A water droplet falling in the atmosphere is spherical. assume that as the droplet passes through a cloud, it acquires mass at a rate proportional to ka where k is a constant (k>0) and a is its cross-sectional area. consider a droplet of initial radius r0 that enters a cloud with a velocity v0. assume no resistive force and show:
a. that the radius increases linearly with the time
b. that if r0 is negligibly small then the speed increases linearly with the time within the cloud.
Answers
A water droplet's radius will increase linearly with time if it acquires mass at a rate proportional to its cross-sectional area while passing through a cloud. This will cause its speed to also increase linearly with time within the cloud if its initial radius is very small.
a. As the water droplet falls through the cloud, it acquires mass at a rate proportional to its cross-sectional area. Since the droplet is initially spherical, its cross-sectional area is proportional to its radius squared, i.e., \(a \propto r^{2}\)
Therefore, the rate of increase in mass of the droplet is proportional to k times r². By Newton's second law, the acceleration of the droplet is proportional to the net force acting on it, which is equal to the gravitational force minus the buoyant force.
Since there is no resistive force acting on the droplet, the buoyant force is proportional to the volume of the droplet, which is proportional to r³. Thus, the acceleration of the droplet is proportional to \((k \times r^2) - (constant \times r^3)\). Therefore, the radius of the droplet will increase linearly with time as it falls through the cloud.
b. If the initial radius of the droplet, r0, is negligibly small, then its initial mass and velocity will also be small. As it falls through the cloud, it will acquire mass at a rate proportional to its cross-sectional area, which is proportional to r². Therefore, the rate of increase in mass will be proportional to r².
The acceleration of the droplet will be proportional to the net force acting on it, which is equal to the gravitational force minus the buoyant force. Since the initial velocity of the droplet is small, the buoyant force will also be small, and can be neglected. Thus, the acceleration of the droplet will be proportional to r².
By Newton's second law, the velocity of the droplet will increase linearly with time, since the acceleration is proportional to r², which is proportional to the rate of increase in mass of the droplet.
In summary, if a water droplet falling in the atmosphere acquires mass at a rate proportional to its cross-sectional area as it passes through a cloud, then its radius will increase linearly with time, and if its initial radius is negligibly small, then its speed will increase linearly with time within the cloud.
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Related Questions
the following expressions are for kinetic energy (k), spring potential energy (usp), and gravitational potential energy (ug): k
Answers
The kinetic energy of an object is equal to 1/2mv^2, where m is the mass of the object and v is the velocity of the object.
The spring potential energy of an object is equal to 1/2kx^2, where k is the spring constant and x is the displacement of the object from the equilibrium position. The gravitational potential energy of an object is equal to mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.
The Three Types of EnergyThere are three types of energy that are important in physics: kinetic energy, spring potential energy, and gravitational potential energy. Kinetic energy is the energy of motion, spring potential energy is the energy stored in a spring, and gravitational potential energy is the energy associated with gravity.
Kinetic energy is important because it is the energy that objects have when they are in motion. The kinetic energy of an object is equal to 1/2mv^2, where m is the mass of the object and v is the velocity of the object. This means that the kinetic energy of an object increases as the mass of the object increases or as the velocity of the object increases.
Spring potential energy is important because it is the energy that is stored in a spring. The spring potential energy of an object is equal to 1/2kx^2, where k is the spring constant and x is the displacement of the object from the equilibrium position. This means that the spring potential energy of an object increases as the spring constant increases or as the displacement of the object from the equilibrium position increases.
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Is torque only produced when the force is applied perpendicular to the moment arm?
Answers
The Torque is only produced when the force is applied perpendicular to the moment arm.
What is moment of force?The equal and opposite force acting at a point from the axis of rotation is called the moment.
M = F x r
Moment of force is also called as Torque.
Moment arm is the distance of the point of application of force from the axis of rotation of the body.
Thus, the perpendicular component only, produces the torque.
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need help asap, thank you !
In the absence of air resistance, a projectile launched at an angle of 33 above the horizontal will have the same range as a projectile launched at which of the following angles? O 38 O 57⁰ 0:45. 07
Answers
A projectile is launched at an angle of 33⁰ above the horizontal, then the projectile launched at an angle of 90 - 33 = 57⁰ will have the same range as the projectile launched at 33⁰. The correct option is (B) 57⁰.
In the absence of air resistance, a projectile launched at an angle of 33 above the horizontal will have the same range as a projectile launched at an angle of 57⁰.
The range of a projectile can be determined by using the range formula.
R = ((v^2 * sin(2θ))/g) Where
R is the range of the projectile,
v is the velocity of the projectile,
θ is the angle at which the projectile is launched, and
g is the acceleration due to gravity.
In the absence of air resistance,
the horizontal component of velocity of a projectile remains constant throughout the flight.
So, the range of a projectile depends only on its initial velocity and the angle at which it is launched.
If a projectile is launched at an angle θ,
the time of flight of the projectile can be calculated by using the following formula:
T = (2v * sin(θ))/g
The maximum height reached by the projectile is given by the formula:
H = (v^2 * sin^2(θ))/2gIf a projectile is launched at an angle θ, then the range of the projectile will be the same as the range of the projectile launched at an angle of (90 - θ).
So, if a projectile is launched at an angle of 33⁰ above the horizontal, then the projectile launched at an angle of 90 - 33 = 57⁰ will have the same range as the projectile launched at 33⁰.
Therefore, the correct option is (B) 57⁰.
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course: Electricity and magnetism
6.1B A current of 10 amp flows through a wire of 1 mm² cross section. If the density of charge carriers in the wire is 1027/m³, find the average drift velocity of the electrons.
Answers
The average drift velocity of the electrons is is approximately 6.25 x 10^6 m/s.
To find find the average drift velocity of the electrons, we have to make use of the drift velocity formula. The drift velocity formula is used to relate the average drift velocity of charge carriers in a conductor to the applied electric field. It is used to understand the motion of electrons when an electric current is flowing.
The drift velocity formula is:
\(I = nAvq\)
Where:
I is the current (in Amperes),
n is the density of charge carriers,
A is the cross-sectional area of the wire,
v is the average drift velocity of electrons,
q is the charge of an electron.
In this case, we have been given current as 10A, cross-sectional area of the wire is 1mm². The density of charge carriers in the wire is 1027/m³. So, by substituting all the given identities in the equation and rearranging the equation to find out "v", we get:
\(v = I / (nAq)\)
\(v = (10 A) / ((10^{27} /m^{3} ) * (1 * 10^{-6} m^{2}) * (1.6 * 10^{-19} C))\)
\(v = (10 A) / (1.6 * 10^{-12} A * m^{2} * C * 10^{27} /m^{3} )\)
\(v = 6.25 * 10^{6} m/s\)
Therefore, the average drift velocity of electrons in the wire is approximately 6.25 x 10^6 m/s.
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Answer:
Average drift velocity of the electrons is Approx. 6.25*10^6 m/s.
Given, Current= 10A
Cross sectional area = 1mm^2
Density of charge= 1027/m^3
Formula to find velocity= I/(nAq)
= 10/(1027*1*10^-6*1.6*10^-19)
=6.25*10^6m/s
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the answer will b bc grass hopppers cant swin
Answers
Answer:
ya thats right they cant swim
Explanation:
What is the relationship between the distance objects and the gravitational force between them.
Answers
Answer:
It the gravitational pull decreases as the objects distance increases
Explanation:
T/F: the schmidt corrector plate largely cures spherical aberration, giving a wide, flat field of view.
Answers
True, the Schmidt corrector plate largely cures spherical aberration, providing a wide, flat field of view.
The Schmidt corrector plate is an optical component that is specifically designed to address spherical aberration, which is a common issue in optical systems. Spherical aberration occurs when light rays entering a lens or mirror at different distances from the optical axis are not focused at the same point, resulting in a blurry or distorted image. By using a Schmidt corrector plate, the light rays are corrected before they reach the primary mirror, significantly reducing spherical aberration and producing a clearer, sharper image.
This optical innovation allows for a wide, flat field of view, which is particularly useful in applications such as astronomy and astrophotography, where capturing large areas of the sky with minimal distortion is crucial. The use of a Schmidt corrector plate in a telescope, for example, can greatly enhance the clarity and detail of celestial objects, enabling astronomers to study them more effectively.
In summary, the Schmidt corrector plate is a vital optical component that effectively addresses spherical aberration and contributes to a wide, flat field of view in various optical systems.
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Provide a conceptual definitions for each of the following variables used to describe waves: wavelength, period, velocity, amplitude, frequency, intensity, and phase.
Answers
The conceptual definitions for terms describing waves are:
1. Wavelength: The distance between two consecutive points in a wave that are in the same phase, usually measured from crest to crest or trough to trough.
2. Period: The time it takes for one complete cycle of a wave to pass a given point, usually measured in seconds.
3. Velocity: The speed at which a wave propagates through a medium, typically measured in meters per second (m/s).
4. Amplitude: The maximum displacement of a point in a wave from its equilibrium position, often representing the energy or intensity of the wave.
5. Frequency: The number of complete wave cycles that occur in one second, typically measured in hertz (Hz).
6. Intensity: The amount of energy carried by a wave per unit time and area, often related to the amplitude and frequency of the wave.
7. Phase: The position of a point in a wave relative to the wave's cycle, usually measured in degrees or radians and used to describe the timing relationship between different parts of a wave or between multiple waves.
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For what value of v does γ = 1.0205? Observe that for speeds lower than this value, time dilation and length contraction are effects amounting to less than2.05%.
Answers
The value of v for which γ = 1.0205 is approximately 0.197c.
The Lorentz factor γ is given by γ = 1/√(1 - v^2/c^2), where c is the speed of light. We can solve for v by setting γ equal to 1.0205 and solving for v. This gives us v = √(1 - 1/γ^2) * c.
Substituting γ = 1.0205 gives v ≈ 0.197c. This means that for speeds lower than 0.197c, the effects of time dilation and length contraction are less than 2.05%. In other words, if an observer is traveling at speeds below 0.197c, they will experience only small differences in time and length measurements compared to a stationary observer. However, as the speed approaches the speed of light, these effects become more and more significant, leading to phenomena like time dilation and length contraction.
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Assume a simply supported beam with span of 15m. It will be exposed to a dead load of 20kN/m (including self-weight) and a live load of 2kN/m along the full span. At the same time, it will be experiencing a concentrated dead load of 23kN + a live load of 1kN at midspan, as well as an additional dead load of 15kN located at 4m from the right support.
The beam has a rectangular cross-section with a width of 600mm and total height of 1000mm. The beam is reinforced with 10- 25M tensions bars at effective depth of 920 mm. The maximum aggregate size used is 20mm, and has the following material properties: f’c = 25MPa ,fy = 400 MPa.
Please perform the following task:
1) Draw the governing shear and bending moment diagram for the factored load.
2) Calculate the moment resistance of the cross section.
3) Comment if this cross section is adequately designed to resist the factored bending moment. (LRFD)
Answers
The values of all sub-parts have been obtained.
(1). The maximum factored load the beam can withstand is 45.2 kN/m.
(2). The moment resistance of the cross-section is 291735.65 Nm.
(3). The factored moment demand is 27939.6 Nm
1) To draw the governing shear and bending moment diagram for the factored load, we need to first calculate the maximum factored load that the beam can withstand.
The maximum factored load on the beam is given by:
Dead Load = 20 kN/m + 15 kN
= 35 kN/m.
Live Load = 2 kN/m + 1 kN
= 3 kN/m.
Total Factored Load = 1.2 x Dead Load + 1.6 x Live Load
= 1.2 x 35 kN/m + 1.6 x 3 kN/m
= 45.2 kN/m.
The maximum factored load the beam can withstand is 45.2 kN/m.
The shear force and bending moment diagrams for the given factored load can be obtained as shown below:
Shear Force Diagram:
Bending Moment Diagram:
2) To calculate the moment resistance of the cross-section, we can use the formula:
MR = σst A'(d - a/2) + 0.85f'c A''(d - a/2)
Where, σst = yield stress of tension steel [σst = fy / γst],
γst = safety factor for tension steel [γst = 1.15A']
A' = area of tension steel, [A'' = b(d - a)].
Where,
b = width of the beam [b = 600 mm],
d = total height of the beam [d= 1000 mm],
a = effective depth of tension steel [a = 920 mm]
f'c = compressive strength of concrete [f'c = 25 MPa],
MR = σst A'(d - a/2) + 0.85f'c A''(d - a/2)
MR = (400 / 1.15) x 10 x (1000 - 920/2) + 0.85 x 25 x 590 x (1000 - 920/2)
MR = 291735.65 Nm
The moment resistance of the cross-section is 291735.65 Nm.
3) To check if this cross-section is adequately designed to resist the factored bending moment (LRFD), we need to calculate the factored moment demand and compare it with the moment resistance.
The factored moment demand is given by:
MF = ϕ x Mu
Where,ϕ = resistance factor = 0.9, Mu = factored bending moment
Mu = 1.2 x Dead Load x L2 / 8 + 1.6 x Live Load x L2 / 8 + 1.2 x (Dead Load + Live Load) x L2 / 2
= 1.2 x 35 x 152 / 8 + 1.6 x 3 x 152 / 8 + 1.2 x 38 x 152 / 2
= 31044 Nm
MF = ϕ x Mu
= 0.9 x 31044
= 27939.6 Nm
The factored moment demand is 27939.6 Nm, which is less than the moment resistance of the cross-section, i.e., 291735.65 Nm.
Therefore, this cross-section is adequately designed to resist the factored bending moment.
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the smooth and accurate execution of movement as conceived in the mind and executed by the body parts
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The smooth and accurate execution of movement as conceived in the mind and executed by the body parts describes ; The central nervous system.
Although your question is incomplete an answer is provided which falls within the scope of your question
The human brain receives, interprets and transfer signals it deduces from the impulses it received to the various sense organs ( body parts ) for execution. and this process involves coordination within the nervous system.
The central nervous system is a category of the Nervous system of a human and it consists of the spinal cord and the human brain. and the peripheral nervous system
Hence we can conclude the smooth and accurate execution of movement as conceived in the mind and executed by the body parts describes, The central nervous system.
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A jet is flying at a velocity of 30m/s. It speeds up to 150m/s in 40s.
Calculate its acceleration.
Answers
Answer:
acceleration= Final velocity - initial velocity/time taken
or u can put the formula by their symbols
a= V-u/t
a=150m/s - 30m/s= 120
120/40s= 3s
so the answer is 3s.
An old woman is worried about time. She walks at a rate of 2 meters per second and travels a
distance of 454 meters. How long does it take her to complete the motion?
Please help ASAP!! BRAINLIST please explain thankyou!!!
Answers
Answer:
227 seconds.
Explanation:
Speed is equal to distance divided by time. s = d/t
We can rearrange this algebraically to solve for the time it will take to cover a certain distance at a certain speed. Time is equal to distance divided by speed. t = d/s
Then we substiture our known values for the variables and solve for our unknown.
t = 454m / 2m/s = 227s
Answer:
If the lady is traveling 2 meters per second and she travels 454 meters then you will have to divide 454 by 2 to get the amount of time she walked.
454 divided by 2 = 227
This means that the lady traveled for 227 seconds or about 3.78 minutes.
If your face is 62 cm in front of a plane mirror, where is the image of your face located?
62 cm in back of the mirror
62 cm below the mirror
62 cm in front of the mirror
31 cm in front of the mirror
Answers
\( \huge \mathrm{ Answer࿐ }\)
The correct option is :
\(\hookrightarrow\) 62 cm in back of the mirror
_____________________________
Explanation :Plane mirror always make a virtual and erect Image which is as far from the mirror as the object is !
_____________________________
\(\mathrm{ \#TeeNForeveR}\)
A motorboat sets out in the direction N 62°18' E. The speed of the boat in still water is 36.9 mph. If the current is flowing directly south, and the actual direction of the motorboat is due east, find the speed of the current and the actual speed of the motorboat.
Answers
Therefore, the speed of the current is 12.8 mph, and the actual speed of the motorboat is 39.7 mph.
To solve this problem, we can use the formula:
v = d/t
where v is the speed of the boat in still water, d is the distance traveled by the boat, and t is the time taken.
Let’s assume that the speed of the current is c and the actual speed of the motorboat is m. Then we can write:
m×cos(62°18') = v + c
m×sin(62°18') = 0
where v = 36.9 mph.
Solving these equations for m and c, we get:
m = 39.7 mph
c = 12.8 mph
Therefore, the speed of the current is 12.8 mph, and the actual speed of the motorboat is 39.7 mph.
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Which of the following actions will induce an emf in a conductor?
a. Move a magnet near the conductor.
b. Move the conductor near a magnet.
c. Rotate the conductor in a magnetic field.
d. Change the magnetic field strength.
e. all of the above
Answers
Answer:
b . Move the conductor near a magnet
Answer:
(e) all the above....
Explanation:
That's all
Cause you know.......
compared to spiral galaxies, elliptical galaxies are:
Answers
flat disk like shape
________________
o0o0o0o0o0o0o0o0
A racecar traveling at a velocity of 18.5 m/s, accelerates at a rate of 2.47 m/s2 and covers a distance of 79.78 m. Determine the final velocity of the racecar.
Answers
Answer:
The final velocity of the race car is 27.14 m/s
Explanation:
Given;
initial velocity of the race car, u = 18.5 m/s
acceleration of the race car, a = 2.47 m/s²
distance covered by the race car, s = 79.78 m
Apply the following kinematic equation to determine the final velocity of the race car.
v² = u² + 2as
v² = (18.5)² + 2(2.47)(79.78)
v² = 736.363
v = √736.363
v = 27.14 m/s
Therefore, the final velocity of the racecar is 27.14 m/s
Can someone Plzzz help meee.
Answers
solid...............
A given mass of gas has a pressure of 80N/m² at a temperature of 40°C. if the temperature is reduced to 27°C with the volume remaining constant, the new pressure is A. 46.ON/m² B. 75.ON/m² C. 80.0N/m² D. 85.0N/m²
Answers
Answer:
Correct Answer: Option B
Explanation:
Explanation
P1/T1 = P2/T2
80/(273+47) = P1/(273+27) = 75Nm-2
Answer: 75.0 Nm^-2
Explanation:
P1/T1 = P2/T2 80/(273+47) = P1/(273+27) = 75Nm-2
The specific heat capacity of oxygen is 918 J/kg °C. The specific heat capacity of water is 4181 J/kg °C. Which substance will require more energy to raise its temperature by 1°C?
Oxygen and water
Answers
Answer:
Water
Explanation:
Answer:
So, water has a specific heat of exactly 1.00 calorie per gram per °C. Because one calorie is equal to 4.18 J, it takes 4.18 J to raise the temperature of one gram of water by 1°C. In joules, water's specific heat is 4.18 J per gram per °C.
The answer is water.
how is this possible
Answers
Answer: I'm sorry what's wrong with your money
Explanation:
Answer: LOL YO I HAVE 5K IN GROUP FUNDS
Explanation:
Explain how the length of a convex mirror is obtained by the coincidence method
Answers
By adjusting the position of the convex mirror until the images formed by both mirrors coincide, we can obtain the length of the convex mirror.
The length of a convex mirror can be obtained using the coincidence method. This method involves the use of a concave mirror and a convex mirror, along with an object placed between them. The object should be placed at the same distance from both mirrors, so that the images formed by the two mirrors coincide.
To use the coincidence method to determine the length of a convex mirror, we need to first find the focal length of the concave mirror. This can be done by placing an object at a known distance from the mirror and measuring the distance between the mirror and the image formed. Using the formula for the focal length of a concave mirror, we can then calculate the focal length.
Once we know the focal length of the concave mirror, we can use it along with the convex mirror to obtain the length of the convex mirror. We place the object between the two mirrors, at the same distance from both mirrors. We then adjust the position of the convex mirror until the images formed by both mirrors coincide. The distance between the two mirrors is then equal to the sum of the focal lengths of the two mirrors, which gives us the length of the convex mirror.
In conclusion, the coincidence method is a useful way to determine the length of a convex mirror. It involves the use of a concave mirror, a convex mirror, and an object placed at the same distance from both mirrors.
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Please help this is really confusing
Answers
A resistor has a resistance of 120 12. How much current is in the resistor if there is a potential difference of 12.0V across the resistor?
A. 160 A
B. 0.43 A
C. 0.10 A
D. 2.3 A
Answers
Answer:
c 0.10
Explanation:
V=IR
12.0V=I x 120.12ohms
I=0.099
I= 0.10
A lawn mower that weighs 196 N is pushed along the ground at a constant speed with a force of
240 N applied to the handle, which makes an angle of 40 degrees with the ground. With what force does the ground push upward on the mower?
Answers
Answer:(i) The magnitude of the force that is pressing the lawn-mower directly into the ground is 25 N
(ii) The magnitude of the effective force that moves the mower forward is approximately 43.3 N
(iii) Because there are no net downward force acting on the lawn-mower
Explanation:
An iron block of mass 10 kg rests on a wooden plane inclined at 30° to the horizontal. It is found
that the least force parallel to the plane which causes the
block to slide up is 100 N. Calculate the coefficient of friction
between the two surfaces.
Answers
I assume the 100 N force is a pulling force directed up the incline.
The net forces on the block acting parallel and perpendicular to the incline are
∑ F[para] = 100 N - F[friction] = 0
∑ F[perp] = F[normal] - mg cos(30°) = 0
The friction in this case is the maximum static friction - the block is held at rest by static friction, and a minimum 100 N force is required to get the block to start sliding up the incline.
Then
F[friction] = 100 N
F[normal] = mg cos(30°) = (10 kg) (9.8 m/s²) cos(30°) ≈ 84.9 N
If µ is the coefficient of static friction, then
F[friction] = µ F[normal]
⇒ µ = (100 N) / (84.9 N) ≈ 1.2
Which body composition test would be the best to measure the effects of a vitamin d supplement and a 6-month weight-training program in teenage girls?
Answers
The body composition test that would be the best to measure the effects of a vitamin D supplement and a 6-month weight-training program in teenage girls is Dual-energy X-ray absorptiometry (DEXA) scan.Dual-energy X-ray absorptiometry (DEXA) scan would be the best to measure the effects of a vitamin D supplement and a 6-month weight-training program in teenage girls.
It is one of the most accurate ways to measure body composition as it can differentiate between muscle, bone, and fat tissues within the body. A DEXA scan provides detailed information about fat and lean mass distribution throughout the body. It can also show changes in bone density that might occur as a result of increased physical activity and/or supplementation with vitamin D.
If vitamin D levels are insufficient in teenage girls, they may be more prone to stress fractures and other bone-related injuries. Furthermore, resistance training programs can help improve bone density and reduce the risk of injury. This is why measuring body composition changes in teenage girls after a vitamin D supplement and weight training program is essential.
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When you have more than one battery in a circuit you __________ (add, subtract, multiply, divide) the values of the individual batteries to get the overall voltage of the circuit.
Answers
Answer: When you have more than one battery in a circuit, you add the values of the individual batteries to get the overall voltage of the circuit.
Explanation:
1. What innate capacities do newborns have?