Answers
The constant angular acceleration (in rad/s2) of the centrifuge is 194.02 rad/s².
Constant angular acceleration
Apply the following kinematic equation;
ωf² = ωi² - 2αθ
where;
ωf is the final angular velocity when the centrifuge stops = 0ωi is the initial angular velocity θ is angular displacementα is angular accelerationωi = 3400 rev/min x 2π rad/rev x 1 min/60s = 356.05 rad/s
θ = 52 rev x 2π rad/rev = 326.7 rad
0 = ωi² - 2αθ
α = ωi²/2θ
α = ( 356.05²) / (2 x 326.7)
α = 194.02 rad/s²
Thus, the constant angular acceleration (in rad/s2) of the centrifuge is 194.02 rad/s².
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Related Questions
PLEASE HELP!!!!
1. What is 'red shift'?
2. What is 'blue shift'?
3. What is the dopple shift/effect?
4. What is the difference between the blue shift and the red shift?
Answers
Hi There. So the 'red shift' and the 'blue shift' are all apart of the Doppler shift. But they are polar opposites.
Question 1:
Red shift means the frequency and associated wavelength of visible light has shifted toward the red part of the spectrum of EM radiation, as opposed to blue shift which means the frequency and associated wavelength has shifted toward the blue part of the spectrum. Red shift is a lower frequency / longer wavelength, and blue shift is a higher frequency / shorter wavelength. You could be wondering what causes red shift, and there are a few reasons for it. One of the causes is relativistic motion, often known as the Doppler Effect, which was initially noticed with sound waves and moving observers and sources. The light looks redder as a source moves away from an observer (they move away from each other, regardless of which one is traveling with respect to some reference frame), and bluer as the two move closer to one another. The term gravitational red shift refers to another reason. As a photon (a quantum of EMR) moves away from the surface of a mass aggregation, such as a star, the intensity of the field's magnitude decreases by the square of the distance, and the photon accelerates. A photon experiences the reverse consequence as it passes through a g-field with a rising magnitude of pressure, but there is considerable disagreement over what happens to the little amount of kinetic energy obtained from the field. Gravitational red shift is then seen. EM in nature is another factor. The phosphor coating on the interior of the glass tube is struck by UV radiation that is emitted by the arc carried via the mercury vapor in fluorescent lamps. The UV photons' energy is absorbed by the phosphor coating, which subsequently emits heat and visible light. The transition from UV to visible light and heat is a classic red shift. The identical red shift phenomena is explained by three separate methods.
Question 2:
The displacement of the spectrum to shorter wavelengths in the light coming from distant celestial objects moving toward the observer. Ever notice the sound of a car or train is higher pitched when it's heading toward you, and becomes lower as it goes away? Light does the same thing. If you look at an object that's heading away from you quickly enough, it will appear more red than it actually is. If something is heading towards you, it will appear more blue. This becomes very useful for astronomers; if you know a certain object's composition, you can tell how fast it's moving by the color change.
Question 3:
The apparent difference between the frequency at which sound or light waves leave a source and that at which they reach an observer is known as the "Doppler effect," and it is caused by the relative velocity of the wave source and the observer. This phenomena is used in astronomical observations, Mössbauer effect studies, radar, and modern navigation. The earliest description of it was published in 1842 by Austrian scientist Christian Doppler. The apparent pitch of a blowing horn is a fantastic illustration of the Doppler effect since it increases as you move closer to it before decreasing as you pass it. Similar to this, when a star is observed from Earth, its light shifts toward the violet end of the spectrum (higher frequency or shorter wavelength) when the star and Earth are getting closer and toward the red end of the spectrum (lower frequency or longer wavelength) when the star and Earth are getting farther apart. The Doppler effect is often used in contemporary models of the cosmos to study stellar motion and search for double stars. see redshift as well.
Question 4:
Blueshift is the name for an object's light while it is travelling toward us, and redshift is the name for an object's light when it is going away from us.
Thank you,
Eddie
Three professional wrestlers are fighting over a champion’s belt, and each exerts a force on the belt. Wrestler 1 exerts a force F1=40.0 N in the +x-direction, wrestler 2 exerts a force F2=80.0 N in the negative y-direction, and wrestler 3 exerts a force F3=60.0 N at an angle of 36.9° counterclockwise (anticlockwise) from the +x-direction.
Answers
The resultant force of the three professional wrestlers on the championship belt is 98.35 N.
Component of the forces in x - direction
The component of the forces in x -direction is calculated as follows;
Fx = 40 N + 60(cos 36.9)
Fx = 40 N + 47.98 N
Fx = 87.98 N
Component of the forces in y - directionThe component of the forces in y -direction is calculated as follows;
Fy = -80 N + 60(sin 36.9)
Fy = -43.95 N
Resultant forceR = √Fx² + Fy²
R = √( 87.98² + 43.95²)
R = 98.35 N
Thus, the resultant force of the three professional wrestlers on the championship belt is 98.35 N.
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A thin-walled hollow sphere has a radius 4cm from the center
of the sphere, the eletric field points radially inward and
has a magnitude of 1.5 × 10^4NC^-1 How much charge is on the surface
Answers
A thin-walled hollow sphere has a radius of 4 cm from the center
of the sphere, the electric field points radially inward and
has a magnitude of 1.5 × 10⁴ N/C then the charge on the surface would be 2.6690×10⁻⁹ C
What is an electric charge?Charged material experiences a force when it is exposed to an electromagnetic field due to the physical property of electric charge. You can have a positive or negative electric charge.
The electric field inside a spherical shell is given by the formula
E = q/4πεr²
where q is the charge on the surface
r is the radius of the sphere
ε is the electrical permeability
By substituting the respective values in the given formula
1.5 × 10⁴ = q/4π(8.85✕ 10⁻⁻¹²)(.04²)
q = 2.6690×10⁻⁹ C
Thus, the charge on the surface would be2.6690×10⁻⁹ C
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Warm-Up
Type your response in the box.
When the Moon comes directly between the Sun and Earth, a solar eclipse occurs. The eclipse may be a total eclipse,
where the Sun is completely blocked by the Moon, or an annular eclipse, where you can see a ring of sunlight
surrounding the Moon. What do you think makes a total eclipse occur instead of an annular eclipse?
Answers
Answer: Both total and annular eclipses depend on the distances between Earth, the Moon, and the Sun. A total solar eclipse occurs when the Moon is closer to Earth, thus taking up a larger portion of the sky. The Moon is then able to cover the entire Sun.
Explanation: Edmentum answer
It's your first day on the job without your mentor as a member of mission control.
Your shift begins and your counterpart, who happens to be in their 10th year in this
position, speaks to you for about 45 minutes as they end their shift and you begin
yours. What were they talking to you about?
getting you up to date with recent mission developments
sanitation protocol that all employees must memorize
connecting you with each of the astronauts in space at the time
how to change settings for each system that's in use
Answers
Explanation:
getting me up to date with recent mission development
Consider the f(x) = cos(Bx) function shown in the figure in blue color. What is the value of parameter B for this function? This parameter is called angular frequency in physics and it is denoted by ω.
As a reference the g(x) = cos(x) function is shown in red color, and green tick marks are drawn at integer multiples of π.
Answers
The value of parameter B (angular frequency) for this function is 2.7.
What is amplitude of a wave?
The amplitude of a wave is the maximum displacement of the wave. It can also be described at the maximum upward displacement of a wave curve.
f(x) = Acos(Bx)
where;
A is amplitude of the waveB is angular frequency of the waveWhat is angular frequency of a wave?Angular frequency is the angular displacement of any element of the wave per unit time.
From the blue color; at y = -0.9, x = -7.5 cm
-0.9 = cos(-7.5B)
7.5B = arc cos (0.9)
7.5B = 2.7
B = 7.5/2.7
B = 2.7
Thus, the value of parameter B (angular frequency) for this function is 2.7.
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Write a properly formatted hypothesis statement to answer this question: How does the amount of salt added to ice affect the rate at which the ice will melt?
Specify how you plan to change the independent variable by using terms such as increase or decrease. Also, specify how the dependent variable will change in response by using terms such as increase, decrease, or stays the same.
Criteria pts
Correct placement of IV 5
Correct placement of DV 5
If, then format 5
IV indicates either "increases" or "decreases" 5
DV indicates either "increases", "decreases", or "stays the same" 5
Answers
The hypothesis will be:
H₀ = The amount of salt added to ice will not affect the rate at which the ice will melt.
H₁ = The amount of salt added to ice will affect the rate at which the ice will melt.
The independent variable which is can be changed by increasing the rate of salt added to the equation.
The dependent variable which is ice will change or melt in response as it will decrease if the rate of the salt added increases.
What is the effect of salt on the melting temperature of ice?Salt does not really lower the temperature of an ice cubes, it is known to just lowers their freezing point, that is lowers their melting point.
Note that if salt is around, ice cubes are known to be colder to be solid, and they tend to melt at a temperature that is said to be lower than the freezing point of pure water.
If the ionic compound salt is known to be added, it tends to lowers the freezing point of the water, which implies that the ice on the ground is not able to freeze that layer of water at all.
Therefore, The hypothesis will be:
H₀ = The amount of salt added to ice will not affect the rate at which the ice will melt.
H₁ = The amount of salt added to ice will affect the rate at which the ice will melt.
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A worker uses a pulley system to raise a 225
N carton 16.5 m. A force of 129 N is exerted
and the rope is pulled 33.0 m. What is the IMA
of the system?
Answers
Answer:
1.74
Explanation:
"How do you calculate the mechanical advantage of a block and tackle pulley?
To calculate the mechanical advantage, we can either divide the weight of the object being lifted by the force required to lift it or we can divide the amount of rope we have to pull by the distance the object moves."
If we use the rope method the mech advantage is 33.0/16.5 = 2
now if we use the forces MA = 225/129 =1.74 <==== this is not equal to '2' as we first found due to energy being lost to friction/deformation of rope etc. SO I would say the true mechanical advantage = 1.74
Efficiency = 1.74/2 = 87%
Quark gluon plasma (qgp) is what kind of state of matter I.e. it’s equation of state is what?
Answers
a 10 kg block reaches a point with a velocity of 15 m per second and slides down a rough track my the coefficient of the kinetic energy between the two surface ab and the block iis0.52
4. A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface? how to draw the question?
Answers
It is to be noted that the magnitude of the electric flux through the hemisphere surface is πR²E. (Option D)
What is an Electric Flux?
The characteristic of an electric field known as electric flux may be thought of as the quantity of electric lines of force (or electric field lines) that cross a certain region.
According to this theory, electric field lines begin with positive electric charges and end with negative charges.
What is the calculation for the above?
Recall that the A hemispherical surface (half of a spherical surface) of radius R.
In order to derive the Magnitude of the electric flux we use the following formula:
Ф = ∈ x Area of the Curve Surface
⇒ Ф = ∈ x πR²
⇒ Ф = πR²∈
Thus, option D is the correct answer.
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Full Question:
A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface?
A) 2πR²∈
B) 0
C) 4 πR²∈/3
D) πR²∈
state whether the table represents a relation function both or neither x y 4 -20 1 -17 4 -14 16 5 10 0 -19 -16
Answers
state, whether the table represents a relation function both or neither x y 4 -20 1 -17 4 -14 16 5 10 0 -19 -16 Reconstruction was successful in that it allowed the United States to once again function as a single country by 1877. The states' rights vs. federalism controversy, which had been a point of contention since the 1790s, was also eventually resolved during reconstruction.
By most other standards, reconstruction was a failure: radical Republican legislation eventually failed to shield former slaves from white persecution and to bring about significant alterations to the South's socioeconomic structure. The federalism question, which had been a topic since the 1790s practically immediately, was at hand when President Rutherford B. Former Confederate officials and slaves returned to the South after Hayes withdrew federal soldiers from the region in 1877. These newly powerful white southern legislators established anti-progressive laws like voter ID requirements and black codes with the help of a conservative Supreme Court in an effort to roll back the rights that blacks had won during Radical Reconstruction. With its rulings in the Slaughterhouse Cases, the Civil Rights Cases, and United States v., the U.S. Supreme Court strengthened this anti-progressive movement federalism.
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Drag each tile to the correct location.
Gas cloud 1 is likely to form a star. Gas cloud 2 is not. Based on this information, match the given conditions with each cloud.
Its temperature stays well
below 14 million Kelvin.
its volume shrinks and density
increases due to gravity.
It is spread out, with a greater volume and
lesser concentration of elements.
Its hydrogen atoms retain their electrons.
gas cloud 1
Its temperature surpasses
14 million Kelvin.
Its hydrogen atoms shed their electrons.
gas cloud 2
Answers
The most appropriate conditions that matches Gas cloud 1 include the following:
"Its volume shrinks and density increases due to gravity.""Its hydrogen atoms shed their electrons.""Its temperature surpasses 14 million Kelvin."The most appropriate conditions that matches Gas cloud 2 include the following:
"Its hydrogen atoms retain their electrons.""Its temperature stays well below 14 million Kelvin.""It is spread out, with a greater volume and lesser concentration of elements."What is a star?A star can be defined as a giant astronomical object that contains a luminous sphere of plasma and two (2) main hot gases (hydrogen and helium), and it is bounded together by its own gravitational force.
The conditions of a gas cloud.Since Gas cloud 1 is likely to form a star, the most appropriate conditions that matches it include the following:
"Its volume shrinks and density increases due to gravity.""Its hydrogen atoms shed their electrons.""Its temperature surpasses 14 million Kelvin."Since Gas cloud 2 is not likely to form a star, the most appropriate conditions that matches it include the following:
"Its hydrogen atoms retain their electrons.""Its temperature stays well below 14 million Kelvin.""It is spread out, with a greater volume and lesser concentration of elements."Read more on stars here: brainly.com/question/12175185
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The following coplanar forces pull on a ring 200N at 30 degrees and 500N at 80 degrees and 300N at 240 degrees and an unknown force. Find the magnitude and direction of the unknown force of the ring is to be in equilibrium
Answers
MAGNITUDE AND DIRECTION OF A VECTOR
Given a position vector →v=⟨a,b⟩,the magnitude is located by |v|=√a2+b2. The direction is equal to the angle formed with the x-axis, or with the y-axis, depending on the application. For a position vector, the direction is found by tanθ=(ba)⇒θ=tan−1(ba)
What is the formula of magnitude?
The formula to determine the extent of a vector (in two dimensional space) v = (x, y) is: |v| =√(x2 + y2). This formula is derived from the Pythagorean theorem. the procedure to determine the magnitude of a vector (in three dimensional space) V = (x, y, z) is: |V| = √(x2 + y2 + z2)
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main answer is given below,
• An object of mass 2.0 kg moves in uniform circular motion on a horizontal friction less table. The radius of the circle is 0.75 m and the centripetal force is 10.0 N. The work done by this force when the object moves through one-half of a complete revolution is
Answers
Answer:
23.562
Explanation:
First it is good to work out the circumference:
2 pi r
2 pi .75
circumference = 4.7124
Next we need half of this because it is half a resolution. This will be our distance travelled.
half = 2.3562
word done = force x distance
work done = 10 x 2.3562
work done = 23.562
(I didn't see the need for mass...)
What is the gravitational acceleration on the board of the Deepsea Challenger when it is in the Mariana Trench, 11 km below the surface of the Pacific Ocean?
It is slightly less than 9.81 m/s2.
It is very large due to the high pressure.
It is zero.
It is significantly less than 9.81 m/s2.
Answers
The gravitational acceleration on the board of the Deepsea Challenger when it is in the Mariana Trench, 11 km below the surface of the Pacific Ocean is very large due to the high pressure. That is option B
What is gravitational acceleration?The gravitational acceleration is the acceleration of an object that is under free fall. The acceleration due to gravity is 9.81 m/s2. above the sea level.
One of the factors that affect gravitational acceleration is depth. This is because as the depth increases so will pressure increase.
Increase in pressure leads to increase in gravitational acceleration.
Therefore, the gravitational acceleration on the board of the Deepsea Challenger when it is in the Mariana Trench, 11 km below the surface of the Pacific Ocean is very large due to the high pressure.
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PLEASE HELP 20!!+BRAINLIEST
It is critical for scientists to be able to describe components of a system quantitatively. Explain why it is important to be able to describe a system quantitatively, using an example from your investigation about habitable worlds
Answers
It is important to be able to describe a system quantitatively because there exist many variables that show a continuous range of variation.
What is quantitative research?Quantitative research is any type of investigation based on scientific variables that express their values as a continuous range of variation.
For example, there are genetic traits such as height and weight that show quantitative variation, thereby they need to be expressed as ranges.
In conclusion, it is important to be able to describe a system quantitatively because there exist many variables that show a continuous range of variation.
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On space missions with international teams, every country involved wants the flight
director to be chosen from their country because their national space organization
receives a significant amount of funding if they lead the mission.
True
False
Answers
False, their national space organization receives a significant amount of funding if they lead the mission.
The team typically sends about 30,000 remote control commands from the ground to the space station to manage the platform. Highly interactive, hands-on, tactile, and highly rewarding.
A mission control center (MCC, sometimes called a flight control center or operations center) is a facility that typically manages spaceflight from the launch point to landing or the end of the mission. This is part of the ground segment of spacecraft operations.
The station serves as a microgravity and space laboratory where scientific research in fields such as astrobiology, astronomy, meteorology, and physics is conducted.
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Lifting a 81-kg barbell and weights from rest up to a speed of 1.0 m/s in 0.50 s, resisted by the combined weight of the barbell and weights, requires what applied force in N to two significant digits?
Answers
Answer:
960 N
Explanation:
answer should have two signif digits
a = change in velocity divided by change in time
1 m/s / .5 s = 2 m/s^2
F = ma a = g + 2 m/s^2 = 9.81 + 2 = 11.81 m/s^2
81 kg * 11.81 m/s^2 = 956.61 N = ~ 960 N (two sig digits)
(Please let me know if this is incorrect....I am not SURE )
Summarize the step you might use to Carry out an investigation using scientific method
Answers
The summary of the step you might use to carry out an investigation using scientific method include:
ObservationHypothesisExperimentConclusionWhat is Scientific method?This is defined as a systematic approach which helps to predict how several elements in the universe works.
This usually starts with observing a phenomenon and making a hypothesis. This is usually followed by conducting experiment to ascertain its authenticity before a conclusion is drawn.
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a motorist drives along a straight road at a constant speed of 15 m/s. just as she passes aparked motorcycle police officer , the officer starts to accelerate at 2m/s2 to over take her. assuming the officer maintains this acceleration,
a) determine the time it takes the police to reach the motorist the speed and
b) the total displacement of the officer as he overtakes the motorist
Answers
Explanation:
Distance traveled by motorist =(15.0m/s)t
Distance traveled by policeman =1/2(2.00m/s2)t2
(a) Intercept occurs when 15.0t =t2or t=15.0s.
(b) x(officer)=1/2(2.00m/s2)t2= 225m
The technology in the picture produces which energy conversion?
O A. Light energy to electrical energy
• B. Thermal energy to kinetic energy
C. Chemical energy to kinetic energy
D. Kinetic energy to electrical energy
Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Option D[tex]\textsf{ \underline{\underline{Explanation} }:}[/tex]
The given picture shows a dam, and as we know dam ises water current to produce electricity. as the water current has high kinetic energy, so when it hits and rotates the turbine, the generator produces electricity.
Hence, the correct option will be :
❖ D. Kinetic energy to electrical energy
A weight lifter lifts a mass of 250 kg with a force of 5000N to a height of 5m. a. What is the workdone by the weight lifter? b. What is the workdone by the gravity? c. What is the net workdone on the object?
hii friends
Answers
Answers are:
a. The work done by the weight lifter W = 25000 Joule
b. The work done by the gravity W = 12250 Joule
c. The net work done on the object W = 12750 Joule
What is Work ?
Work is the product of force and distance in the direction of the force applied. That is, W = F x h
The S.I unit is Joule.
Given that a weight lifter lifts a mass of 250 kg with a force of 5000N to a height of 5m.
The given parameters are;
Mass m = 250 kgForce F = 5000 NHeight h = 5 ma. The work done by the weight lifter will be
W = F x h
W = 5000 x 5
W = 25000 Joule
b. The work done by the gravity will be
W = mg x h
W = 250 x 9.8 x 5
W = 12250 Joule
c. The net work done on the object will be
W = 25000 - 12250
W = 12750 Joule
Since the work done by the gravity is in opposite direction to the work done by the weight lifter, the net work done on the object will be the difference between the two.
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A ball is released from the top of a tower of height h meters. it takes T seconds to reach the ground . what is the position of the ball in T/3 seconds ?
Answers
Answer:the
8/9 h
Explanation:
Height = 1/2 a T^2 now change to T/3
now height = 1/2 a (T/3)^2 = 1/9 1/2 a T^2 <===== it is 1/9 of the way down or 8/9 h
What does the Q stand for in the enthalpy of fusion equation?
Answers
The Q in the enthalpy of fusion equation stands for heat energy absorbed or released.
What is enthalpy?In thermodynamics, enthalpy is a measure of the heat content of a chemical or physical system.
The enthalpy of fusion is the amount of heat energy required to convert a unit mass of a solid at its melting point into a liquid without an increase in temperature.
Its units are usually Joules per gram (J/g) or calories per gram (cal/g).
The enthalpy of fusion equation is given as follows:
Q = m·ΔHf
Where;
Q = heat energym = massΔHf = heat of fusionTherefore, the Q in the enthalpy of fusion equation stands for heat energy absorbed or released.
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The _____ is locked into a gravitational pull with our Milky Way, so both are actually
orbiting each other and slowly closing the gap between the them.
Kepler-22
Andromeda galaxy
PSR B1620-26 b
O Proxima-b
Answers
Answer:
Andromeda galaxy is the correct answer.
Glucose solution is administered to a patient in a hospital. The density of the solution is 1.308 kg/l. If the blood pressure in the vein is 35.7 mmHg, then what is the minimum necessary height of the IV bag above the position of the needle?
Answers
The minimum necessary height of the IV bag above the position of the needle is 0.37 m.
Minimum necessary height
The minimum necessary height of the IV bag above the position of the needle is calculated as follows;
P = ρgh
where;
ρ is density = 1.308 kg/L = 1308 kg/m³g is acceleration due to gravity = 9.8 m/s²p is pressure = 35.7 mmHg = 4759.609 Pah is height, (m) = ?h = P/ρg
h = (4759.609) / (9.8 x 1308)
h = 0.37 m
Thus, the minimum necessary height of the IV bag above the position of the needle is 0.37 m.
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A 7950-kg railroad car travels alone on a level frictionless track with a constant speed of 15.0 m/s . A 2950-kg load, initially at rest, is dropped onto the car.
What will be the car's new speed?
Express your answer to three significant figures and include the appropriate units.
Answers
The new speed of car is 10.9 m/s
According to the principle of momentum conservation, momentum is only modified by the action of forces as they are outlined by Newton's equations of motion; momentum is never created nor destroyed inside a problem domain.
Mass of the railroad car, m₁ = 7950 kg
Mass of the load, m₂ = 2950 kg
It can be assumed as the speed of the car, u₁ = 15 m/s
Initially, it is at rest, u₂ = 0
Let v is the speed of the car. It can be calculated using the conservation of momentum as :
[tex]m_1u_1 + m_2u_2 = (m_1 + m_2) v[/tex]
[tex]v =\frac{m_1u_1}{m_1+m_2}[/tex]
[tex]v = \frac{7950*15}{7950+2950}[/tex]
[tex]v= 10.9 m/s[/tex]
Therefore, the new speed of care is 10.9 m/s
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PLEASE read this carefully.
A solid, homogeneous sphere with a mass of m0, a radius of r0 and a density of ρ0 is placed in a container of water. Initially the sphere floats and the water level is marked on the side of the container. What happens to the water level, when the original sphere is replaced with a new sphere which has different physical parameters? Notation: r means the water level rises in the container, f means falls, s means stays the same. Combination answers like 'r or f or s' are possible answers in some of the cases.
The new sphere has a radius of r < r0 and a mass of m > m0.
The new sphere has a mass of m > m0 and a density of ρ < ρ0.
The new sphere has a density of ρ < ρ0 and a radius of r > r0.
Answers
For each of the given scenarios and based on the volume, mass, and density of the spheres, the water level is given as follows:
Scenario 1: The water level will rise; r
Scenario 2: The water level may rise or fall; r or f
Scenario 3: The water level will fall; f
What is the relationship between volume, density, and mass of the objects?The density, volume and mass of an object are related by the formula below:
Density = mass/volumeThe rise in the level of fluid when an object is placed in that fluid depends on the weight, volume and density of that object.
This is given by Archimedes' principle which states that the upthrust acting on a body immersed fully or partially in a fluid, is equal to the weight of the fluid displaced.
Based on the above, the water level in each of the scenarios is described thus:
Scenario 1: The new sphere has a radius of r < r0 and a mass of m > m0.
The new has a smaller volume and a greater mass and density. The water level will rise.
Scenario 2: The new sphere has a mass of m > m0 and a density of ρ < ρ0.
The new sphere has a greater volume and will float. Therefore, the water level may rise or fall.
Scenario 3: The new sphere has a density of ρ < ρ0 and a radius of r > r0.
The new sphere has a greater volume but less mass. Therefore, the water level will fall.
In conclusion, the rise or fall of the water level in the container depends on the volume, mass, and density of the spheres.
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The Sun subtends an angle of about 0.5∘ to us on Earth, 150 million km away.
Estimate the radius of the Sun.
Express your answer to two significant figures and include the appropriate units.
Answers
The radius of the Sun is approximately 654497.9 kilometers.
A subtended angle in geometry is an angle created by a common point (in this case, the Earth) that crosses two points of a nearby circular arc (the Sun in this case). Below is a visual illustration of the subtended angle.
The law of cosine can be used to calculate the sun's radius, which is 654497.950 kilometers in kilometers.
The Sun's radius is nearly 109 times bigger than the Earth's. The Earth's radius is 6378 kilometers. Or to put it another way, both dimensions are 1: 109 ratios.
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Two drums are rolling down a hill. The drums are the same size and mass.
Drum #1 has most of its mass concentrated at the rim, while drum #2 has
most of its mass concentrated in the center. Which of the following
statements are correct? Select all that apply.
Drum #1 will reach the bottom of the hill first because its moment of inertia is
greater.
Drum #1 will have a greater center of mass speed and reach the bottom of the
hill first.
Drum #2 will have a greater center of mass speed and reach the bottom of the
hill first.
Drum #2 will reach the bottom of the hill first because its moment of inertia is
smaller.
Answers
Hi there!
Drum #2 will have a greater center of mass speed and reach the bottom of the hill first.
The moment of inertia can be thought of as inertia for rotation.
If mass is concentrated at the rim, the drum has a GREATER moment of inertia compared to if the mass is more concentrated towards the center.
Using the Rotational Equivalent of Newton's Second Law:
[tex]\Sigma \tau = I\alpha[/tex]
**Sum of torques = Moment of inertia * angular acceleration
From this equation, we know that if 'I' increases, 'α' decreases, and thus, the speed of the object's center of mass decreases and it will reach the bottom later.
Therefore, drum #2 with the smaller moment of inertia (mass concentrated at the center) will have a greater angular acceleration ⇒ greater center of mass speed ⇒ read the bottom first.