg/m^3\times 343 m/s = 2401.0 Ns/m^3$$\), substituting the given values in the equation for amplitude ratio:\($$\frac{A_t}{A_i} = \frac{2Z_2}{Z_1+Z_2}$$$$\frac{A_t}{A_i} = \frac{2(2401.0 Ns/m^3)}{(442.47 Ns/m^3)+(2401.0 Ns/m^3)} = 0.919$$\), the theory predicts the ratio of the transmitted amplitude to the incident amplitude of the sound wave to be 0.919.
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