Answer:The equation of motion for the graduate student in the Schwarzschild geometry is given by:
(1 - 2m/r) dt/dr = 1
We need to find how many help messages reach the fellow student stationed at a fixed value of r = ro, at unit intervals of the proper time T.
a) To find the total number of help messages, we can use the fact that the proper time T is related to the coordinate time t by:
dt/dT = (1 - 2m/r)
We can rewrite this equation as:
dT/dt = 1/(1 - 2m/r)
This equation tells us how the proper time interval dT between successive help messages is related to the coordinate time interval dt as measured by the fellow student.
When the graduate student reaches r = 3m, the equation of motion becomes:
(1 - 2m/3m) dt/dr = 1/3
dt/dr = 3/2
Integrating both sides, we get:
t = (3/2)r + C
where C is an integration constant. At r = ro, the coordinate time is:
t = (3/2)ro + C
The proper time at this point is:
T = ∫(dt/√(1 - 2m/r)) = ∫(1/(1 - 2m/r))^(1/2) dt
Substituting t = (3/2)r + C and dt/dr = 3/2, we get:
T = ∫(1/(1 - 2m/(3m)))^(1/2) (3/2) dr = ∫(3/2)(r/3m - 1)^(1/2) dr
Making the substitution u = r/3m - 1, we get:
T = (2/3)∫u^(1/2) du = (4/9)(r/3m - 1)^(3/2) + D
where D is an integration constant. At r = ro, the proper time is:
T = (4/9)(ro/3m - 1)^(3/2) + D
The proper time between successive help messages is 1 unit, so we have:
(4/9)(r/3m - 1)^(3/2) + D - (4/9)(ro/3m - 1)^(3/2) = 1
b) Rearranging the equation above, we can solve for the elapsed proper time between successive messages as measured by the fellow student:
ΔT = (4/9)[(r/3m - 1)^(3/2) - (ro/3m - 1)^(3/2)]
This gives us the elapsed proper time between successive help messages as a function of the radial coordinate r. We can use this formula to calculate the proper time interval between any two successive messages, given the values of r and ro.
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How does quantum theory explain the emission spectra of atoms?
The quantum theory opines that electron in atoms occur a discreet energy levels.
What is the quantum theory?The quantum theory was initiated by the idea of Max plank. In this idea, energy was viewed as occurring in discrete amounts. This idea was first applied to the phenomenon of the black body radiation hence the Plank Equation; E = hf.
Now Neils Bohr pushed the idea further by putting forward the opinion that when an electron in atom is found in an orbit, it does not radiate energy. The atom was thus visualized as being composed of several energy levels and radiation can only occur when an electron moves from a higher to lower energy level.
This implies that the energy of each electron in an atom is quantized. Thus implies that it has a value which an integral multiple of a fundamental amount.
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A car is traveling north on a straight road at 20 mys and a drone is flying east at 6 mys at an elevation of 25 m. At one instant the drone passes directly over the car. How fast is the distance between the drone and the car changing 5 seconds later
The distance between the drone and the car will be 20,3 m/s.
What is average velocity?
In physics, velocity is a quantity that identifies the displacement of a body in a given time. Thus, the average velocity measures in an average time interval, the speed of displacement of a body.
With that being said, Suppose that both car and drone starts from 0 and move towards north and east, respectively. So, after T time:
Distance covered by the car, [tex]y = 20.T.m[/tex]
Distance cover by the drone, [tex]x = 6.T.m[/tex]
Considering the elevations of 25m, the actual distance between them at any T instant:
[tex]A = \sqrt{(20T)^{2} } + (6T)^{2} +25^{2}[/tex]
Speed, [tex]V = \frac{ds}{dt} = \frac{[2(20T).20+2(6T).8}{\sqrt{(20.5)^{2}+(6T)^{2}+25^{2} } }[/tex]
[tex]V = 20,3 m/s[/tex]
So, the distance between the drone and the car will be 20,3 m/s.
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Answer:
20.3 m/s
Explanation:
dx / dt = 20 m / s
dy / dt = 6 m / s
dj / dt = ? when t = 5 s
The trick here is that the drone is flying at an elevation of 25 m.
x^2 + y^2 = j^2
Implicit Differentiation: 2x dx / dt + 2y dy / dt = 2j dj / dt
We are not given x and y values. Solve by d = vt. Distance = velocity * time
x = 20(5) = 100 m
y = 6 (5) = 30 m
Now we need to solve for j, but we need to solve the hypotenuse z of the right triangle first.
z = [tex]\sqrt{(100)^2 + (30)^2[/tex] ≈ 104.4 m
A mistake occurs when z is used as the distance between the drone and the car. Visualize the distance between the drone and the car as the right triangle where j is the hypotenuse, z is the x value, and 25 m is the y value.
j = [tex]\sqrt{(104.4)^2+(25)^2[/tex] ≈ 107.35 m
dj / dt = 1 / 2(107.35)((4000 + 360)) ≈ 20.3 m/s
A geologist finds that a Moon rock whose mass is 8.94 kg has an apparent mass of 6.18 kg when submerged in water. What is the density of the rock
Density of rock = 3.23 Kg/m^3
Given:
mass of Moon rock = 8.94 kg
apparent mass of Moon rock = 6.18 kg
To Find:
density of the rock
Solution: It is a universal fact that mass of an object remains constant whether measured on earth or on moon.
Mass of rock on moon/earth = 8.94 kg
When the block is immersed in water then;
Loss in weight = weight of water displaced
Loss in weight = 8.94 - 6.18 = 2.76 kg
As we know that water has a density of 1g/cm^3 (1000kg/m^3)
Volume of water = volume of the rock = Mass/density = 2.76 kg
density of rock mass/volume = 8.94/2.76 = 3.23 Kg/m^3
Density of rock = 3.23 Kg/m^3
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How much is the velocity of a body when it travels 600m in 5 minutes?
answer
so unit of velocity is m/s
displacement=600m
5minutes should be converted to seconds
5×60=300 seconds
so,
velocity= displacement÷time
= 600m ÷300s
=2m/s or 2ms^-1
Answer:
2 m/s
Explanation:
we have given
distance traveled by body =600m
time taken = 5*60 =300 sec( si unit of time is second)
velocity =?
we know that
velocity =distance traveled/ time taken
=600/300
= 2 m/s
Rosa pours a cup of boiling water into a pot of room-temperature water. According to the second law of thermodynamics, what will occur
Thermal energy from the room-temperature water will continuously flow to the boiling water.
The second law states, in a straightforward manner, that heat cannot naturally go "uphill." When a pan of boiling water and a pan of ice are in touch, the hot water cools and the ice melts and warms up.THE FIRST LAW OF THERMODYNAMICSAdiabatic Process - is a procedure that is carried out without the system's heat content changing. Water is heated to a temperature of 1000C during the boiling process, making it an isothermal process. As steam, the excess heat leaves the system.Learn more about first law of thermodynamics brainly.com/question/3808473
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What happens in a parallel circuit when you increase the number of bulbs
As more bulbs are added in parallel, the current strength will decrease OR. As more bulbs are added in parallel, the current strength will increase.
A 70 n force pulls a box straight up 5 m above the ground. How much work is done on the box?
The work done on the box is 350 Joule.
When is Work done on an object ?Work is done on an object when the displacement of the object is not perpendicular to the direction of the applied force. The unit of Work is Joule (J)
Given that 70N force pulls a box straight up 5 m above the ground.
Work is the product of force F and the distance S. That is,
W = F x S
Where
Force F = 70 NDistance S = 5 mSubstitute the two parameters into the formula above
W = 70 x 5
W = 350 J
Therefore, the work done on the box is 350 Joule.
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As the number of protons in an atom’s nucleus increases
a) The overall stability of the atom decreases
b) The number of electrons must increase to maintain the atom’s overall neutral charge
c) The more neutrons are required to stabilize the nucleus
d) All of the above
As the number of protons in an atom’s nucleus increases, the number of electrons must increase to maintain the atom’s overall neutral charge; option B.
What is atomic number of an element?Atomic number is the number of protons present in the nucleus of an atom.
The atomic number of atoms of elements increase with increase in atomic number.
In conclusion, atomic number increases the size down a group and decreases atomic size across a period.
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A 500.0 kg elevator is pulled upward with a constant force of 5500.0 N for a distance of 50.0 m. What is the work done by the 5500.0 N force on the elevator?
Group of answer choices
a. -2.45 x 105 J
b. -5.20 x 105 J
c. 2.75 x 105 J
d. 3.00 x 104 J
C. The work done by the 5500.0 N force on the elevator is 275,000 J.
Work done by the applied force
The work done by the 5500.0 N force on the elevator is calculated as follows;
W = Fd
where;
F is the applied forced is the displacementW = 5500 x 50
W = 275,000 J
Thus, the work done by the 5500.0 N force on the elevator is 275,000 J.
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Block A has a weight of 60 lb and block B has a weight of 10 lb. Determine the speed of block A after it moves 5 ft down the plane, starting from rest. Neglect friction and the mass of the cord and pulleys.
The speed of Block A is 7.18 ft/s.
From energy conservation we know that the initial kinetic energy is equal to final kinetic energy.
Block A has weight of 60 lb.
Block B has weight of 10 lb.
In the question it is said that block A moves from rest at a distance of 5ft.
Relative motion constraint-
2sA + sB =l
differentiating we get:
So, 2ΔsA + ΔsB = 0
→ ΔsB = -2ΔsA
2 vA + vB =0
→ vB = -2vA
Now applying principle of work and energy
TA0 +TBO + ΣwO-AB = TA+TB
1/2 mA v²A₀ + 1/2 mBv²B₀ + wAΔsA + wBΔsB = 1/2 mAv²A + 1/2 mBv²B
0 + 0 +6(5) - 10(10) = 1/2 (-60/32-2) v²A +1/2 (10/32.2) 2v²A
vA = 7.18 ft/s
So, the speed of block A is 7.18 ft/s.
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A 4 kg toy car moves horizontally on a rough road with coefficient of kinetic friction 0.2. It accelerates from rest to 20 m/s in 10 s. Find (a) the total work done on the car
The total work done on the car is 784Joule.
What's the acceleration of the car?As per Newton's equation of motion, V= U+atU= initial velocity= 0 m/sV= vinal velocity= 20m/s
t= time = 10s
a= acceleration
So, 20= 0+ 10a=> a= 20/10= 2m/s²
What's the distance covered by the car in 10 seconds?As per Newton's equation of motion,V²-U² = 2aS
S= distance covered by the carSo, 20²-0=2×2×S=4S=> 400= 4S
=> S= 400/4= 100m
What's the work done on the car due to frictional force?Work done by frictional force= frictional force × distance
= (0.2×4×9.8)×100
= 784Joule
Thus, we can conclude that the work done on the car is 784Joule.
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What type of energy is solar energy? and how is it used to fuel us and the machines we use every day?
According to the research, solar energy is a renewable energy used in generating electricity and obtaining thermal energy.
What is solar energy?It is a type of energy derived from natural sources known as renewable energy that is obtained from solar radiation that reaches the Earth in the form of light, heat or ultraviolet rays.
Solar energy can be used to generate electricity, hot water supply and home heating.
Therefore, we can conclude that according to the research, solar energy is a renewable energy used in generating electricity and obtaining thermal energy.
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Read the following question and answer it using complete sentences. Be sure to fully explain your answer.
What energy conversion is happening when wave power is used?
Wave power involves conversion of mechanical energy to electrical energy.
What is wave power?We know that energy conversion is part of the postulations of the first law of thermodynamics which states that energy can neither be created nor destroyed but can be transformed from one form to another.
Now, the wave power can convert the regular up and down movement of the ocean waves into a source of electricity. This implies that the energy that is taking place here is the conversion of mechanical energy to electrical energy.
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Which meteorological parameter is expressed as the ratio between the air’s actual water vapor content and the amount of water vapor required for saturation at that temperature?
Which meteorological parameter is expressed as the ratio between the air’s actual water vapour content and the amount of water vapour required for saturation at that temperature: relative humidity.
Water vapour is the primary form of atmospheric moisture. Although its storage in the atmosphere is comparatively small, water vapour is extremely important in forming the moisture supply for dew, frost, fog, clouds, and precipitation.
Water vapour is also the most important greenhouse gas in the atmosphere. Water vapour can be produced from the evaporation or boiling of liquid water or from the sublimation of ice.
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Thinking about planck's law, which star would give off the most orange light?
Thinking about Planck's law, the Red star would give off the most orange light.
According to Planck's Law, distinct atoms and molecules can emit or take in power in discrete portions simplest. The smallest amount of strength that can be emitted or absorbed inside the form of electromagnetic radiation is called quantum.
Planck's Law describes the quantity of spectral radiance at a particular wavelength radiated through a black body in equilibrium. The equation is E=hv.
The floor temperature of a celeb determines the color of mild it emits. Blue stars are warmer than yellow stars, which are hotter than red stars. The bright orange celebrity Arcturus is particularly noteworthy for its massive right motion, The color is a characteristic of their floor temperatures.
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An object starts at rest. Its acceleration over 30 seconds is shown in the graph below:
Answer:6m/s
Explanation:as you can see before twenty seconds there was no change in speed,but between twenty to thirty seconds,the speed changed from 0m/s to 6m/s,so change in speed is 6m/s.
The speed of an object between 20 and 30 seconds shown in the graph is 70 m/s.
Given:
Time, ΔT = 30-20 = 10s
Acceleration, a = 7 m/s²
The speed can be computed from the acceleration and time. The standard unit of velocity is meters per second.
For the given case, the speed can be computed from the acceleration and time given in the graph.
The speed is given as:
a = v/t
v = at
v = 7×10
v = 70 m/s
Hence, the speed of an object between 20 and 30 seconds shown in the graph is 70 m/s.
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An AP Physics student is attempting an FRQ problem. They arrive at the following expression for the total distance an object has traveled:
d = 2vh/g
All you know about the variables in this problem are their dimensions:
[v] = distance/time, [h] = distance, and [g] = distance/time^2.
Given this information, explain why the student’s answer must be wrong.
The student's answer is wrong because the unit of his answer is meter - seconds which is not unit of distance (meter).
Total distance traveled by an object
The total distance traveled by an object projected upward is calculated from third equation of motion a shown below.
Equation for the motion of the objectv² = u² - 2gh
where;
v is final velocityu is initial velocityg is acceleration due to gravityat maximum height, the final velocity is zero, v = 0
0 = u² - 2gh
2gh = u²
h = u²/2g
The equation for the total distance an object has traveled during upward projection is "h = u²/2g".
Dimension of the student's answer;d = (2vh)/g = (m/s x m) / (m/s²) = (m²/s) / (m/s²) = m.s
Thus, the student's answer is wrong because the unit of his answer is meter - seconds which is not unit of distance (meter).
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Suppose we have two planets with the same mass, but the radius of the second one is twice the size of the first one. How does the free-fall acceleration on the second planet compare to the first planet
The free-fall acceleration on the second planet is one-fourth the value of the first planet.
Calculation:
Consider the mass of planet A to be, M
the mass of planet B to be, Mₓ = M
the radius of planet A to be, R₁
the radius of planet B to be, R₂
The acceleration due to gravity on planet A's surface is given as:
g = GM/R₁² - (1)
Similarly, the acceleration due to gravity on planet B's surface is given as:
g' = GM/R₂² [where, R₂ = 2R₁]
= GM/4R₁² -(2)
From equation 1 & 2, we get:
g/g' = GM/R₁² ÷ GM/4R₁²
g/g' = 4/1
Thus we get,
g' = 1/4 g
Therefore, the free-fall acceleration on the second planet is one-fourth the value of the first planet.
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2. A spacecraft travels at 2 x 108 m/s relative to Earth. An astronaut on board listens to a CD that lasts 50 min.
How long would the CD last as measured by a stationary clock on Earth?
3. A linear particle accelerator is a special machine that accelerates charged particles to nearly the speed of light
and channel them into a beam. When used in research, the beam hits targets and the atoms split. Scientists
gather information about sub-particles, atoms and molecules to further help understand the laws of physics.
A proton of a mass 1.67 x 10–27 kg is accelerated to 0.999 994c. Calculate the ratio of the proton’s relativistic
momentum to the non-relativistic momentum
This is a time dilation exercise. The time taken for the CD to last as measured by a clock on earth is given as: 67.08 minutes.
What is time dilation?Under the theory of special relativity, time dilation is the "slowing down" of a clock as determined by an observer in relative motion with respect to that clock.
Recall that the equation for time dilation is given as:
t = t₀/√(1- (v²/c²)
Where:
t₀ is the observer in the space craft
t is the observer on earth
v is the speed of the space craft which is given as 2 x 10⁸m/sec
c is the speed of light which is given as 3 x 10⁸m/sec
Hence
v/c = 2 x 10⁸/ 3 x 10⁸
= 2/3
Thus,
t = 5/√(1-(4/9)
= 50 √(9/5)
= 150/√5
= 150 /2.2361
= 67.08 min
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In the roman soldier model for refraction, a muddy stream crosses the road they are on walking on at 45. Will the soldiers in the front row all hit the water at the same time?
There are different refractive errors that are common and some of them are:
Nearsightedness (myopia) makes far-away objects look blurry.Farsightedness (hyperopia) makes nearby objects look blurry.Astigmatism can make far-away and nearby objects look blurry or distorted.Presbyopia makes it hard for middle-aged and older adults to see things up closeWhat is Refraction?This refers to the study of light phenomena that deflects when it passes through a medium in an oblique manner to another medium of a varying density.
Hence, we can see that there are everyday examples of refraction in simple terms which occurs and some of them are:
GlassHuman eyesIce crystalsPickle jarMicroscope, etc.Hence, we can see that your question is incomplete, so I gave you a general overview to help you get a better understanding of the concept of refraction.
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In the paralleling technique, the central ray of the x-ray beam must be _____ to the film sensor and the long axis of the tooth.
The film sensor and the long axis of the tooth must be aligned perpendicular to the central ray of the x-ray beam when using the paralleling approach.
To find the answer, we need to know above the paralleling technique in the dental x-ray.
What is paralleling technique?The paralleling technique is the most dependable method for capturing periapical x-rays because it produces high-quality images with little distortion. The central x-ray beam should be pointed perpendicular to the long axis of the tooth in issue, and the film should be positioned parallel to it.The paralleling technique is the most dependable method for capturing periapical x-rays because it produces high-quality images with little distortion.The central x-ray beam should be pointed perpendicular to the long axis of the tooth in issue, and the film should be positioned parallel to it.When preparing for an x-ray, it is imperative to keep in mind the root anatomy.The maxillary occlusal plane of the patient should also be parallel to the ground.Thus, we can conclude that, the film sensor and the long axis of the tooth must be aligned perpendicular to the central ray of the x-ray beam when using the paralleling approach.
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When making segmented bends, the bend radius is the distance from the center point of the circle or object to
When making segmented bends, the bend radius is the distance from the center point of the circle or object to the centerline of conduit.
What is centerline of conduit.Segment bending is a technique for bending conduit in which numerous tiny bends are combined to form a single, bigger bend. Measure from the elbow's center at the bend's CenterPoint to the intersection of the "degrees of bend" lines to determine your centerline radius (see image above). In fact, the CLR may be determined by obtaining this measurement from any point on the elbow. The distance between segments is calculated by dividing the developed length by the number of shots. When making segmented bends, the bend radius is the distance from the center point of the circle or object to the centerline of conduit. To calculate the degrees per shot, divide 90 degrees by the quantity of shots. Regardless of how many lanes a road or highway has, centerline miles are used to quantify their length. Centerline of conduit miles between the two sides of a divided highway might differ slightly due to divergences and curves. Compared to lane miles, centerline miles provide a more understandable indication of a road's overall length.
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Increases in the planet's temperature over the past few decades can be attributed to
Excess Carbon Monoxide(CO) attributed to increases in the planet's temperature over the past few decades
While carbon monoxide (CO) poisoning is the world's most common cause of poisoning death, correlations between CO poisoning and weather are yet unknown.
The incidence risk of acute CO poisoning is influenced by temperature changes, however, the effects vary in Taiwan depending on the season and the person. Our research quantifies the effects of environmental variables and offers essential support for healthcare professionals to create preventive measures to lower the incidence of acute CO poisoning.
An earlier study conducted in Beijing found a negative correlation between temperature and the frequency of acute Carbon Monoxide poisoning. While the impact of other significant weather variables (such as relative humidity and wind speed) on this issue is still unknown, prior research has mostly focused on the relationship between temperature variations and CO poisoning.
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Is the star moving toward earth, away from earth, or is there not enough information provided to determine its motion?
If a star is moving towards Earth, shift towards the blue end of the spectrum, this is called blue shift. If the star is moving away from Earth the light from that star will be red and is called red shift .
The faster a star moves towards the earth, the more its light is shifted to higher frequencies. In contrast, if a star is moving away from the earth, its light is shifted to lower frequencies on the color spectrum
if a star is moving towards Earth, it appears to emit light that is shorter in wavelength compared to a source of light that isn't moving. Because shorter wavelengths correspond to a shift towards the blue end of the spectrum, this is called blue shift.
If the star is moving away from Earth, its light will lose energy to reach Earth, therefore the light from that star will be red and is called red shift
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Normally, whem I shut my door, it takes quite a bit of effort to shut it, but when my window is open, even if I just pull it slightly then let go, it slams automatically. It isn't an issue, I just want to know the physics behind it. Is it something to do with difference in pressure?
Answer:
gravity
Explanation:
gravity pulls anything with with weight towards the earth.
Answer
The reason why this occurs is because if there is any apparent wind being pushed towards the direction of the door, there will be an attempt of equalizing pressure and thus it will slam, or close very loudly when you even just push it shut with some effort.
Explanation
This has happened to me a variety of times, I would have the garage open, and it would be a little bit windy, and when I tried to close it, it would slam shut.
Airflow is a significant factor in the pressure appliance.
Your question at the end is correct (Differences in air pressure.)
Apologies for the late response, but I was interested in this as well.
P waves ________. P waves ________. are faster than S waves and surface waves have higher amplitudes than do S waves propagate only in solids produce the strongest ground shaking
P waves are faster than S waves and surface waves.
Surface wavesA surface wave in physics is a mechanical wave that travels at the interface of two different media. Gravity waves on the surface of liquids, like ocean waves, are an example that is frequently used. When two liquids with different densities come together, gravity waves can also form at that junction. Solid surfaces can experience elastic surface waves like Rayleigh or Love waves. The way that electromagnetic waves can be steered along a gradient in refractive index or at the boundary between two substances with varying dielectric constants is known as "surface wave" propagation. A guided wave that travels relatively close to the Earth's surface constitutes a ground wave in radio transmission.
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1. What happens to the apparent weight when the objects are submerged in water?
A rocket takes off from Earth and starts flying to Mars. What happens to the force of gravity between the rocket and Earth as the rocket approaches Mars
The force of gravity between Earth and Mars will decrease.
The gravitational law is given as-
F = G mM/r²
here, m= mass of rocket
M = mass of earth
r = distance between earth and rocket
So, as rocket takes off from earth and fly towards mars then the distance starts to increase between earth and rocket, and the gravitational pull between them starts to weaken. Then a point will reach when rocket will far from gravity of earth and could probably enter the gravity of Mars.
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Fire spreading from a wall to a nearby couch due to radiant heat transfer is an example of: Select one:
Fire spreading from a wall to a nearby couch due to radiant heat transfer is an example of heat reflectivity.
What is heat reflectivity?
When sunlight and other light sources strike a material's surface, its reflectance is measured. This number can be used to characterize a surface's characteristics in terms of surface finish. Another name for reflection is reflectivity.
This is a measurement of the amount of energy that material reflects at a specific wavelength. A value between 0 and 1 can also be used to represent reflectivity (or a percentage between 0 and 100).
Sigma and other top businesses have created a range of other forms of heat reflective fabric in the 50 years after the creation of space blankets, including Fabric and aluminum foil laminates, fabric laminates with metalized thin films.
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help me and I will be your friend forever.
Answer:
1. iodine
2. convection
3. radiation
4. conduction
5. gases
6. expansion
7. freezing point
8. absorber
9. thermos flask
10. mercury