Number of oxygen molecules in each breath is 2.9X10^21
Given that the volume of air inside a breath (V) = 6.0×10^−4 m^3
oxygen in fresh air = 20%
volume of oxygen in fresh air = 20/100 x 6.0×10^−4 = 1.2x10-4m^3
pressure in the lungs (P)= 1.0×10^5 pa
Temperature of air (T) =300K
Using ideal gas equation find the number of moles of oxygen
PV = nRT
Then n = 1.0×10^5 x 1.2x10-4 / 8.314 x 300 = 4.8x10-3mol
We know the number of molecules in 1 mol is 6.023x10^23
Then the number of molecules in 4.8x10-3mol of oxygen is =
4.8x10-3molx 6.023x10^23 = 2.9x10^21
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a light ray strikes one face of the zirconia crystal at an angle of incidence of 18. once inside, what is the ray's angle with respect to the face of the crystal?
The ray's angle in relation to the crystal's face is 71.6°. We used the illustration of light moving through water toward the boundary with a less dense medium, like air, to explain TIR.
The refracted ray lies along the border with a 90° angle of refraction when the angle of incidence in water reaches a specific critical value.
Due to that,
Angle of incidence = 27°
We must determine the refraction angle.
Snell's law is used.
Fill out the formula with the value
Using the refraction formula, we must determine the angle of the ray with regard to the crystal's face. Fill out the formula with the value
Hence, the angle of the ray with regard to the crystal's face is 71.6°.
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a proton at rest travels through potential of 1000 v then goes to uniform 0.04 t magnrtic field. what is the radius of protons resulting orbit
The radius of protons resulting orbit is 8.43 mm.
What is radius?
The reason the bone is called the radius is because it behaves like the radius (of a circle). It revolves around the ulna, and the distance from the ulna (the circle's center) to the edge of the radius, which is known as the styloid process of the radius, is where it connects to the hand's bones (the circle).
What is protons ?
Protons include the H+ ion or the hydrogen atom's nucleus. Regardless of the isotope, each hydrogen atom has one proton, each helium atom has two, each lithium atom has three, and so on.
Potential difference, V=100V
Magnetic field ,B=0.004T
Force, F=qV= 2mv 2 (K.E.)
⇒V= [tex]\sqrt{2qv/m}[/tex]
for radius of path, mv²/ R = qvB
R = mv/ qB = m/qB* [tex]\sqrt{2qv/m}[/tex]
R= 1/ 0.004 * [tex]\sqrt{9.1 * 10-31 * 2* 100 / 1.6*10-19}[/tex]
= 843.17 * 10⁻⁵m
= 8.43 mm
Hence, the radius of protons resulting orbit is 8.43 mm.
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when a mass m hangs from a vertical wire of length l, waves travel on this wire with a speed v.A. what will be the speed of these waves if we triple M without stretching the wire?
B. what will be the speed of these waves if we replace the wire with an identical one, except twice as long?
C. What will be the speed of these waves if we replace the wire with one of the same length, but two times as heavy
D. what will be the speed of these waves if we stretch the wire to thrice its original length
E. What will be the speed of these waves (in terms of V) if we increase M by a factor of 18.0, which stretches the wire to double its origina length?
A. The speed of the waves will remain unchanged if the mass is tripled without stretching the wire.
B. The speed of the waves will be halved if the wire is replaced with an identical one, except twice as long. This is because the waves will have to travel twice the distance in the same amount of time.
C. The speed of the waves will remain unchanged if the wire is replaced with one of the same lengths, but two times as heavy.
D. The speed of the waves will be halved if the wire is stretched to thrice its original length. This is because the waves will have to travel thrice the distance in the same amount of time.
E. The speed of the waves will be halved if the mass is increased by a factor of 18.0 and the wire is stretched to double its original length. This is because the waves will have to travel twice the distance in the same amount of time. The speed of the waves will thus be V/2.
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A braking force of 6000 N was applied to a 1000-kg automobile bringing it to a complete stop in 75 m.
–How much work was done in stopping the automobile?
–How did the kinetic energy of the automobile change?
–What relationship could be used to find the initial velocity of the automobile before the brakes were applied?
–Calculate the initial velocity of the automobile before the brakes were applied.
a) The work done is 450 kJ
b) The kinetic energy gets lesser with time
c) The relation is v^2 = u^2 - 2as
d) The initial velocity is 30 m/s
What is the work done?We know that the work that is done is the product of the force and the distance that is moved by a body. We know that work is said to be done when the force that is applied moves a distance in the direction of the force.
1) Work done = Force * distance
= 6000 N * 75 m
= 450 kJ
2) The kinetic energy of the automobile would decrease with time.
3) To obtain the initial velocity we have to use the relation;
v^2 = u^2 - 2as
v = final velocity
u = initial velocity
a = acceleration
s = distance covered
Given that;
F = ma
a = F/m
a = 6000 N / 1000-kg
a = 6 m/s^2
The we have;
0^2 = u^2 - (2 * 6 * 75)
u^2 = (2 * 6 * 75)
u = √ (2 * 6 * 75)
u = √900
u = 30 m/s
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four railroad cars, each of mass 2.50 3 104 kg, are coupled together and coasting along horizontal tracks at speed vi toward the south. a very strong but fool- ish movie actor, riding on the second car, uncouples the front car and gives it a big push, increasing its speed to 4.00 m/s southward. the remaining three cars continue moving south, now at 2.00 m/s. (a) find the initial speed of the four cars. (b) by how much did the potential energy within the body of the actor change? (c) state the relationship between the process described here and the process in problem 25.
The final three vehicles continue to travel south at a speed of 2.00 m/s. The four automobiles' initial speed is u=2.5 m/s.
What does a scientific energy mean?The definition of energy is the "capacity to accomplish work, which is the ability to apply a force producing the displacement of an item." Despite this unclear description, energy simply refers to the power that propels motion. Potential and kinetic energy are the two categories.
How is energy produced?The majority of electricity is produced by steam turbines using fossil fuels, nuclear energy, biomass, geothermal, & solar thermal energy. Steam turbines, hydro generators, wind turbines, & solar photovoltaics are some further prominent electricity generation systems.
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a car traveling at 20 m/s follows a curve in the road so that its centripetal acceleration is 5 m/s2. what is the radius of the curve?
A car traveling at 20 m/s follows a curve in the road so that its centripetal acceleration is 5 m/s. 160 m is the radius of the curve.
To find the radius of the curve, we can use the formula for centripetal acceleration:
a = v^2 / r
where a is the centripetal acceleration, v is the velocity, and r is the radius of the curve. In this case, we know that the velocity of the car is 20 m/s and the centripetal acceleration is 5 m/s2. We can solve for the radius of the curve by rearranging the formula and substituting the known values:
r = v^2 / a
= (20 m/s)^2 / 5 m/s2
= 800 m / 5 m/s2
= 160 m
Therefore, the radius of the curve is 160 m.
The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. It is a vector quantity to accelerate (in that they have magnitude and direction). The direction of the net force acting on an object determines the direction of its acceleration. When a vehicle turns, its velocity vector is altered by an acceleration in the new direction. The acceleration of the car in its present direction of motion is referred to as a linear acceleration (or tangential acceleration in circular motions).
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the left cart is heavier and it crashes into the lighter right cart that is initially at rest. what do you expect to happen?
when heavier left cart crashes with lighter right cart which is initially at rest, the lighter right cart gain acceleration and start moving.
This concept is based on conservation of momentum, Conservation of momentum is a major law of physics which states that the momentum of a system is constant if no external forces are acting on the system.
when heavier left cart crashes into the lighter right cart that is initially at rest, the right lighter cart will gain acceleration and start moving in the direction of motion of heavier cart and left heavier cart will remain in motion in the same direction.
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suppose you looked up in the sky from the southern hemisphere and observed the moon illuminated as it appears above. at which lettered position in its orbit is the moon located at this moment?
The moon is currently placed in the Waning Gibbous position in its orbit, as seen when we gazed up at the sky in the southern hemisphere and saw the moon illuminated as it appears.
In the Southern Hemisphere, unlike the Northern Hemisphere, the moon light increases in coverage from left to right in the waxing phase and the dark portion increases in coverage from left to right in the waning phase. One half of the moon is illuminated by the sun while the other is under shade. Anyone can see that the moon has a brilliant side facing the Sun and a dark side facing away from it. These lit and dark areas of the surface change in proportion as the moon orbits the Earth.
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find the slope of the tangent line to the curve 1 + y = sin(xy2) at the point (π, −1).
0.1894 is slope of tangent to the curve 1+y=sin(x[tex]y^2[/tex]) at point( π,-1)
what is slope of tangent?The instantaneous rate of change of the specified function at a point is represented by the tangent. The derivative of the function at a given position is equal to the slope of the tangent at that location.
The slope of the tangent at a curve is given by:
slope = [tex]\frac{dy}{dx}[/tex]
let the slope be m
The given curve is:
1+y=sin(x[tex]y^2[/tex])
differentiating both side of the equation with respect to x we get:
[tex]\frac{dy}{dx}[/tex] = cos([tex]xy^2[/tex]) * [tex]\frac{d(xy^2)}{dx}[/tex]
=> [tex]\frac{dy}{dx}[/tex] = cos([tex]xy^2[/tex]) * ( [tex]y^2 + 2x \frac{dy}{dx}[/tex])
putting the value of x and y in the above equation we get
[tex]\frac{dy}{dx}[/tex] = cos([tex]-[/tex]π) * [tex]1+2\frac{dy}{dx}[/tex] π
=> [tex]\frac{dy}{dx}[/tex] = [tex]1+2\frac{dy}{dx}[/tex] π
=> [tex]\frac{dy}{dx}[/tex] = -1/(1-2π)
=> [tex]\frac{dy}{dx}[/tex] = 0.1894
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suppose we sort an array using insertion sort. for an array of size 100,000, it takes 2 seconds. approximately how many seconds will it take for an array of size 800,000?
It takes 128 seconds for sorting an array using insertion sort having size 800000.
The straightforward sorting algorithm known as insertion sort produces the final sorted array one item at a time through comparisons. In comparison to more sophisticated algorithms like quicksort, heapsort, or merge sort, it performs significantly worse on huge lists.
The worst-case (and average-case) complexity of the insertion sort method is O ([tex]n^2[/tex]).
To put it another way, in the worst situation, the time needed to sort a list is inversely proportional to the square of the number of entries in the list.
The best-case time complexity of the insertion sort algorithm is O(n).
Therefore, we may argue that by considering the worst-case scenario for the problem.
We have, [tex]O(100000)^2[/tex] = 2 Sec
So for the array of size 800,000, it will take
[tex]= 8^2 \times O(100,000) = 8^2 \times 2[/tex]
=64*2 = 128 seconds
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assuming a constant dew point temperature, how do temperature and relative humidity typically vary over a 24-hour period?
Changes in relative humidity are more common than changes in dew point. Assuming dew point to be relatively constant over a 24-hour period, relative humidity values change regularly throughout the day as temperatures rise and fall.
When the temperature and dew point are close, the relative humidity is higher than when the temperature and dew point are far apart. At the same temperature and dew point, the air is "saturated" and the relative humidity is 100%.
Clouds form when the temperature drops below the dew point. On the ground, temperatures often drop below the dew point, such as during heavy rains or foggy mornings.
The "relative humidity" of air describes the relationship between temperature and dew point.
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what is the voltage drop across a 5.0-ω resistor if the current through it is 5.0 a?
Answer:
voltage = 25V
Explanation:
In Ohm's law R = V/I then 5ohm = V/5A => V = 5 * 5 = 25V
Technetium‑99m, an important radionuclide in medicine, has a half‑life of 6.0 hours. What percentage of a sample of technetium‑99m will remain undecayed after each of the given times?
After specific periods, 12.5g of a technetium-99m sample will still be intact.
What is radionuclide used for?Radionuclide scan is used for disease identification, classification, and tracking. The radionuclide is injected into the vein after being consumed in very small amounts. Various radionuclides are transported to various organs via human blood. Examples of radionuclides include strontium-90, cesium-137, and radium-226. Some are produced artificially, either on purpose or as consequences from nuclear reactions, while others are found produced naturally in nature.
Briefing:Consider the fact that first order kinetics governs radioactive decay. So, keep in mind
ln [A]t=−kt + ln[A]₀ and by extension,
t[tex]\frac{1}{2}[/tex]=1n(2)/k
Now, let's derive the rate constant,
k=1n(2)/t[tex]\frac{1}{2}[/tex]
=0.116h⁻¹
Given
t=6h,
1n=Aτ/A₀
Aτ=12.5g
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Chevrolet Corvette Sting Ray developed 360 horsepower and hada displacement of 327 cubic inches. Express this displacement inliters (L) by using only the conversions 1 L = 1000 cm3 and1 in. = 2.54 cm.
The displacement in litres is 5.36 L.
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects.
Horsepower = 360
Displacement 327 inches³
1 L = 1000 cm³
1 inch = 2.54 cm
Displacement in litres is =
First find displacement in cubic centimetre =
= d = 327 inch³ X (2.54 cm / 1m)³
= d = 327 X 2.54
= d = 5358.57 cm³
We know that, 1 L = 1000 cm³,
Thus,
The displacement in Litres is =
= d = 5358.57 cm³ X (1L / 1000 cm³)
= d = 5.36 L
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what maximum power can be radiated by a 15 cm -diameter solid lead sphere? assume an emissivity of 1.
This object's surface has an emissivity of 0.809.
Due to that,
15.0 cm in diameter
Climate = 112 °C
71.3 W Power
We must determine the area.
Using the area formula
Fill out the formula with the value
We must determine this object's surface's emissivity.
Using the emissivity formula
when area is A
Temperature is T.
Boltzmann constant of Stefan
power P
Fill out the formula with the value
As a result, this object's surface has an emissivity of 0.809.
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if a car is traveling westward and slowing down, what is the direction of the force on the car that causes it to slow down?
If the car is traveling westward and slowing down, then the direction of the force on the car that causes it to slow down must act to eastward direction.
If the car is slowing down, a force must be pulling in the direction opposite to its velocity. In the given situation the car is moving westward and slowing down, so force that will slow it down will act towards eastward i.e. acceleration will be in eastward direction and negative because direction of acceleration is opposite to its motion.
what is acceleration:
Acceleration is the rate at which velocity changes with time, in terms of both speed and direction. A point or an object moving in a straight line is accelerated if it speeds up or slows down.
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rank the objects from least to greatest mass, according to the stars that produce each. a. neutron star b. black hole c. white dwarf group of answer choices
Rank the objects from least to greatest mass, according to the stars that produce each:
White DwarfNeutron StarBlack holeA property of a body that is a measure of inertia is usually viewed as a measure of the amount of matter contained in the body that causes it to have weight in a gravitational field. Mass is a dimensionless quantity that describes the amount of matter in a particle or object.
The mass of an object is a measure of its inertial properties or the amount of matter it contains. The weight of an object is a measure of the force exerted on it by gravity, or the force required to support it. Mass can best be understood as the amount of matter present in an object or body. Everything around us has mass.
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which of the following defines a function f for which f(-x)=-f(x)
b) f(x) = cos(x) is the equation the satisfies the given conditon f(-x) = f(x)
To check for every function if they satisfies the conditon f(-x ) =f(x)
for option a)
f(x) = sin(x)
f(-x) = sin(-x)
=> -sin(x)
so in this option f(x) ≠ f(-x) so this option is not correct
for option b)
f(x)=cos(x)
f(-x) = cos(-x)
=> cos(x)
so in this option f(x) = f(-x) so this option is correct
for option c)
f(x) = log(x)
f(-x) = log(-x)
=> log(1/x)
so in this option f(x) ≠ f(-x) so this option is not correct
for option d)
f(x) = [tex]e^x[/tex]
f(-x) = [tex]e^-^x[/tex]
=> [tex]\frac{1}{e^x}[/tex]
so in this option f(x) ≠ f(-x) so this option is not correct
so only option B is correct.
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Complete question:
which of the following defines a function f for which f(-x)=-f(x)
a) f(x) = sin(x)
b) f(x) = cos(x)
c) f(x) = log(x)
d) f(x) = [tex]e^x[/tex]
White light separates into all the colors of the visible spectrum when it is passed through a?
White light separates into all the colors of the visible spectrum when it is passed through a prism.
A prism is an optical device made from transparent material, typically glass, that refracts light and separates it into its constituent wavelengths. This separation of light into its component colors is called dispersion. White light is composed of all the colors of the visible spectrum and when it is passed through a prism, the prism refracts the light and splits it into its individual colors.
When white light passes through a prism, the light is bent, or refracted, at different angles depending on its wavelength. The different wavelengths of light correspond to different colors in the visible spectrum, so when the white light is refracted, it separates into various colors.
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planet dreidel has a radius that is twice as large as the radius of earth and dreidel has three times the mass that earth has. harry weights 1200 n on earth, and is taken to the surface of planet dreidel, how much would harry weigh on the new planet?
Harry's weight is 1200 N on earth, then Harry's weight on the planet Dreidel is 355 N.
The force of gravity or the weight of an object on a planet is affected by the gravitational acceleration on that planet.
R[tex]__e[/tex] = R
R[tex]__p[/tex] = 2R
ρ[tex]__p[/tex] = 1/3 ρ[tex]__e[/tex]
w[tex]__e[/tex] = 1200 N
Determine the ratio of the mass of the earth to the mass of the planet through the relationship:
ρ = m/V → m = ρV
So:
[tex]\frac{me}{mp} = \frac{ p_e V_e}{p_pV_p}[/tex] (1)
Where is the volume of the planet. If both the earth and the planet are considered a ball, then it has the shape:
V = 4/3πR³
So, if we substitute the form above into the equation, we will get:
[tex]\frac{me}{mp} = \frac{p_eR_e^3}{p_pR_p^3} \\\\\frac{me}{mp} = \frac{p_eR_e^3}{1/3p_p(2R)^3}\\\\\frac{me}{mp} = \frac{3}{8}[/tex] (2)
The weight of an object is expressed as:
[tex]w =G\frac{mM}{r^2}[/tex]
If we take the comparison of the object's weight when it is on the earth's surface from the planet's surface it meets the:
[tex]\frac{w_e}{w_p} = \frac{me}{mp} (\frac{R_p +R}{R_e} )^2\\\\\frac{1200}{w_p} = \frac{3}{8} (\frac{2R +R}{R} )^2\\\\\frac{1200}{w_p} = \frac{3}{8} (\frac{9}{1} )^2\\\\w_p= \frac{1200 (8)}{3 (9)} \\\\w_p= \frac{9600}{27} = 355 N[/tex]
Hence Harry's weight on the new planet is 355 N.
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an object has a relativistic momentum that is 8.50 times greater than its classical momentum. what is its speed?
An object has a relativistic momentum that is 8.50 times greater than its classical momentum, then its speed is 8.5 × 10^8 m/s.
The relationship between an object's mass and velocity is known as its momentum. De Broglie wavelengths and kinetic energy can be derived from it. The classical momentum formula, p = mv, is no longer valid for objects moving at speeds close to the speed of light. Instead, in the case of relativity, p0 = mv where γ = 1/√1−(v/c)^2 is the Lorentz factor, The object's mass is m, and its speed is v.
p0 = mv/√1−(v/c)^2
We can define as: given that an object's relativistic momentum is 8.5 times larger than its classical momentum
p0 = 8.5p
p0 = mv/√1−(v/c)^2 = p/√1−(v/c)^2
8.5p = p/√1−(v/c)^2
1−(v/c)^2 = (1/8.5)^2
0.993 = v/3x10^8 = 8.5x10^8m/s
Hence the object's speed is 8.5 × 10^8 m/s.
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Angelina jumps off a stool. as she is falling, the earth’s gravitational force on her is larger in magnitude than the gravitational force she is exerting on the earth.a. Trueb. False
Answer:
False
Explanation:
By Newtons 3rd law, “To every action, there is an equal and opposite reaction", the answer is false because there is an equal weight and force upwards and downwards.
False.
Check Newton's 3rd law of motion: For every action, there is an EQUAL opposite reaction.
Check the formula for the strength of the grvitational force between two objects. The formula doesn't say anything about which object is m1 and which object is m2. The gravitational force is the same in both directions.
Angelina's weight on the Earth is the SAME as the Earth's weight on Angelina.
Also, the weight of a mosquito on Earth is the same as the Earth's weight on the mosquito.
A child sitting on the outer edge of a merry - go - round and a child sitting halfway between the outer edge and the center have the same angular velocity .
Answer: This is hard! I don't know for sure what is the answer but I think the answer is because the merry go round is moving at a certain speed???
Explanation: I don't know
a car that is initially moving at 7.50 m/s begins to accelerate forward uniformly at 0.550 m/s2 . a. how long after beginning to accelerate does it take the car to move 3.50 km? b. how fast is the car moving just as it has traveled 3.50 km
The car, which needs time after beginning to accelerate to move 3.5km, will take 100 seconds.
The car will move as it has traveled 3.50 km at 62.5 m/s.
Question A
Vi = car initial velocity
a = increase in velocity of the car per second
s = distance travelled by the accelerating car in time t
VF = velocity of the accelerating car at time t
Since acceleration is constant (accelerate forward uniformly from question), we will use kinematic equations.
Velocity Final = Vi + acceleration * time
s = Vi * t + 1/2 * acceleration * time²
Velocity Final² = Vi² + 2 * acceleration * distance (s)
Given from question
Vi = 7.5 m/s
a = 0.55 m/s²
s = 3.5km
t = ?
S = Vi * t + 1/2 * acceleration * time²
3500m = 7.5m/s * t + 1/2 * 0.55 * t²
0.55t² + 15t - 7000 = 0
We will use roots of a quadratic equation to find t
ax² + bx + c = 0
x = (-b ± (√b² - 4*ac)) / 2a
t = (-15 ± (√15² + 4 * 0.55 * 7000)) / 2 * 0.55
t = -15 ± 125 / 1.1
t = -140 / 1.1 ║t = 110 / 1.1
t = -127.27 ; 100
So, the equation of 0.55t² + 15t - 7000 = 0 is satisfied with two values of t = -127.27 & 100
Since, we are talking about time, we will eliminate minus value and we will use the positive value.
Therefore, the time needs to accelerate to move the car by 3.5km after the beginning is 100 seconds.
Question B
Given from question
S = 3.5km = 3500m
Velocity Final = ?
Velocity Final² = Vi² + 2*acceleration*distance (s)
Velocity Final² = 7.5² + 2 * 0.55 * 3500
Velocity Final² = 3,906.25
Velocity Final = 62.5m/s
Since we already found the accelerating car travelled 3500m in 100s. we could also use the other formula :
Velocity Final = Vi + acceleration * time
= 7.5 + (0.55*100)
= 62.5 m/s
Therefore, the car is moving 62.5m/s after traveled 3.50km.
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During laboratory investigation, students determined a large block of iron to have a density of 7.75 g/mL. If the block were to be cut in half, what would be the density of the smaller block?a. 7.75 g/mLb. 15.5 g/mLc. 3.88 g/mLd. 5.58 g/mL
If the density of the whole block is 7.75 g/mL, then the density of half of it is also 7.75 g/mL. (a)
The density of any substance is the same ... mass/volume ... no matter how big or small the sample is.
If the substance is pure, then its density is always the same. It doesn't matter whether your sample is a tiny drop in the middle of your finger-nail or a super-tanker full of it.
explain how the difference between the observed lapse rate and the adiabatic lapse rate causes air parcels to move toward or away from their original location
The observed lapse rate refers to the decrease in temperature with increasing tropospheric altitude. This is the temperature of the environment at different altitudes. It does not imply air movement. Adiabatic cooling relates only to rising air cooling by expansion.
The ambient Leakage Rate is the rate at which the air temperature increases. Our surroundings change as we rise into the atmosphere. Dry adiabaticity is when an unsaturated air mass expands and cools as it rises through the atmosphere or heats and compresses as it descends.
So the rising air cools slowly as it rises. The wet adiabatic decay rate is generally less negative than the dry adiabatic decay rate. If the environmental decay rate is greater than the dry adiabatic decay rate, the atmosphere is said to be absolutely unstable. This means that the rising air mass will always cool more slowly than its surroundings even if it is not saturated.
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assume that all of the potential energy went into kinetic right as it is about to hit the bottom. what would be the value for the kinetic energy?
The potential energy of an object diminishes while its kinetic energy rises. The increase in kinetic energy perfectly offsets the reduction in potential energy. The idea of work is another crucial one.
Before it touches the ground, where can you obtain kinetic energy?The mass of the object and the square of its velocity are directly related to its kinetic energy: K.E. = 1/2 m v2. When a mass is measured in kilograms and a speed is measured in meters per second, the kinetic energy is measured in kilogram-meters squared per second squared.
When a body is moving downward, what will happen to its kinetic and potential energy?due to the rule of conservation of energy, which states that total energy is always constant. Kinetic energy will therefore rise, whereas potential energy will fall.
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a gold ingot weighs 5.50 lbs. if the density of gold is 19.31 g/cm3, and the length and width of the ingot are 12.0 cm and 3.00 cm respectively, what is the height of the ingot? (1 lb
Given that a gold ingot has a mass of 5.50 lbs, a density of 19.31 g/cm3, and dimensions of 12.0 cm in length and 3.00 cm in width, the ingot's height is 3.59 cm.
Given that The density of the gold ingot (d) = 19.31 g/cm3
Mass of gold ingot (m) = 5.50 lbs
Converting lbs to g we have 1 lb = 453.592 g then
5.5lbs = 5.5 x 453.592 = 2494.756 g
Length of gold ingot (l) = 12cm
Width of gold ingot (w) = 3cm
Let height of gold ingot be hcm
Volume of gold ingot (v) = length x width x height
Generally, Density (d) = Mass(m)/Volume(v)
19.31 = 2494.756/12x3xh
h = 2494.756/12x3x19.31 = 3.59cm
Hence the height of gold ingot is 3.59cm
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The planet Earth orbits around the Sun and also spins on its own axis.
- Calculate the angular momentum, in kilogram meters squared per second, of the Earth in its orbit around the Sun.
- Calculate the angular momentum, in kilogram meters squared per second, of the Earth spining on its axis.
- How many times larger is the angular momentum of the Earth in its orbit than the angular momentum of the Earth spinning on its axis?\
In Newtonian physics, an object's mass and velocity are combined to form momentum, more precisely linear momentum or translational momentum. It is a mechanically accepted amount.
The angular momentum can be found by the formula:
L = m · v · r
Where:
mass of Earth = m = 10²⁴ ×5.972 kg
v = velocity of Earth around the Sun = 2.978×10⁴ m/s
r = distance from Sun = 1.496×10¹¹ m
Now, apply the formula:
L = 5.972×10²⁴ · 2.978×10⁴ · 1.496×10¹¹
= 2.661×10⁴⁰ kg·m²/s
The angular momentum of Earth in its motion around the Sun is 2.661×10⁴⁰ kg·m²/s.
It is a mechanically accepted amount. It has both a magnitude and a direction, making it a vector quantity. If an item has a mass of m and a velocity of v (also a vector quantity), then it has momentum of p.
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a coal-fired generating station with a thermodynamic efficiency of 35% produces an average output of 600 mwe. assume that coal is pure carbon and that cao is used to sequester all of the co2 that is produced. what is the mass of cao (in kg) required each year?
The mass of CAO required each year to sequester the CO2 produced by the coal-fired generating station is 1232 kg.
To determine the mass of CAO required each year to sequester the CO2 produced by a coal-fired generating station, we need to know the amount of CO2 produced by the station and the mass of CAO needed to sequester a given amount of CO2.
The amount of CO2 produced by the station can be calculated using the equation:
CO2_produced = (1 / efficiency) × energy_output
where CO2_produced is the amount of CO2 produced, efficiency is the thermodynamic efficiency of the generating station (35% in this case), and energy_output is the average output of the station (600 MWe in this case).
Plugging these values into the equation gives us:
CO2_produced = (1 / 0.35) × 600 MWe = 1714 MWe
To convert the energy output from megawatt-hours (MWh) to kilograms of CO2, we can use the conversion factor of 0.00053 kg CO2/MWh:
CO2_produced = 1714 MWe × 0.00053 kg CO2/MWh = 916 kg CO2
To determine the mass of CAO required to sequester this amount of CO2, we need to know the mass of CAO needed to sequester a given amount of CO2. The mass of CAO needed to sequester a given amount of CO2 can be calculated using the equation:
CAO_mass = CO2_mass / (CAO_molecular_weight / CO2_molecular_weight)
where CAO_mass is the mass of CAO needed to sequester the CO2, CO2_mass is the mass of CO2 to be sequestered, CAO_molecular_weight is the molecular weight of CAO, and CO2_molecular_weight is the molecular weight of CO2.
The molecular weights of CAO and CO2 are 56 g/mol and 44 g/mol, respectively. Plugging these values into the equation gives us:
CAO_mass = CO2_mass / (CAO_molecular_weight / CO2_molecular_weight) = 916 kg CO2 / (56 g/mol / 44 g/mol) = 1232 kg CAO
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