Answer:
Twice.
Explanation:
The momentum of an object is given by :
p = mv
Where
m is mass and v is the velocity
If the mass of the ball were doubled, m'=2m and v'=v=3 m/s
New momentum,
p'=m'v'
p'=2m × v
p'=2mv
or
p'=2p
So, the new momentum becomes twice the initial momentum.
A trough is 8m long and has ends which are isosceles triangles with height 3m and width (across the top) of 3m. The trough has a spout at the top of the tank with height 2m. The tank is full of water. (a) How much work is required to pump all of the water out of the tank? (NOTE that the density of water is rho = 1000 kg/m3 and the acceleration due to gravity is 9.8 m/s2 . (b) Suppose the pump breaks down after 4 × 105 J of work has been done. What is the depth of the remaining water in the tank
Answer:
(a) the work required to pump all of the water out is 1.0584 x 10⁶ J
(b) the depth of the remaining water in the tank is 1.87 m
Explanation:
Given;
length of trough, L = 8m
height of the isosceles triangle, h = 3m
width of the isosceles triangle, w = 3m
length of spout, b = 2m
The center mass of isosceles triangle is given by;
\(\frac{1}{3} \ of \ height \ of \ the \ triangle = \frac{1}{3} *3 = 1 \ m\) (this is the height below the top of the trough)
The total height water will be pumped, H = 1m + b
H = 1m + 2m = 3m
Determine the volume of the trough;
Volume of the trough = area of the triangle x length of the trough
Volume of trough = \(\frac{1}{2}*3*3*(8) = 36 \ m^3\)
(a) The work done in pumping all of the water out;
The work done in pumping all of the water out = potential energy of water at that height, H;
W = mgH
where;
m is mass of water
m = ρV
m = (1000 kg/m³) x (36 m³)
m = 36,000 kg
The work done = mgH
= 36,000 x 9.8 x 3
= 1.0584 x 10⁶ J
(b) after 4 × 10⁵ J of work has been done, the energy required to pump out the remaining water is given by;
ΔE = 1.0584 x 10⁶ J - 4 × 10⁵ J = 658,400 J
The depth of the remaining water is calculated as
658,400 J = mgh
where;
h is the height of the remaining water
658,400 = (36,000 x 9.8)h
658,400 = 352,800h
h = 658,400 / 352,800
h = 1.87 m
Please show work! A particle vibrates according to the equation x(t) = 0.65 cos(7.4 t)
Determine the frequency. Thanks!!
D. The frequency of the wave is determined 1.2 Hz.
What is frequency of a wave?The frequency of a wave describes the number of waves that pass a fixed place in a given amount of time.
General wave equation;
y = A cos(ωt)
where;
A is the amplitude of the waveω is the angular frequency of the waveFrom the given wave equation;
x(t) = 0.65 cos(7.4t)
ω = 2πf
7.4 = 2πf
f = 7.4/2π
f = 1.18 Hz
f = ≈ 1.2 Hz
Thus, the frequency of the wave is determined 1.2 Hz.
The correct option is D.
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A ball is launched from the surface of a planet. Air resistance and other frictional forces are neglected. The graph shows the position of the ball every 0.20 s.
a. Use this graph to determine:
I. The components of the initial velocity of the ball
II. The angle to the horizontal the ball was launched at
III. The acceleration of free fall on this planet.
b. Make a copy of the graph and draw two arrows to represent the velocity and the acceleration vectors of the ball at t = 1.0 s.
c. The ball is now launched under identical conditions from the surface of a different planet where the acceleration due to gravity is twice as large. Draw the path of the ball on your graph.
The angle to the horizontal the ball was launched at can be determined using trigonometry. Once you have the initial horizontal and vertical velocities, you can use the tangent function to calculate the launch angle.
What are the velocities ?Velocity is a physical quantity that describes the rate at which an object changes its position. It is a vector quantity, which means it has both magnitude and direction. The magnitude of velocity is the speed of the object, while its direction is the direction of motion.
What is time ?Time is a concept that refers to the sequence of events that occur in a continuous progression, from the past, through the present, and into the future. It is a way to measure the duration or the length of events or periods, and it is a fundamental aspect of our experience and understanding of the world.
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1. Which distance is the greatest?
O 7000 meters
O 99.99 meters
O 4.5 x 10³ meters
O 9.0 x 10² meters
Answer:
7000 meters
Explanation:
obviously 99.99 is less than 7000
10 cubed is 10 × 10 × 10, 1000, × 4.5 is 4500, which is less than 7000
10 squared is 100, which × 9 is only 900, which is also less than 7000
have a good day
Describe cytochrome c and how it can be used to provide evidence of evolutionary relationships. Then, explain how a scientist might determine which two species in a group of five species are more closely related using evidence from cytochrome c. You may use the evidence in the graph to support your answer.
Write 4-6 sentences:
Answer:
the c is in the cycle lab where they were created and then it cycles then it reoves it to the right.
Explanation:
In this example we will analyze the forces acting on your body as you move in an elevator. Specifically, we will consider the case where the elevator is accelerating. Suppose that you stand on a bathroom scale that rests on the floor of an elevator. (Don’t ask why!) Standing on the scale compresses its internal springs and activates a dial that indicates your weight in newtons. When the elevator is at rest, the scale reads 600 N. Suppose that the elevator is accelerating downward at 2.50 m/s2 . What does the scale read during the acceleration?
Answer:
The reading of the scale during the acceleration is 446.94 N
Explanation:
Given;
the reading of the scale when the elevator is at rest = your weight, w = 600 N
downward acceleration the elevator, a = 2.5 m/s²
The reading of the scale can be found by applying Newton's second law of motion;
the reading of the scale = net force acting on your body
R = mg + m(-a)
The negative sign indicates downward acceleration
R = m(g - a)
where;
R is the reading of the scale which is your apparent weight
m is the mass of your body
g is acceleration due to gravity, = 9.8 m/s²
m = w/g
m = 600 / 9.8
m = 61.225 kg
The reading of the scale is now calculated as;
R = m(g-a)
R = 61.225(9.8 - 2.5)
R = 446.94 N
Therefore, the reading of the scale during the acceleration is 446.94 N
three small balls each of mass 13.3g are suspended separately from a common point by silk threads, each 1.17m long. The balls are identically charged hang at the corners of equilateral triangle 15.3 cm on a side. Find the charge on each ball
The charge on each ball is 6.1 ×10⁻⁸ C.
What is force?The definition of force in physics is: The push or pull on a massed object changes its velocity.
An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude. A spring balance can be used to calculate the Force. The Newton is the SI unit of force. Force is a vector quantity and it has both magnitude and direction.
Let the balls have equal charge of q. Then, electrostatic force acting on each particle = √3 q²/r² dyne = √3 q²/15² dyne =0.0076 q².
Weight of each ball = 13.3 ×980 dyne = 13034 dyne.
As the electrostatic force and the weight acts perpendicular to each other.
Hence, 0.1/√3 = 0.0076 q²/13034
q = 6.1 ×10⁻⁸ C
Hence, the charge on each ball is 6.1 ×10⁻⁸ C.
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A car traveling 93 km/h is 240 m behind a truck traveling 74 km/h . How long will it take the car to reach the truck?
When the automobile arrives at the truck, the two distance functions are equal.
95t−0.210=75t
95t−75t=0.210
25t=0.210
t=0.210
25t=0.0084 hr = 0.504 min = 30.24 s
How fast does light travel in air?Light always moves in a straight line. Light in air travels at 1.0003 times the speed of light in a vacuum, slowing it from 299,792,458 metres per second to 299,702,547 metres per second.
Homepage for Einstein's Big Idea. E = mc2. It's the most famous equation in the world, "Mass multiplied by the speed of light squared equals energy." On the most fundamental level, the equation states that energy and mass (matter) are interchangeable; they are various manifestations of the same thing.
The distance a wave travels in a particular length of time, such as the number of metres per second, is referred to as its wave speed.
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Answer:
t=45.4717
Explanation:
Find the speed of the car
93km/h x 1000m/1km x 1hr/3600s =25.833
Find the speed of the truck
74km/h x 1000m/1km x 1hr/3600s=20.555
(25.833-20.555)t=240
t=45.4717
200N force was used to move 150N block on an inclined plane of length 12m with a height of 4m. The efficiency of the inclined plane will be
Answer:
42.1%
Explanation:
Applying,
E(%) = (M.A/V.R)×100............. Equation 1
Where E(%) = Percentage efficiency, M.A = mechanical advantage, V.R = Velocity ratio.
But,
M.A = L/E............... Equation 2
Where L = Load, E = Effort.
From the question,
Given: L = 150 N, E = 200 N
Substitute these values into equation 2
M.A = 200/150
M.A = 1.33
Also,
V.R for Inclined plane = 1/sin∅ =
V.R = 1/sin∅............... Equation 2
Where ∅ = angle of the inclined plane.
Where,
tan∅ = 4/12
∅ = tan⁻¹(4/12)
∅ = 18.43°
Therefore,
V.R = 1/sin18.43
V.R = 3.16.
Substituting the value of M.A and V.R into equation 1
E(%) = (1.33/3.16)×100
E(%) = 42.1%
At the end of a race a runner decelerates from a velocity of 9.00 m/s at a rate of 0.300 m/s2.
(a) How far does she travel in the next 15.0 s?
(b) What is her final velocity?
(a)In the next 15.0s, she traveled 101.250 m.
(b) 4.50 m/s is the runner's final speed.
Given:- initial velocity = 9m/s , deacceleration = 0.3 m/s2
distana(d), she moves in time (t)=15 s,
and we must determine this using the second equation of motion.
S = ut + 1/2 at2,
where s = the distance
u = initial velocity
t = time
a=-d = 0.300m/s
t=15.0
By putting all values in the formula above,
we have
d = (9.00)x(15.0)-1/2 (0.300) (15.0)²
d= 101.250 m.
In the next 15.0s, she traveled 101.250 m.
final speed (v) =?
from 1 Equation of Motion : v = u+at.
To solve, v=?
u=9.00 m/s
a= -d= 0.300 m/s²
t=15.0
v=u+at
v= 9 - 0.300 X15.0
= 4.50 m/s
4.50 m/s is the runner's final speed.
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Why are theories constructed
A) During the experiment
B) after data is collected from an experiment
C) before the experiment
D) after there is numerous data collected
Answer:
The correct answer is d.
Theories are constructed after there is numerous data collected during the experiment.
Explanation:
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what is the pressure of a tank of uniform cross sectional area 4.0m2 when the tank is filled with water a depth of 6m when given that 1 atm=1.013 x 10^5pa density of water=1000kgm-3 g=9.8m/s2
The pressure of the tank, when filled with water at a depth of 6 m, is approximately 580.124 atmospheres (atm). To calculate the pressure of the tank, one can use the equation: Pressure (P) = Density (ρ) × g × Depth (h)
Pressure (P) = Density (ρ) × g × Depth (h)
Given: Density of water (ρ) = 1000 kg/m³
Acceleration due to gravity (g) = 9.8 m/s²
Depth (h) = 6 m
Using the given values, one can calculate the pressure:
Pressure = 1000 kg/m³ × 9.8 m/s² × 6 m Pressure
= 58800 kg·m⁻¹·s⁻²
Now, let's convert the units to pascals (Pa) using the conversion 1 atm = 1.013 x \(10^5\) Pa:
Pressure = 58800 kg·m⁻¹·s⁻² × (1 atm / 1.013 x\(10^5\) Pa)
Pressure = 580.124 atm
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What is the correct clases for this drugs
Compazine
heelp me please
Explanation:
Compazine belongs to class of drugs called Antiemetic Agents, Antipsychotics, Phenothiazine.
How many light years are there in one mile?
Answer:
1.70108e-13 , this is the answer hope it helps
Which is the closeness of measured values to an accepted value of data?
O reproducibility
O significance
O accuracy
O precision
Answer:
O accuracy
Explanation:
Accuracy is the closeness of measured values to an accepted value of data. The accepted value of data is the true value.
The difference between the measured value and the true value is the error.
Precision is the ability to reproduce a given set of readings from an experiment. The nearness of results or measurements to on another is the precision. But the nearness of the measured value to the standard true value is a measure of its accuracy.person pulls a toboggan for a distance of 35.0 m along the snow with a rope directed 32.0o above the snow. The tension in the rope is 105.0 N. How much work is done on the toboggan by the tension force?
The amount of work done on the toboggan by the tension force of 105 N with a rope directed 32° above the snow is 3.12 KJ
W = F d cos θ
W = Work done
F = Force
d = Distance
θ = Angle between force and displacement vector
d = 35 m
F = 105 N
θ = 32°
W = 105 * 35 * cos 35°
W = 105 * 35 * 0.85
W = 3123.75 N m
W = 3.12 KJ
Work done is energy transferred to make an object move to a distance. Its unit is Joules which is denoted as J. It is the amount of work done by a force of 1 Newton to move a distance of 1 meter.
Therefore, the amount of work done on the toboggan by the tension force is 3.12 KJ
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What is the basic form of matter which cannot be broken down any further?
a compound
an element
a chemical reaction
an organism
Answer:
An element
Explanation:
An element is a pure substance that cannot be broken down any smaller.
Answer:
Element
Explanation:
Due to the fact that elements make up a compound and the compound and other elements allow is to be able to make a chemical reaction and organisms are made from elements
A jar of tea is placed in sunlight until it reaches an equilibrium temperature of 33.1 ◦C . In an attempt to cool the liquid, which has a mass of 185 g , 90.3 g of ice at 0.0 ◦C is added. At the time at which the temperature of the tea is 26.3 ◦C , find the mass of the remaining ice in the jar. The specific heat of water is 4186 J/kg · ◦ C . Assume the specific heat capacity of the tea to be that of pure liquid water. Answer in units of g.(2 significant digits pls)
90.1 g of ice are still present in the container. Calculating the heat received by the ice to melt and the heat lost by the tea is necessary until it reaches an equilibrium temperature of 33.1 ◦C .
How do you calculate the amount of heat needed to melt ice?Consider how much energy is required to melt one kilogramme of ice at zero degrees to produce one kilogramme of water at zero degrees. The energy required to melt one kilogramme of ice is determined by Q = mLf = (1.0 kg)(334 kJ/kg) = 334 kJ using the equation for a change in temperature.
In order to calculate how much heat is gained by the ice melting, we must first calculate how much heat is lost by the tea as it cools from 33.1 °C to 0.0 °C.
Tea loses the following amount of heat: q1 = m1CT1 = 0.185 kg) (4186 J/kg C) (33.1 C - 0.0 C) = 26298.93 J.
Heat required for ice to melt is given by the formula: q2 = m2Hf = (0.0903 kg)(333.55 kJ/kg) = 30062.56 J
We may set q1 = q2 to get the mass of ice still present because the system is in thermal equilibrium:
m2 = q2/Hf = 333.55 kJ/kg / 30062.56 J = 0.0901 kg
Finally, we round the mass to two significant digits and convert it to grammes:
m2 = 90.1 g
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A certain satellite travels in an approximately circular orbit of radius 8.8 × 10^6 m with a period of 6 h 12 min. Calculate the mass of its planet from this information.
The mass of the planet is 5.98 × 10^24 kg.
To calculate the mass of the planet, we can use Kepler's Third Law of Planetary Motion. This law states that the square of the period of revolution of a planet around the sun is directly proportional to the cube of the semi-major axis of its orbit.
First, we need to convert the period of the satellite's orbit to seconds. We know that there are 60 minutes in an hour, so the period can be expressed as (6 × 60 + 12) minutes, which equals 372 minutes. Multiplying this by 60 seconds, we get a period of 22,320 seconds.
Next, we need to find the semi-major axis of the orbit. In a circular orbit, the semi-major axis is equal to the radius of the orbit. Therefore, the semi-major axis is 8.8 × 10^6 m.
Now, we can apply Kepler's Third Law to calculate the mass of the planet. The formula is T^2 = (4π^2/GM) × a^3, where T is the period of revolution, G is the gravitational constant, M is the mass of the planet, and a is the semi-major axis of the orbit.
Rearranging the formula, we can solve for the mass of the planet:
M = (4π^2/G) × a^3 / T^2
Plugging in the values, we get:
M = (4 × π^2 / 6.67430 × 10^-11) × (8.8 × 10^6)^3 / (22,320)^2
Evaluating this expression, we find that the mass of the planet is approximately 5.98 × 10^24 kg.
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The first P-wave of an earthquake travels 5600 kilometers from the epicenter and arrives at a seismic station at 10:05 a.m. At what time did this earthquake occur?
Ahhhhhh I have a Regent's test in 2 hours and I don't know how to solve this type of question! Any help would be appreciated.
Anyone know what the steps to do this are? I dont even need an answer, just how to get to it. Thank you!
The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.
The p-waves travel with a constant velocity of 7 km/s
The time can be calculated by using the formula
t = d / v
where
T1 = 10:05 a.m
d is the distance they take to travel from the epicenter
v is the speed of the p-waves
On average, the speed of p-waves is
v = 7 km/s
d = 5600 km (given)
Substituting the values in the formula;
t = d / v
t = 5600 ÷ 7
t = 800 seconds
Converting into minutes,
t = 800 ÷ 60
t = 13.3
≈ 13 mins
T1 - 13 mins = T2
10:05 - 13 mins = 9.52 am
It means the earthquake occurred prior 13 minutes, that is at 9.52 am.
Therefore, the earthquake occurred at 9.52 am.
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Fill in the magnitude of net force for each case. Including the solution plss
Net forces in all above cases will be
A) F net = 0
B) F net = 1 N
C) F net = 5 N
D) F net = 5N
E) F net = 5 N
F) F net = 5 N
G) F net = 9.9 N
H) F net = 9.9 N
A) net force = upward force - downward force
= 4 - 4 = 0
B) net force = rightward force - leftward force = 4 - 3 = 1 N
C) net force
using Pythagoras theorem
F net = \(\sqrt{4^{2} + 3^{2} }\) = \(\sqrt{25}\) = 5 N
D) F net = \(\sqrt{-4^{2} + (-3)^{2} }\) = 5 N
E) balancing horizontal forces
rightward force - leftward force = 5 - 2 = 3 N
using Pythagoras theorem
F net = \(\sqrt{4^{2} + 3^{2} }\) = 5 N
F) balancing vertical forces
-5 + 2 = -3 N
using Pythagoras theorem
\(\sqrt{(-4)^{2} +(-3) ^{2} }\) = 5 N
G) using Pythagoras theorem
F net = \(\sqrt{7^{2} + 7^{2} }\) = 9.9 N
H ) balancing horizontal forces
10 - 3 = 7 N
\(\sqrt{7^{2} + 7^{2} }\) = 9.9 N
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what happens to the weight and mass of an object transported from earth to the moon
When an object transported from earth to the moon, its mass remains same but weight becomes 1/6th that on earth..
What is mass?In physics, mass is a quantitative measurement of inertia, a basic characteristic of all matter.
It essentially refers to a body of matter's resistance to changing its speed or location in response to the application of a force. The change caused by an applied force is smaller the more mass a body has.
What is weight?The amount of a body's weight indicates how much gravity is pulling on it. Weight is calculated using the method w = mg. Since weight is a force, it has the same SI unit as a force, which is the Newton (N).
So, mass of an object is intrinsic property of the object - it remains same in earth and in moon. But weight is the amount of gravitational attraction force. Moon has nearly 1/6th gravitational attraction field. So, the weight of the object on moon will be 1/6th that on earth.
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. A mass m is traveling at an initial speed of 25.0 m/s. It is brought to rest in a distance of 62.5 m by a net force of 15.0 N. The mass is
Answer:
m = 3 kg
The mass m is 3 kg
Explanation:
From the equations of motion;
s = 0.5(u+v)t
Making t thr subject of formula;
t = 2s/(u+v)
t = time taken
s = distance travelled during deceleration = 62.5 m
u = initial speed = 25 m/s
v = final velocity = 0
Substituting the given values;
t = (2×62.5)/(25+0)
t = 5
Since, t = 5 the acceleration during this period is;
acceleration a = ∆v/t = (v-u)/t
a = (25)/5
a = 5 m/s^2
Force F = mass × acceleration
F = ma
Making m the subject of formula;
m = F/a
net force F = 15.0N
Substituting the values
m = 15/5
m = 3 kg
The mass m is 3 kg
At last you are in a place where the heat and high density are no longer bothering you. However, although the density is very low, the gas around you is extremely high in temperature. In fact, the temperature is so high that it is emitting lots of X rays, which are creating cancer-causing mutations in your body at a rapid rate. Well, at least the view is great! There are no stars anywhere within about 10,000 light-years of you, but at slightly greater distances your sky is brightened by many beautiful, star-filled structures, some with majestic spiral shapes. Where are you?A) You are in the universe when it was about 200 million years old, just before galaxies began forming.B) You are in the center of the Milky Way Galaxy, looking outward into the Local Group.C) You are somewhere between the Andromeda and Milky Way galaxies in the Local Group.D) You are in intergalactic space within a rich cluster of thousands of galaxies.E) You are in the outskirts of a galaxy whose nucleus is a powerful quasar.
Since at slightly greater distances your sky is brightened by many beautiful, star-filled structures, some with majestic spiral shapes. The place that you are is option D) You are in intergalactic space within a rich cluster of thousands of galaxies.
What is the name of intergalactic space?There is virtually little chance that such primitive life might "infect" those planets because of the extremely low density of intergalactic space. Life without any form of star is a whole different - and even more speculative - topic. Processes outside of thermal equilibrium are essential to life.
Interstellar space is the term for the area between stars, whereas intergalactic space refers to the area between galaxies. The enormous empty voids between galaxies are these.
Therefore, an actual distance between galaxies is known as intergalactic space. The universe appears to have a foam-like structure, with groupings and clusters of galaxies lying along filaments that take up about a tenth of the entire amount of space, according to studies of the large scale distribution of galaxies.
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See full question below
At last you are in a place where the heat and high density are no longer bothering you. However, although the density is very low, the gas around you is extremely high in temperature. In fact, the temperature is so high that it is emitting lots of X rays, which are creating cancer-causing mutations in your body at a rapid rate. Well, at least the view is great! There are no stars anywhere within about 10,000 light-years of you, but at slightly greater distances your sky is brightened by many beautiful, star-filled structures, some with majestic spiral shapes. Where are you?
A) You are in the universe when it was about 200 million years old, just before galaxies began forming.
B) You are in the center of the Milky Way Galaxy, looking outward into the Local Group.
C) You are somewhere between the Andromeda and Milky Way galaxies in the Local Group.
D) You are in intergalactic space within a rich cluster of thousands of galaxies.
E) You are in the outskirts of a galaxy whose nucleus is a powerful quasar.
100 POINTS AND BRAINLIEST! What were the Magdeburg Hemispheres?
Answer:
Magdeburg hemispheres are two half-spheres of equal size. Placing them together traps air between them. This air is merely trapped, and not compressed, so the pressure inside is the same as the pressure of the atmosphere outside the spheres. The spheres thus pull apart with nearly no resistance.
The Magdeburg hemispheres are a pair of large copper hemispheres, with mating rims. They were used to demonstrate the power of atmospheric pressure. When the rims were sealed with grease and the air was pumped out, the sphere contained a vacuum and could not be pulled apart by teams of horses.
Cara is building a model of the solar system, which includes the Sun. She plans to include a written description to provide details about each piece in her model. In order for her model to be realistic, which of the following should she include in her representation of the Sun?
Answer:
she should write about how big is it and what the sun looks and how far away is it from earth.
the combined effect of all forces acting on an object is the ___ force
Answer:
net force
Explanation:
Consider two di˙erent streams of air, both with a relative humidity of 65%. Stream A has a temperature of 15◦C, and stream B has a temperature of 25◦C. The mass flow rate of dry air is the same in both streams. Which stream has a higher mass flow rate of water
Answer:
stream B.
Explanation:
Stream B has higher mass flow rate of water due to higher temperature i.e. 25◦C as compared to stream A which has a lower temperature i. e. 15◦C because temperature affect the viscosity of liquid. Higher temperature make liquid or water thinner which means lower viscosity. This thinning of liquid make easier the flow of water in the pipes or other medium with the increase in temperature.
The __________________ is the entire range of Electromagnetic Waves.
Absorption
Opaque
Electromagnetic Spectrum
Refraction
✧・゚: *✧・゚:* *:・゚✧*:・゚✧✧・゚: *✧・゚:* *:・゚✧*:・゚✧✧・゚: *✧・゚:* *:・゚✧*:・゚✧✧・゚: *✧・゚:* *:・゚✧*:・゚✧
Answer:
I think its the electromagnetic spectrum
19. Assume this process is 10% efficient, how much work is done by the gas expanding into the atmosphere?
The amount of work done by the gas is proportional to the pressure and the change in volume, as well as the efficiency of the process. If the pressure and volume are known, the work done by the gas can be calculated by multiplying these values by the efficiency of the process.
The amount of work done by a gas when it expands is proportional to the change in volume, pressure, and temperature. According to the first law of thermodynamics, the energy of a closed system is conserved, so the work done by the expanding gas is equal to the energy transferred from the gas to the environment in the form of work. Therefore, the work done by the gas is equal to the change in energy of the system. Assume that the process is 10% efficient. Then, only 10% of the energy available to the system is converted into work. This means that the remaining 90% of the energy is lost to the environment in the form of heat. As a result, the amount of work done by the gas expanding into the atmosphere is given by the formula
W = E x η, where W is the work done by the gas, E is the energy available to the system, and η is the efficiency of the process. The energy available to the system is determined by the difference between the internal energy of the gas before and after the expansion. The internal energy of a gas is determined by its temperature, pressure, and volume.
Assuming that the temperature and pressure are constant, the change in internal energy is proportional to the change in volume. Therefore, the energy available to the system is equal to the product of the pressure and the change in volume: E = P x ΔV, where P is the pressure of the gas and ΔV is the change in volume during the expansion. Substituting this equation into the formula for work, we get W = P x ΔV x η.
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