Answer:
Any scientific investigation in its simplest form involves collecting information, while a controlled experiment is a tightly controlled investigation that tests a hypothesis.
Explanation:
All the scientific investigations start with a particular question. The question decides what type of investigation should research take. A controlled experiment is an investigation which allows a particular variable to change and all other variable controlled to remain constant to see the effect on dependent variable to test a particular hypothesis while other types of investigations are used to increase the knowledge or information about the particular research subject.
An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is the average angular acceleration in rad/s^2
(b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation?
(a) To find the average angular acceleration in rad/s^2, we need to convert the given rotational speed from rpm (revolutions per minute) to rad/s (radians per second) and divide it by the time taken. First, let's convert 100,000 rpm to rad/s:
Angular speed (ω) in rad/s = (100,000 rpm) * (2π rad/1 rev) * (1 min/60 s) = (100,000 * 2π) / 60 rad/s.
Next, we divide the angular speed by the time taken to find the average angular acceleration:
Average angular acceleration = (Angular speed) / (Time taken) = [(100,000 * 2π) / 60] / (2 * 60) rad/s^2.
Simplifying the equation gives us the average angular acceleration in rad/s^2.
(b) To find the tangential acceleration of a point 9.50 cm from the axis of rotation, we use the formula:
Tangential acceleration = (Angular acceleration) * (Radius).
Given that the average angular acceleration is calculated in part (a), and the radius is given as 9.50 cm (0.095 m), we can substitute these values into the equation to find the tangential acceleration.
Tangential acceleration = (Average angular acceleration) * (Radius) = [(100,000 * 2π) / 60] / (2 * 60) * 0.095 m.
Calculating this expression gives us the tangential acceleration in m/s^2.
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if you are driving in germany at a whopping 185 km/hr, what is your speed in miles per hour (mph
If you are driving in Germany at 185 km/hr, your speed in miles per hour (mph) is approximately 114.953 mph.
To convert kilometers per hour (km/hr) to miles per hour (mph), we can use the conversion factor. The conversion factor for km/hr to mph is 0.621371. This means that for every kilometer traveled in one hour, the equivalent distance traveled in miles is approximately 0.621371 miles.
To convert km/hr to mph, we simply multiply the speed in km/hr by this conversion factor. Therefore, we have,
185 km/hr * 0.621371 = 114.953135 mph (rounded to three decimal places)
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Aurora binge drinks. what does this most likely mean for aurora? a she drinks enough alcohol to become intoxicated. b she only drinks at social occasions. c she drinks one or two drinks every night. d she avoids alcohol altogether.
The most likely mean for aurora. She drinks one or two drinks every night. Option C is correct.
What is Binge-drinking?Binge-drinking is explained as having five or more drinks in one sitting for males, and four or more drinks in one sitting for women.
The majority of people who binge-drink do not have a serious alcohol problem. Binge-drinking, on the other hand, is a dangerous risk behavior linked to significant injuries and a variety of disorders.
Hence, option C is correct.
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What is equilibrium?
when there are no forces
when all forces acting on an object remain the same
when an object does not move
when the forces acting on an object change
Answer:
when all forces acting on an object remain the same
None of the choices is correct.
Equilibrium is the condition when all forces acting on an object are balanced. Then, the object doesn't accelerate. It continues in constant, uniform motion. It moves at a constant speed (which may be zero), and in a straight line.
a fragment of bone is discovered during an archaeological dig. the bone contains carbon-14 isotopes of the element carbon. the bone is approximately 23000 years old. calculate what proportion of the carbon-14 isotopes remains. give your answer to the nearest whole fraction. the half life of carbon-14 is 5730 years.
When a fragment of bone containing carbon-14 isotopes of the element carbon is discovered during an archaeological dig, and it is estimated to be approximately 23,000 years old, one can calculate the proportion of the carbon-14 isotopes that remains.
The half-life of carbon-14 is 5,730 years. Carbon-14 has a half-life of 5,730 years, which implies that half of the carbon-14 atoms will decay every 5,730 years. This property of carbon-14 may be used to determine the age of ancient artefacts and fossils. By determining the proportion of carbon-14 remaining in a sample, we may determine how old it is.According to the problem, the bone is around 23,000 years old. We can utilize the following formula to calculate the proportion of carbon-14 isotopes that remain: Proportion remaining = (1/2)^(number of half-lives)We can first calculate the number of half-lives that have occurred since the bone was alive. The number of half-lives is calculated as follows:Number of half-lives = (time elapsed) / (half-life)Number of half-lives = 23,000 / 5,730Number of half-lives = 4.016So the number of half-lives that have occurred since the bone was alive is 4.016. We can now use this number to calculate the proportion of carbon-14 isotopes that remains:Proportion remaining = (1/2)^(4.016)Proportion remaining = 0.105Therefore, the proportion of carbon-14 isotopes that remains is 0.105, or approximately 1/10 (to the nearest whole fraction).For such more question on Proportion
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1. What is the wave speed of a wave that has a frequency of 100 Hz and a wavelength of 0.30 m?
30 m/s
2. What is the wave speed of a wave that has a frequency of 50 Hz and a wavelength of 0.10 m?
0.772m
3. What is the frequency of a wave that has a wave speed of 20 m/s and a wavelength of 0.50 m?
40 Hz
4. What is the frequency of a wave that has a wave speed of 80 m/s and a wavelength of 0.20 m?
5. What is the frequency of a wave that has a wave speed of 120 m/s and a wavelength of 0.40 m?
6. What is the wavelength of a sound wave that has a speed of 340 m/s and a frequency of 440 Hz?
7. What is the wavelength of a sound wave that has a speed of 340 m/s and a frequency of 880 Hz?
8. What is the wavelength of a sound wave that has a speed of 250 m/s and a frequency of 400 Hz?
9. What is the wave speed of a wave that has a frequency of 50 Hz and a wavelength of 2.0 m?
10. What is the wave speed of a wave that has a frequency of 100 Hz and a wavelength of 0.50 m?
Answer:
1. v = 30 m/s
2. v = 5 m/s
3. f = 40 Hz
4. f = 400 Hz
5. f = 300 Hz
6. λ = 0.772 m
7. λ = 0.386 m
8. λ = 0.625 m
9. v = 100 m/s
10. v = 50 m/s
Explanation:
The relationship between frequency, wavelength, and speed of a wave is given by the following formula:
\(v = f\lambda\)
where,
v = speed of wave
f = frequency of wave
λ = wavelength
1.
f = 100 Hz
λ = 0.3 m
Therefore,
v = (100 Hz)(0.3 m)
v = 30 m/s
2.
f = 50 Hz
λ = 0.1 m
v = (50 Hz)(0.1 m)
v = 5 m/s
3.
v = 20 m/s
λ = 0.5 m
\(f = \frac{v}{\lambda} = \frac{20\ m/s}{0.5\ m}\)
f = 40 Hz
4.
v = 80 m/s
λ = 0.2 m
\(f = \frac{v}{\lambda}=\frac{80\ m/s}{0.2\ m}\)
f = 400 Hz
5.
v = 120 m/s
λ = 0.4 m
\(f = \frac{v}{\lambda}=\frac{120\ m/s}{0.4\ m}\)
f = 300 Hz
6.
v = 340 m/s
f = 440 Hz
\(\lambda = \frac{v}{f}=\frac{340\ m/s}{440\ Hz}\\\)
λ = 0.772 m
7.
v = 340 m/s
f = 880 Hz
\(\lambda = \frac{v}{f}=\frac{340\ m/s}{880\ Hz}\\\)
λ = 0.386 m
8.
v = 250 m/s
f = 400 Hz
\(\lambda = \frac{v}{f}=\frac{250\ m/s}{400\ Hz}\\\)
λ = 0.625 m
9.
f = 50 Hz
λ = 2 m
v = (50 Hz)(2 m)
v = 100 m/s
10.
f = 100 Hz
λ = 0.5 m
v = (100 Hz)(0.5 m)
v = 50 m/s
Answer:
it B
Explanation:
I KNOW IT
x Methane, has a molar mass of 16.03 grams per mole. How many particles o of methane are present in 120 grams?
In order to determine the number of particles of methane, use the following expression:
number of particles = (mass /molar mass ) x Avogadro's number
in this case, you have:
molar mass = 16.03 grams/mole
mass = 120 grams
Avogadro's number = 6.02*10²³ particles/mol
replace the previos values of the parameters into the formula for the number of particles:
number of particles=(120 grams/ 16.03 grams/ mol)x(6.02*10²³particles/mol)
= (7.46 mol) x (6.02*10²³ particles/mol)
= 4.50*10²⁴ particles
Hence, the number of particles of methane, in 120 grams, is 4.50*10²⁴
A 70-kg skier leaves a ski jump at a velocity of 14m/s. What is the skier's momentum at that instant?
a. 5 Nos
c. 980 Nos
b. 50 Nos
d. 9800 Nos
Answer: 980 N*s
Explanation:
If the antenna elements are horizontally polarized dipoles with Eθ = âθ jµ (kIol / 4πr) e^(-jkr) |cos θ| what is the expression for the total radiated field of the array? (5 pts)
E_total(θ) = Σ (Eθ e^(j(kd(i-1)cos(θ) + βi)))
This expression represents the total radiated field of the array, considering the individual contributions from horizontally polarized dipole elements with the given electric field Eθ and taking into account their positions and phase shifts within the array.
To find the expression for the total radiated field of the array, we need to consider the individual contributions of each dipole element in the array and sum them up. Since the antenna elements are horizontally polarized dipoles, we can express the radiated electric field Eθ for a single dipole as:
Eθ = âθ jµ (kIol / 4πr) e^(-jkr) |cos θ|
Here, âθ represents the unit vector in the θ direction, j is the imaginary unit, µ is the permeability, k is the wave number, Iol is the current at the location of the dipole, r is the distance from the dipole, and θ is the angle between the observation point and the dipole axis.
Now, we need to consider an array of N dipoles, each with its own location and phase shift. For simplicity, let's assume that all dipoles have the same current amplitude I0 and are uniformly spaced with a distance d along the x-axis.
To find the total radiated field for the array, we need to sum the contributions of each dipole element:
E_total(θ) = Σ E_i(θ)
where E_i(θ) is the radiated field of the i-th dipole, and the summation goes from i=1 to N.
For each dipole in the array, we need to account for the phase shift due to its position along the x-axis and the additional phase shift βi introduced by the array feeding network:
E_i(θ) = Eθ e^(j(kd(i-1)cos(θ) + βi))
So, the total radiated field of the array is given by:
E_total(θ) = Σ (Eθ e^(j(kd(i-1)cos(θ) + βi)))
This expression represents the total radiated field of the array, considering the individual contributions from horizontally polarized dipole elements with the given electric field Eθ and taking into account their positions and phase shifts within the array.
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an astronaut stands on the surface of an asteroid. the astronaut then jumps such that the astronaut is no longer in contact with the surface. the astronaut falls back down to the surface after a short time interval. which of the following forces cannot be neglected when analyzing the motion of the astronaut?
The following force that cannot be neglected when analyzing the motion of the astronaut is the gravitational force between the astronaut and the asteroid.
An increase in space station mass has no effect on electric field strength, and an increase in orbital radius reduces electric field strength. There must be another object that balances the gravitational pull on the comet at that point.
Gravity is affected by object size and the distance between objects. A measure of the amount of matter in an object is its mass. Objects with more mass fall faster than objects with less mass. Gravity decreases as the distance between two objects increases.
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A black hole is:____.
a. an object so diffuse that light leaving it is bent totally back to center of the universe.
b. an object so diffuse that light approaching it is blocked from view.
c. an object so dense that light leaving it is bent totally back to the nearest star.
d. an object so dense that light leaving it is bent totally back to the object.
A black hole is: (d) an object so dense that light leaving it is bent totally back to the object. A black hole is a region in space where gravity is extremely strong, and nothing, including light, can escape its gravitational pull.
Black holes are formed from the remnants of massive stars that have undergone gravitational collapse. When a star exhausts its nuclear fuel, its core collapses under its own gravity. If the core's mass exceeds a certain threshold known as the Chandrasekhar limit, the collapse continues until it forms a black hole.
The extreme density of a black hole results in a gravitational field so intense that it warps the fabric of spacetime around it. This bending of spacetime causes light and other electromagnetic radiation to follow curved paths, and if they come close enough, they can be trapped by the intense gravitational pull of the black hole, unable to escape.
Hence, light leaving a black hole is bent back toward the object, making it impossible for any light to be emitted or seen from within the event horizon, the boundary beyond which nothing can escape the black hole's gravity.
Therefore, (d) an object so dense that light leaving it is bent totally back to the object is correct answer.
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A change of position is called
o distance
O velocity
O speed
O displacement
a 2.00 m long guitar wire with a linear mass density of 12 g/m is under a tension of 8000 n. what is the fundamental frequency of the resonant vibration of this wire?
A 2.00 m long guitar wire with a linear mass density of 12 g/m is under a strain of 8000 n, and the fundamental frequency of the resonant vibration of this wire is 204.1 Hz.
The frequency of an event is its repetitions per unit of time. As a contrast to spatial frequency, it is also sometimes referred to as temporal frequency, and as a contrast to angular frequency, it is sometimes referred to as ordinary frequency. A physical body's mass is its total amount of matter. Inertia, or the body's resistance to acceleration (change of velocity) when a net force is applied, is also measured by this property.
The formula for a string's fundamental frequency is f = 1/2*L(T/M)^1/2.
where L is the string's length and T is its tension.
M is the string's linear mass density, which is equal to 204.1Hz at f = 1/2*200(8000/0.012)^1/2.
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Which type of platform lift has the lifter starting by holding the bar off the ground with straight arms then hinging
forward until the bar lowers slightly past their knees and finally driving their hips forward until standing at the original
position?
The type of platform lift that starts with holding the bar off the ground with straight arms, hinging forward until the bar lowers slightly past the knees, and then driving the hips forward until standing at the original position is called a Deadlift.
The Deadlift is a compound exercise that primarily works the muscles in the legs, hips, and back, including the glutes, hamstrings, quadriceps, and erector spinae.
It is a staple exercise in many strength and powerlifting training programs, as well as a functional movement that can improve overall fitness, athletic performance, and daily life activities.
Construction lifts are strong tools. Encompassing boom scissor lifts, lifts, forklifts and other types of aerial and man lifts, construction lifts mention to any lifting machinery that quality an aerial platform supported by a vehicle-mounted extension.
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which correctly describes how the energy of a wave on the electromagnetic spectrum depends on wavelength and frequency?
Answer:
The answer to this question is given below in this explanation section.
Explanation:
"electromagnetic spectrum depends on wavelength and frequency"
When electromagnetic radiation interacts with single atoms and molecule,its behavior also depends on the amount of energy per quantum(photon)it carries wave number =1/wavelength in cm speed of light=wavelength x frequency energy = Planck's constant x frequency.
Electromagnetic radiation interacts with matter in different parts of the spectrum.
Electromagnetic radiation interacts with matter in different ways in different parts of the spectrum.The types of interaction can be so different that it seems justified to refer to different types of radiation.There is a continuum containing all these different kind of electromagnetic radiation.Thus we refer to spectrum but divide it up based on the different interaction with matter.
Answer:
Energy increases with decreasing wavelength and increasing frequency.
Explanation:
a belt is placed around a pulley 41 cm in diameter and rotating at 242 rpm, what is the linear speed in m/s of the belt
Given
d: diameter
d = 41 cm
We need radius information so we will calculate it:
r: radius
r = d/2
r = 41/2
r = 20.5 cm
Rotating speed
w = 242 rpm
Procedure
At a distance r from the center of the rotation, a point on the object has a linear speed equal to the angular speed multiplied by the distance r. The units of linear speed are meters per second, m/s.
\(v=\omega r\)But before using the formula we need to have all the units in the same system. So we need to go from rpm to rad/s and from cm to m
\(\begin{gathered} 242\cdot\frac{\text{rev}}{\min}\cdot\frac{2\text{ pi rad }}{1\text{ rev}}\cdot\frac{1\text{ min}}{60\text{ s}} \\ 25.34\text{ rad/s} \\ \\ 20.5\text{ cm}\cdot\frac{1m}{100\operatorname{cm}} \\ 0.205\text{ m} \end{gathered}\)Now we can calculate the linear velocity of the belt.
\(\begin{gathered} v=\omega r \\ v=25.34\text{ rad/s}\cdot0.205\text{ m} \\ v=5.1947\text{ m/s} \end{gathered}\)Answer
The linear velocity of the belt would be 5.2 m/s.
water in a lake a is contaminated with 0.5mg/l of tce. bioconcentration factor for tce is 10.6 l/kg. estimate the concentration of tce in fish. show only value without the unit (mg/kg)
If water in a lake a is contaminated with 0.5mg/l of tce. bioconcentration factor for tce is 10.6 l/kg, the estimated concentration of TCE in fish is 5.3.
To estimate the concentration of TCE in fish, you can use the formula:
Concentration in fish = (Concentration in water) × (Bioconcentration factor)
In this case, the concentration in water is 0.5 mg/L and the bioconcentration factor is 10.6 L/kg. Plugging these values into the formula, you get:
Concentration in fish = (0.5 mg/L) × (10.6 L/kg)
Concentration in fish = 5.3 mg/kg
So, the estimated concentration of TCE in fish is 5.3.
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a circuit has a power factor of .8 lagging. the circuit dissipates 100 w of powerwith an input voltage of 500 v. what is the impedance of the circuit expressed in rectangular form? a.1600Ω - j1200Ω b.1200Ω -j1600 Ω
c.1600Ω +j 1200Ω d.1200Ω + j1600Ω
The impedance of the circuit expressed in rectangular form is 1600Ω +j 1200Ω.
So, the correct answer is C
A circuit with a power factor of 0.8 lagging dissipates 100W of power with an input voltage of 500V.
To find the impedance of the circuit in rectangular form, first calculate the apparent power (S) using P = S * power factor. In this case, S = 100W / 0.8 = 125VA.
Next, calculate the reactive power (Q) using Q = √(S² - P²), which is Q = √(125² - 100²) = 75VAr.
The current (I) can be found by dividing the apparent power by the input voltage, I = 125VA / 500V = 0.25A.
Now, using Ohm's Law (V = IZ), we can calculate the impedance (Z) as Z = 500V / 0.25A = 2000Ω.
Finally, we can express the impedance in rectangular form by splitting it into real and imaginary components: Z = 1600Ω + j1200Ω, which corresponds to option (c).
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describe what living in the southeast is like for many people in both cities and outside of cities.
Living in the Southeast for many people, both in cities and outside of cities, offers a distinct blend of cultural, geographical, and climatic characteristics.
In cities such as Atlanta, Charlotte, or Miami, residents experience the bustling energy of urban life with a range of amenities, diverse culinary scenes, and thriving cultural attractions. These cities often have vibrant downtown areas, modern infrastructure, and employment opportunities across various industries. Residents can enjoy a mix of entertainment options, including music festivals, sports events, and a vibrant nightlife. However, they may also encounter challenges such as traffic congestion and higher living costs in some areas. Outside of cities, the Southeast region boasts picturesque landscapes and a more relaxed pace of life. Residents can find charming small towns, close-knit communities, and a stronger connection to nature. The region offers stunning coastlines, scenic mountains, and lush forests, providing ample opportunities for outdoor activities like hiking, fishing, and beach outings. Residents often appreciate the Southern hospitality, a slower lifestyle, and a sense of community. Across the Southeast, the climate is generally characterized by hot summers and mild winters, with some areas prone to hurricanes and tropical storms. The region also showcases its rich history, diverse traditions, and a culinary heritage famous for dishes like barbecue, seafood, and soul food.
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Start
Finish
8 min
Time
0 min
1 min
2 min
3 min
4 min
5 min
6 min
7 min
Temperature
90°C
83°C
78°C
73°C
68°C
64°C
60°C
57°C
54°C
O 45 degrees celsius/min
O 450 degrees celsius/min
O 4.5 degrees celsius/ min
O 0.45 celsius/min
hos
Predict what would happen to the volume of a gas if the pressure on that gas were doubled and then the absolute temperature of that gas were doubled.
The new volume of the gas will remain the same.
Data obtained from the question Initial pressure (P₁) = PInitial temperature (T₁) = TInitial volume (V₁) = VNew pressure (P₂) = 2PNew temperature (T₂) = 2TNew Volume (V₂) =? How to determine the new volumeThe new volume of the gas can be obtained by using the combined gas equation as illustrated below:
P₁V₁ / T₁ = P₂V₂ / T₂
(PV) / T = (2P × V₂) / 2T
Cross multiply
T × 2P × V₂ = PV × 2T
2PT × V₂ = 2PVT
Divide both side by 2PT
V₂ = 2PVT / 2PT
V₂ = V
Thus, the new volume will remain the same
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After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 54.0 cm. The explorer finds that the pendulum completes 99.0 full swing cycles in a time of 139s. What is the magnitude of the gravitational acceleration on this planet?
g_planet = ___ m/s^2
The magnitude of the gravitational acceleration on the unfamiliar planet is approximately 2.83 m/s^2.To find the gravitational acceleration on the unfamiliar planet, we can use the formula:
g = (4π²L) / T²
where g is the gravitational acceleration, L is the length of the pendulum, and T is the time for one full swing cycle.
Substituting the given values, we get:
g = (4π² × 0.54 m) / (99.0 × 2 × π)^2 × 139^2 s^2
Simplifying this expression, we get:
g = 2.83 m/s^2
Therefore, the magnitude of the gravitational acceleration on the unfamiliar planet is approximately 2.83 m/s^2.
To calculate the gravitational acceleration (g_planet) on the unfamiliar planet using the simple pendulum, you can follow these steps:
1. Determine the period (T) of the pendulum, which is the time it takes to complete one full swing cycle.
T = total time / number of cycles = 139s / 99.0 cycles = 1.40404s
2. Use the formula for the period of a simple pendulum:
T = 2π * √(L / g_planet)
Where L is the length of the pendulum (0.54 m), and g_planet is the gravitational acceleration we want to find.
3. Rearrange the formula to solve for g_planet:
g_planet = (4π² * L) / T²
4. Plug in the values:
g_planet = (4π² * 0.54 m) / (1.40404s)²
5. Calculate the result:
g_planet ≈ 9.60 m/s²
So, the magnitude of the gravitational acceleration on this unfamiliar planet is approximately 9.60 m/s².
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The speed of a wave is 70 m/sec. If the wavelength of the wave is 0.7 meters what is the frequency of the wave
Answer:
malesef herşey ingilizce yazıyor hiçbirşey anlayamadım
Explanation:
heeeeeem ben bunlardan anlamam giiiit başkasına sooooor bu arada en iyi seç benü bikere bari seçte bi en iyi cvp olsun
What is the relationship between voltage and current in a circuit, if the resistance remains constant?
if it ran off a dc i think
does a wall or door have more inertia?
Answer:
wall
Explanation:
Answer:
a wall.
Explanation:
How many calories of heat energy would it take to heat 200ml of water from 20ºC to 80ºC?
It would take approximately 16,800 calories of heat energy to heat 200ml of water from 20ºC to 80ºC.
To calculate this, you can use the specific heat capacity of water, which is approximately 1 calorie/gram ºC. Since 1 ml of water is equivalent to 1 gram, we can assume that the specific heat capacity for water in this case is also 1 calorie/ml ºC.
The temperature change is 80ºC - 20ºC = 60ºC.
So, the total heat energy required can be calculated as:
200 ml * 60 ºC * 1 calorie/ml ºC = 12,000 calories.
Therefore, it would take approximately 16,800 calories of heat energy to heat 200ml of water from 20ºC to 80ºC.
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in order for the average velocity to be different from the avergae speed, what has to be true of the object's motion?
Answer:
ok
Explanation:
Acceleration is defined as the rate of change of velocity.
Acceleration = (Change in velocity) / time taken
Acceleration = (Final velocity - initial velocity) / time
As the object velocity changes by the same amount in each second, it means the acceleration is constant.
Which of the following is an adaptation that helps protect the animal?
the strength of an electric field around a charged object depends on both the magnitude of the charge and
the distance from the charged object. The electric field is a measure of the force per unit charge acting on a test charge placed at a particular point in space.
According to Coulomb's Law, the magnitude of the electric force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. As the distance between the charged object and a test charge increases, the electric field strength decreases, and vice versa.
In practical terms, this means that the closer a charged object is to a point in space, the stronger the electric field will be at that point. Conversely, the farther away the object is, the weaker the electric field will be. Understanding the relationship between charge and distance is critical to designing and working with electrical systems, from basic circuits to complex machinery. Accurately predicting the strength of electric fields can help engineers create safer, more efficient systems, and avoid potential hazards.
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An iron rod with an initial length of 12.62 m has its temperature raised from 19o C to 30.6o C. If iron has a coefficient of thermal expansion of 12x10-6 1/oC, what is the change in length of the rod in mm?
ANSWER:
1.757 mm
STEP-BY-STEP EXPLANATION:
The coefficient of linear expansion is given by the following formula:
\(\alpha=\frac{\Delta L}{L\Delta T}\)Where α = coefficiente of linear expasion, ΔL = change in lenght, ΔT = change in tempetature
Solving for ΔL:
\(\Delta L=\alpha\cdot L\cdot\Delta T\)Replacing and we calculate the change in lenght:
\(\begin{gathered} \Delta L=12\cdot10^{-6}\cdot12.62\cdot(30.6-19) \\ \Delta L=0.001757\text{ m}\cdot\frac{1000\text{ mm}}{1\text{ m}}=1.757\text{ mm} \end{gathered}\)The change in length is 1.757 mm