the displacement of a certain object is described by y left parenthesis t right parenthesis equals 5 s i n 4.3 pi t, where t is in seconds. what is the frequency of this object in hz
Answers
The displacement of a certain object is described by y left parenthesis t right parenthesis equals 5sin(4.3πt)., where t is in seconds. The frequency of the object is is 2.15 Hz.
The frequency of an oscillating object is the number of complete cycles it completes per unit of time. In this case, the displacement of the object is described by the equation y(t) = 5sin(4.3πt).
To find the frequency, we can look at the coefficient of t inside the sine function. In this case, the coefficient is 4.3π.
The general formula to calculate the frequency (f) from the angular frequency (ω) is:
f = ω / (2π)
In this case, the angular frequency (ω) is 4.3π.
Substituting the values into the formula:
f = 4.3π / (2π)
The π cancels out, leaving:
f = 4.3 / 2
f = 2.15 Hz
Therefore, the frequency of the object described by the given equation is 2.15 Hz.
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Related Questions
100 J of work was done to lift a 10-N rock and set it at Position A near the edge of a cliff.
1. If the 100 Joules of work lifted the rock to the top of the cliff, how much potential energy did the rock gain?
2. At point C, the rock's potential energy will be
3. The rock's kinetic energy at point A is
4. At point B, some of the rock's potential energy will be changed to Kinetic energy
5. What is the mass of the rock?
6. What is the rock's velocity just before it hits the ground?
The rock to the right is sitting at the top of a ramp. I wonder how much work it required to get that rock up there.
Can you figure it out?
Please show work!
Please Help!!
Answers
By using the concept of work and energy, the below are the answers
1. 100J
2. 100J
3. 0
4. Total energy = K.E + P.E
5. 1.02 kg
6. 14 m/s
Given that 100 J of work was done to lift a 10-N rock and set it at Position A near the edge of a cliff.
1. If the 100 Joules of work lifted the rock to the top of the cliff, how much potential energy did the rock gain?
Work is the product of force and the distance.
The potential energy gained by the rock will be equal to work done in lifting up the rock which is 100 J
2. At point C, the rock's potential energy will be equal to the work done.
That is, at point C, P.E = 100J
3. The rock's kinetic energy at point A is Zero.
That is, at point A, K.E = 0
4. At point B, some of the rock's potential energy will be changed to Kinetic energy. Yes. Because the Total energy = K.E + P.E
5. What is the mass of the rock?
Weight W = mg
where g = 9.8m/s^2
W = 10N
Substitute both into the formula
10 = 9.8m
make m the subject of the formula
m = 10/9.8
m = 1.02 kg
6. What is the rock's velocity just before it hits the ground
Work done = Energy
That is, Work done = maximum P.E = maximum K.E
100 = 1/2m\(v^{2}\)
Substitute mass into the formula
200 = 1.02\(V^{2}\)
V = \(\sqrt{196}\)
V = 14 m/s
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the allowed shapes for orbits under the force of gravity are
Answers
a. What property of sound waves is related to pitch?
b. What property of sound waves is related to volume?
c. What is the Doppler effect? What causes it?
d. Describe the relative speeds of sound in the different states of matter.
Answers
Answer:
A. The property of sound waves that is related to pitch is its frequency. Higher frequency sound waves create higher-pitched sounds, while lower frequency sound waves create lower-pitched sounds.
B. The property of sound waves that is related to volume is its amplitude. Larger amplitude sound waves create louder sounds, while smaller amplitude sound waves create softer sounds.
C. The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It is commonly observed in sound waves, such as the change in pitch of a siren as an ambulance passes by. The Doppler effect occurs because the relative motion between the wave source and the observer causes a change in the effective distance that the wave travels, resulting in a change in its frequency.
D. The speed of sound varies depending on the state of matter it is traveling through. In general, sound travels fastest through solids, slower through liquids, and slowest through gases. In air at room temperature and pressure, sound travels at a speed of approximately 343 meters per second (1,125 feet per second), while in water, sound travels at a speed of about 1,480 meters per second (4,850 feet per second). In solids such as steel, sound can travel at speeds up to 5,960 meters per second (19,550 feet per second)
The reactivity of an element is based on its:
A) Protons
B) Electrons
Answers
Answer: Electrons !!
How harmful are the emissions from cosmetics, hygiene, and cleaning products? Claim
Evidence 1
Evidence 2
Evidence 3
Reasoning
Answers
The claim can be Cosmetics, hygiene, and cleaning product emissions may be dangerous.
Evidence 1: Effect of Air Quality
Volatile organic compounds (VOCs), including formaldehyde, benzene, and toluene, can be found in a variety of cosmetic, hygiene, and cleaning goods. These VOCs have the potential to evaportate and cause indoor air pollution.
Environmental impact is evidence number two
Cosmetics, hygiene, and cleaning goods can have a detrimental environmental impact during manufacturing, usage, and disposal. Microplastics and certain chemicals are among the substances present in these items that may find their way into rivers and endanger aquatic life.
Evidence 3: Worker health effects
Occupational health risks can be present for workers who manufacture and produce hygiene, cleaning, and cosmetic items.
Reasoning: It is clear from the research that emissions from cosmetic, hygiene, and cleaning goods have the potential to be harmful.
Thus, this way, harmful are the emissions from cosmetics, hygiene, and cleaning products.
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Calculate the youngs modulus for the material of the wire
Answers
First, plot the data shown as points.
The points are (0,0), (1.4, 10), (2.8, 20), (4.2, 30), (4.9, 35), (5.8, 40), and (8, 45).
The graph shows a proportional part (a straight line) and a curvy part. So, the limit of proportionality is shown at the end of the straight line segment. The image below shows this limit.
The gradient of the straight-line portion refers to the slope. Let's use the points (1.4, 10) and (2.8, 20).
\(m=\frac{y_2-y_1}{x_2-x_1}=\frac{20-10}{2.8-1.4}=\frac{10}{1.4}\approx7.14\)Therefore, the gradient is 7.14.
The Young modulus formula is
\(E=\frac{\frac{F}{A}}{\frac{\Delta l}{l}}\)Let's use the greater force and the greater extension.
\(E=\frac{\frac{45N}{7\times10^{-8}m^2}}{\frac{8\times10^{-3}m}{2m}}=1.6\times10^{11}\)Therefore, Young Modulus is 1.6x10^11.
What would happen to jupiter if we could somehow double its mass?.
Answers
Answer:
G M m / R^2 attraction of Jupiter to sun where m is mass of Jupiter
m V^2 / R centripetal force acting on Jupiter
R = G M / V^2
The radius would be unchanged, and its orbit would be unchanged
A sample consists of 400 voltage measurements. The sample mean is 35.52 V, and the sample standard deviation is 1.84 V. There are 7 measurements in the bin 39.0 < x ≤ 39.5 V
A.) Estimate the probability (%) that a voltage measurement lies between 39.0 and 39.5 V
B.) Calculate the transformed variable z at the midpoint of this bin, i.e., at x = 39.25 V
C.) Calculate f(z) at x = 39.25 V
D.) Compare the answer of Part (c) with the analytical prediction of f(z) at x = 39.25 V for a Gaussian (normal) pdf
Answers
This indicates that the voltage measurements follow a normal distribution, the estimated probability that a voltage measurement lies between 39.0 and 39.5 V is 1.59%. The solution to section (c) agrees with the mathematical prediction made by f(z) for a Gaussian (normal) pdf at x = 39.25 V.
A.) The proportion of measurements in the bin is 7/400. To estimate the probability that a voltage measurement lies between 39.0 and 39.5 V, we assume that the voltage measurements follow a normal distribution. Since we do not know the population parameters, we use the sample mean and standard deviation as estimates. We can calculate the z-score for the lower and upper bounds of the bin:
\(z_1\) = (39.0 - 35.52) / 1.84 = 1.89
\(z_2\) = (39.5 - 35.52) / 1.84 = 2.16
We can determine the region under the curve between using a calculator for \(z_1\) and \(z_2\) or a conventional normal distribution table :
P(1.89 < z < 2.16) = P(z < 2.16) - P(z < 1.89) = 0.0159
Therefore, An estimated 1.59% of the time, a voltage measurement will fall between 39.0 and 39.5 V.
B.) The transformed variable z at the midpoint of the bin is:
z = (39.25 - 35.52) / 1.84 = 2.03
C.) The normal probability density function (pdf) is:
\(f(z) = (1 / \sqrt{(2\pi)}) * exp(-z^2 / 2)\)
At x = 39.25 V, we can evaluate f(z) using the z-score calculated in part (b):
\(f(z) = (1 / \sqrt{(2\pi)}) * \exp(-2.03^2 / 2) = 0.058\)
Therefore, f(z) at x = 39.25 V is 0.058.
D.) The analytical prediction of f(z) at x = 39.25 V for a Gaussian (normal) pdf is the same as the answer to part (c). Therefore, The solution to section (c) agrees with the mathematical prediction made by f(z) for a Gaussian (normal) pdf at x = 39.25 V.
Normal distribution, also known as Gaussian distribution, is a continuous probability distribution that is widely used in statistics, physics, social sciences, and other fields. The normal distribution is characterized by a bell-shaped curve, where the mean, median, and mode are all equal, and most of the data is located close to the mean.
The curve is symmetrical around the mean, and its shape is determined by two parameters: the mean and the standard deviation. In a normal distribution, the probability density function is described by a mathematical formula, which enables us to calculate the probability of an event occurring within a certain range of values. This is useful for analyzing data and making predictions about future events.
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Complete Question:-
A sample consists of 400 voltage measurements. The sample mean is 35.52 V, and the sample standard deviation is 1.84 V. There are 7 measurements in the bin 39.0 < x ≤ 39.5 V
A.) Estimate the probability (%) that a voltage measurement lies between 39.0 and 39.5 V
B.) Calculate the transformed variable z at the midpoint of this bin, i.e., at x = 39.25 V
C.) Calculate f(z) at x = 39.25 V
D.) Compare the answer of Part (c) with the analytical prediction of f(z) at x = 39.25 V for a Gaussian (normal) pdf
An atomic nucleus has a charge of 40e. what is the magnitude of the electric field at a distance of 1.0 m from the center of the nucleus?
Answers
The electric field is found as 5.76 * 10^-17 Volts.
What is the magnitude of the electric field?Now we know that the electric field is the region in space where the influence of the charge is felt. We are told that the magnitude of the charge is about 40 e.
Reacll that;
E = Kq/r^2
K = electric constant
q = magnitude of charge
r = distance
Thus;
E = 9 * 10^9 * 40 * 1.6 * 10^-19/1^2
E = 5.76 * 10^-17 Volts
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When a marble is at rest what happened
Answers
Answer: the marble will remain in place at a constant velocity of zero
Explanation:
Newton's first law states that a body at rest will remain at rest, and a body in motion will remain in motion in a straight line at a constant velocityunless acted upon by an outside force
10)as a protostar moves onto the main sequence to become a low-mass star, its…
Answers
As a protostar moves onto the main sequence to become a low-mass star, its luminosity increases while its radius decreases.
Determine the protostar stage?During the protostar stage, gravitational contraction causes the star to heat up, and as a result, it emits infrared radiation. As the protostar continues to accrete mass from its surrounding molecular cloud, it eventually reaches a state of hydrostatic equilibrium, where the inward gravitational force is balanced by the outward pressure from nuclear fusion in its core. At this point, the star becomes a main-sequence star.
As the protostar transitions to the main sequence, its nuclear fusion reactions become the primary source of energy, and the release of energy in the form of light significantly increases its luminosity. The star settles into a stable phase of hydrogen fusion in its core, converting hydrogen into helium.
This increase in luminosity is accompanied by a decrease in the star's radius, as the star achieves a more balanced state of gravitational contraction and energy release.
Therefore, during the transition from protostar to a low-mass main-sequence star, the star's luminosity increases while its radius decreases.
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a ball is thrown vertically down from the edge of a cliff with a speed of 5.2m/s how high is the cliff if it took 11s for the ball to reach the ground
Answers
\(\\ \sf\longmapsto h=ut+\dfrac{1}{2}gt^2\)
\(\\ \sf\longmapsto h=5.2(11)+\dfrac{1}{2}(9.8)(11)^2\)
\(\\ \sf\longmapsto h=57.2+4.9(121)\)
\(\\ \sf\longmapsto h=57.2+592.9\)
\(\\ \sf\longmapsto h=650.1m\)
How is energy stored and transferred at 5 different points during the launch and flight of the trebuchet?
Answers
The way that the energy stored and transferred at 5 different points during the launch and flight of the trebuchet are:
Energy storage during the loading phase: When the trebuchet is loaded, the counterweight and the projectile are both raised to a high point on the frame. This increases the gravitational potential energy of the counterweight and the projectile.Energy transfer during the tensioning phase: As the trebuchet is tensioned, the energy stored in the counterweight and the projectile is transferred to the tensioned ropes, cables or chains. This causes the ropes or chains to stretch and store elastic potential energy.Energy transfer during the launch phase: As the trebuchet is released, the energy stored in the tensioned ropes, cables or chains is transferred to the counterweight and the projectile. The counterweight falls, releasing its gravitational potential energy and propelling the projectile forward.Energy transfer during the flight of the projectile: As the projectile flies through the air, the energy stored in the projectile is transferred to the air through friction and air resistance. This causes the projectile to slow down and lose altitude.Energy transfer during the impact phase: As the projectile strikes its target, the energy stored in the projectile is transferred to the target, causing damage or destruction. Any remaining energy in the projectile is absorbed by the target or dissipated as heat or sound.What is the Energy about?Energy is a property of matter that allows it to do work. It is a scalar quantity, meaning it has only magnitude and no direction.
Energy can take many forms, including kinetic energy (the energy an object possesses due to its motion), potential energy (the energy an object possesses due to its position or state), and thermal energy (the energy an object possesses due to its temperature).
Therefore, Energy can also be classified as being either non-renewable or renewable. Non-renewable energy sources, such as fossil fuels, are finite and will eventually run out, whereas renewable energy sources, such as solar or wind power, are replenished naturally and can be used indefinitely.
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A car moving at a speed of 20 m/s has a kinetic energy of 200,000 J from that motion. What is the car's mass?
Answers
Answer:
i think the answer is 1000 kg but i might be wrong
0 K into fahrenheit scale and celsius scale
Answers
Answer:
0
∘
C=273.16
∘
K
0
∘
K=−273.16
∘
C
9
F−32
=
5
C
=−
5
273.16
⇒F=32+9×(−
5
273.16
)=−459.67
∘
F
Explanation:
hope it's helps you..
plz Mark me as brainlistMax Planck and Albert Einstein developed the idea that light is energy radiated at the speed of light in the form of wave packets of energy
called.
A. high energy waves
B. electromagnetic waves
C. photons
D. clusters
Answers
NEED HELP!!! ANSWER THESE 5 QUESTIONS FOR 25 POINTS!!!! PLEASE ANSWER!! I WILL GIVE YOU BRAINEST
1. Why would oxygen levels make a difference in athletic performance?
A.
Muscles need oxygen to function well.
B.
It is just one biometric that is studied.
C.
Oxygen is important for everyone, not just athletes.
D.
Athletes require less oxygen than those who are less active.
2. Dina has been working out for a few weeks. She wants to really focus on developing healthy habits rather than a very specific goal, like losing weight. She knows that tracking can help maintain health. What could she document that would let her see progress?
A.
She should just create a long-term goal.
B.
She could note the lengths and speeds of her morning runs.
C.
She should write down what she weighs when she wakes up in the morning.
D.
She can record what days she exercises and the type of activity.
3. Alonzo thinks that it will be best if he exercises seven days a week since that will make sure that the habit sticks. Is this the BEST way to get into healthy habits that stick?
A.
Yes, the more exercise the better.
B.
No, he needs to plan some days of rest.
C.
Yes, high achievement takes a lot of commitment.
D.
No, he does not have the same schedule every day.
4. Tracking your exercise can help you stick with an exercise routine.
A.
True
B.
False
5. Ezra has a hard time sticking with exercise routines. He does well for a few weeks, but then tends to slack off a bit. What would be the BEST way for Ezra to motivate himself to stay on the program that he creates for himself?
A.
Build in small rewards when he achieves his goals.
B.
Recognize that the next time probably will not work well.
C.
Join an expensive gym so he is more motivated to exercise.
D.
Remind himself of his past failures to motivate him to succeed.
PLEASE NO LINKS!!! IF IT IS NOT THE ANSWER THEN I WILL REPORT
Answers
Answer:
1.A
2.D
3.B
4.A
5.A
Explanation:
Every physical activity requires a specific amount of oxygen for the human organs (heart, lungs, and muscle). Athletes must breathe efficiently to perform at their best, since a high oxygen level reduces fatigue and dizziness and promotes peak performance. Thus option 1. A, 2. D, 3. B, 4. A, 5. A is correct.
What oxygen levels make an in athletic performance?The range of 95-99% represents normal, healthy oxygen saturation levels. And can be simply measured with a fingertip pulse oximeter, a cheap, basic equipment. Your blood oxygen saturation is most likely within the typical range for active, healthy athletes (like you!).
Numerous websites that promote the purported advantages of breathed oxygen can be found by searching for “supplemental oxygen and athletes.” Almost all of them receive funding from businesses that sell oxygen.
Therefore, Because it doesn't function, more oxygen is not regarded as a performance-enhancing substance.
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What is the force needed to accelerate a wagon with a mass of 10 kg at a rate
of 2.0 m/s²?
A. 8.0 N
B. 20 N
OC. 12 N
OD. 5.0 N
Answers
Answer:
B
Explanation:
Remember:
F = m * a
= 10 * 2 = 20 N
The time to accelerate a 10kg object to 2m/s from rest using force F is:
t = mv/F = 20/F
Is there a typo?
Was the 2m/s written, a speed, supposed to be 2m/s 2
2
, an acceleration?
If so, then it takes 20N to accelerate a 10kg object by 2m/s 2
2
… from F = ma.
El profesor de Pedro mencionó en su clase que la distancia promedio de la Tierra a la Luna es de 384 000 000 metros. Ayuda a Pedro a escribir este número en notación científica
Answers
Answer:
384 000 000 en notación científica es 3.84*10⁸
Explanation:
La notación científica es una forma de representar números para simplificar la forma en que se escriben. Esta notación se utiliza para poder expresar muy fácilmente números muy grandes o muy pequeños.
Los números se escriben como un producto:
a*10ⁿ
donde:
a es un número real mayor o igual que 1 y menor que 10.n es un número entero, que recibe el nombre de exponente u orden de magnitud. Representa el número de veces que se desplaza la coma. Siempre es un número entero, positivo si se desplaza a la izquierda, negativo si se desplaza a la derecha.Para escribir el número 384 000 000 en notación científica, se realizan los siguientes pasos:
Se mueve la coma decimal hacia la izquierda tantos espacios hasta llegar a la derecha del primer dígito. En este caso la coma se encuentra al final del número.Se escribe entonces este número, que será el coeficiente a en la expresión a*10ⁿ. En este caso es el valor 3.84, donde el punto representa la coma decimal.Se escribe la base 10 con el exponente igual a la cantidad de espacios que se mueve la coma. Este es un número positivo porque la coma se desplaza a la izquierda. Entoces, como la coma decimal se mueve 8 lugares, n=8Entonces, 384 000 000 en notación científica es 3.84*10⁸
Which of the following is LEAST likely to be the result of a genetic mutation?
A
A horse with a particularly long neck
B
A man with a beard
С
An albino squirrel
D
A plant that produces fewer seeds than normal
Answers
Answer:
B. man with a beard
Explanation:
it is not a genetic mutation because it is completely natural and common unlike the other options.
Hi, can you please help me?
What's the value of v
What is the displacement of the object when its initial position is 10 m and the final position -20 m?
Answers
Answer:
-30m
Explanation:
displacement = final position - initial position, or d = -20-10
A 60-w light bulb radiates electromagnetic waves uniformly in all directions. At a distance of 1. 0 m from the bulb, the light intensity is i0, the average energy density of the waves is u0, and the rms electric and magnetic field values are e0 and b0, respectively.
Answers
At a distance of 1.0 m from the 60 W light bulb, the light intensity is i0, the average energy density of the waves is u0, and the RMS electric and magnetic field values are e0 and b0, respectively.
The intensity of light is defined as the power per unit area and can be calculated using the formula:
i = P/A
Where i is the light intensity, P is the power radiated by the bulb, and A is the area through which the light is spreading.
Given that the power of the light bulb is 60 W, the intensity at a distance of 1.0 m is i0.
The average energy density of the electromagnetic waves can be calculated using the formula:
u = c * ε0 * e0^2 / 2
Where u is the average energy density, c is the speed of light, ε0 is the permittivity of free space, and e0 is the RMS electric field.
The RMS magnetic field value b0 can be related to the RMS electric field value e0 through the equation:
b0 = e0 / c
In conclusion, at a distance of 1.0 m from the 60 W light bulb, the light intensity is i0, the average energy density of the waves is u0, and the RMS electric and magnetic field values are e0 and b0, respectively. These quantities can be calculated using the formulas mentioned above.
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An Olympic high jumper leaps over a horizontal bar. The jumper's center of mass is raised 0.25 m during the jump. Calculate the minimum speed with which the athlete must leave must leave the ground to perform this feat.
Answers
The minimum speed with which the athlete must leave the ground is 2.21 m/s
From the question given above, the following data were obtained:
Maximum Height (h) = 0.25 mFinal velocity (v) = 0 (at maximum height)Acceleration due to gravity (g) = 9.8 m/s²Initial velocity (u) =?v² = u² – 2gh (going against gravity)
0² = u² – (2 × 9.8 × 0.25)
0 = u² – 4.9
Collect like terms
u² = 0 + 4.9
u² = 4.9
Take the square root of both side
u = √4.9
u = 2.21 m/s
Thus, the athlete must leave the ground with a minimum speed of 2.21 m/s.
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Mix 3 liters of 20C water with 4 liters of 40C water and you'll have water at what temperature?
Answers
Mixing 3 liters of water at 20 \(^oC\) with 4 liters of water at 40 \(^oC\) will result in water with 31.43°C temperature.
Temperature of mixed waterThe amount of energy in the final mixture will be equal to the sum of the energy in the initial 3 liters of water at 20°C and the energy in the initial 4 liters of water at 40°C.
Energy = mass x specific heat x temperatureEnergy in the initial 3 liters of water at 20°C = 3 kg x 1 cal/g°C x 20°C = 60 caloriesEnergy in the initial 4 liters of water at 40°C = 4 kg x 1 cal/g°C x 40°C = 160 caloriesThe total energy in the final mixture:
= energy in 3 liters of 20°C water + energy in 4 liters of 40°C water
= 60 calories + 160 calories
= 220 calories
Total energy = mass of the mixture x specific heat x temperature of the mixture
Mass of the mixture is 3 liters + 4 liters = 7 kgspecific heat of water is 1 calorie/gram°CTemperature of the mixture = Total energy / (mass of the mixture x specific heat)Temperature of the mixture = 220 calories / (7 kg x 1 cal/g°C)Temperature of the mixture = 31.43°CTherefore, the final temperature of the mixture will be approximately 31.43°C.
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When tunning the temperature exercise to determine thermal death time and thermal death point one runs a control the control allows a comparison of the percentage of death of the cells from the heat exposure compared to normal growth without exposure to heat True or False
Answers
True. When tunning the temperature exercise to determine thermal death time and thermal death point one runs a control the control allows a comparison of the percentage of death of the cells from the heat exposure compared to normal growth without exposure to heat
Define thermal death time
The concept of thermal death time tells us how long it takes to kill a particular bacterium at a particular temperature. It was initially created for food canning but has since found use in cosmetics and the manufacture of animal feeds (such as chicken and pharmaceuticals) free of salmonella.
The phrase "thermal death point" describes the lowest temperature at which a population of a specific microorganism perishes within ten minutes. In a 10-minute exposure at this TDP, all microbes are eliminated. TDP is one metric for calculating the thermal death of microorganisms. When boiling water to purify it, TDP is a crucial measurement.
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The sphere that refers to Earth's water is called what?
Answers
Tge sphere that refers to Earth's water is Hydrosphere.
What is the distance traveled by a vehicle in 12 minutes if speed is 35 km/h
Answers
Answer:
7km
Explanation:
how do combination lens systems, such as compound microscopes and refracting telescopes, operate?
Answers
The combination of the compound microscopes and refracting telescopes, operate by magnifying the image.
How do they operate?High levels of magnification are produced by the objective lens and eyepiece lens working together. Multiplying the objective lens' and the eyepiece lens' individual magnifications yields the microscope's overall magnification.
In a refracting telescope, the objective lens and eyepiece lens work together to produce high magnification, which makes distant objects look larger and more distinct to the spectator.
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Will mark brainliest
Answers
C: 78.2 m/s
Step by step:
A steel bridge is 500.0 m long when the temperature is 25.00 OC. What is the length on a cold day when the temperature is minus 20.0 oC? The coefficient of expansion for steel is 12 * 10-6.
Answers
Answer:
499.73 m
Explanation:
We'll begin by calculating the change in the temperature. This can be obtained as follow:
Initial temperature (T₁) = 25 °C
Final temperature (T₂) = –20° C
Change in temperature (ΔT) =?
ΔT = T₂ – T₁
ΔT = –20 – 25
ΔT = –45 °C
Finally, we shall determine the length on a cold day at –20° C. This can be obtained as follow:
Length at 25°C (L₁) = 500 m
Coefficient of linear expansion (α) = 12×10¯⁶ /°C
Change in temperature (ΔT) = –45 °C
Length at –20 °C (L₂) =?
α = L₂ – L₁ / L₁ΔT
12×10¯⁶ = L₂ – 500 / (500 × –45)
12×10¯⁶ = L₂ – 500 / –22500
Cross multiply
L₂ – 500 = 12×10¯⁶ × –22500
L₂ – 500 = –0.27
Collect like terms
L₂ = –0.27 + 500
L₂ = 499.73 m
Therefore, the length on a cold day at –20° C is 499.73 m.