Answer:
Explanation:
a = ΣF/m
a = (0.4kg * 9.8m/s^2)/(5.98 * 10^24kg)
a = 6.56 * 10^-25 m/s^2
Describe how transferring energy into the container affected the speed of the marbles.
The speed changes as a result of the energy being transferred into a container filled with magnetic marbles and the kinetic energy produced by the container's gentle shaking. Phase shifts will result from this.
The energy of a system changes together with each phase change it undergoes. These involve kinetic energy transmission to a system. Endothermic reactions occur when a condition changes from being more ordered to being less ordered. Exothermic reactions are always involved in transitions from one state to another that is more organised.
When a substance transforms from one state to another, a phase change occurs in the system. When the system receives enough energy or loses enough energy, these changes take place. Phase changes also happen when the system's pressure is altered.
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Complete Question:
Describe how does transferring energy into a container of magnetic marbles affect the speed by shaking the container gently?
a force of 45 n is used to slide a 10 kg mass 5 m along an inclined plane. if the ramp has a height of 2 meters, what is the actual mechanical advantage of the ramp?
A force of 45 n used, The actual mechanical advantage of the ramp is 2.18.
Weight = 10g
= 10 × 9.81
= 98.10N
Force used = 45 N
Mechanical advantage = Height / Force used = 98.1/45 = 2.18
The inverse relationship between acceleration and mass is stated by Newton's second law, which also states that force and acceleration are directly proportionate. By using kinematic measurements, accelerations can be identified. The correct definition of mass is still a contentious issue, despite the fact that modern physics' reference frame analysis provides a comprehensive description of kinematics. It is not apparent how or not this link holds true on microscales because general relativity provides an equivalency between space-time and mass in the absence of a cogent theory of quantum gravity. By expressing Newton's second rule as an equality, the relative units of force and mass may be determined and the law can be interpreted as a quantitative description of mass.
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the wavelength of blue light is greater than red light and its energy is greater. True or False
Answer:
False
Explanation:
The wavelength of red light is greater than blue light. Its energy is less.
Both statements are false. Search for a graphic of the "electromagnetic spectrum." Many will note the wavelengths of the various regions (IR, UV, Visible, Microwave, etc. Observe the relationships. Red has less energy than blue. That sounds counterintuitive, based on artist's use of red to connote fire or some energetic situation. But the red in a fire obscures human vision to the blues and UV radiation from the same source. A welder uses a UV shield to blocjk these wavelengths, to avoid eye damage.
a boat in the trough of a wave takes 3 s to reach the highest point of the wave. the velocity of the wave is 5 m/s. what is its wavelength?
Answer: A boat in the trough of a wave takes 3 seconds to reach the highest peak of the wave, then its wavelength will be equal to 30 m.
Explanation:
The wavelength of the wave is 15 m.
The wavelength of a wave is the distance between two consecutive crests or troughs. The velocity of a wave is the speed at which it travels. The time it takes for a boat to travel from the trough of a wave to the highest point of the wave is the same as the time it takes for the wave to travel one wavelength.
In this case, the velocity of the wave is 5 m/s and the time it takes for the boat to travel from the trough of the wave to the highest point is 3 s.
wavelength = velocity * time
wavelength = 5 m/s * 3 s = 15 m
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Find the moment of inertia of a point ma 0. 0005gram at perpendicular ditance 3m from it’ axi of rotation
The moment of inertia of the point is from to be 0.0045 Kg-m².
The moment of inertia of any mass that is situated away from the axis of the rotation is given by other relation,
I = MR²
Where,
M is the mass of the body and R is the distance of the body from the axis rotation.
It is given to as that the mass of the body is 0.05 grams and it is situated perpendicularly at a distance of 3 m from the axis of rotation.
Now, putting all the values to find the value of the moment of inertia,
I = 0.0005×9
I = 0.0045 Kg-m²
So, the moment of inertia the point is found to be 0.0045 Kg-m².
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if you quickly run toward the orchestra at a concert, the frequency of the sound you hear will be
As you get closer, the frequency of the sound gets higher. Because the sound waves are compressed relative to you, the frequency increases.
What is the Doppler effect?The Doppler effect can be described as a phenomenon that is observed whenever the source waves are moving w.r.t. an observer. Doppler effect can be defined as the change in the frequency of sound as the source and observer move toward or away from each other.
The Doppler effect can be used to describe when a moving source with respect to an observer, changes in the frequency of any sound produced.
Sound Waves that are emitted by an orchestra traveling toward you get compressed while the waves emitted by an orchestra traveling away from an observer get stretched out.
Therefore, the frequency of the sound of the orchestra gets higher, if you quickly run toward the orchestra.
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the subtle changes in the color of starlight let astronomers find planets, measure the speeds of galaxies, and track the expansion of the universe is called?
Answer:
Redshift, Blueshift, Doppler Effect, or Doppler Shift
Explanation:
When a star is moving towards us, the light waves get compacted and the light appears blue, this is known as blueshift.
When a star is moving away from us, the light waves get spread apart and the light appears red, this is known as redshift.
Both of these are called the doppler effect or doppler shift.
I'm not sure which answer you need but I hope this helps!
maxwell developed his theory of electromagnetism by combining previous discoveries. he added his own original hypothesis that
The hypothesis is that, a changing electric field gives rise to a magnetic field.
What is electromagnetism?
The electromagnetic force that exists between electrically charged particles is the subject of the branch of physics known as electromagnetism. One of the four fundamental forces is the electromagnetic force.
What is electric field?
The physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them, is known as an electric field (or E-field).
What is magnetic field?
The magnetic influence on moving electric charges, electric currents, and magnetic materials is described by a magnetic field, which is a vector field.
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calculate the magnitude of the electric field e = (-11i^+14j^)n/c.
The magnitude of the electric field is 17.80
We are given that,
e = (-11i^+14j^)n/c
x component = -11
y component = 14
To calculate the magnitude of the electric field we can use formula ,
e = √x² + y²
e = √-11² + 14²
e = √121 + 196
e = √317
e = 17.80
Therefore , the magnitude of the electric field would be 17.80.
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True or false :if there is a net force acting on an object it means there is an unbalanced force.
Answer:
true
Explanation:
The object will always accelerate if it has an unbalanced force acting on it in that direction
determine the empirical formula for maleic acid. enter the atoms in order of c, h, and o.
The empirical formula is CHO.
Maleic acid generates 1.599g of CO2 and 0.327g of H2O from a sample of 1.054 g.
So, use molar masses to calculate mass.
1.599 grams of [tex]CO_2[/tex] at (12.01 grams of carbon)/(44.01 grams of carbon) = 0.436 grams of carbon
0.037 grams of hydrogen are equal to 0.327g of H2O at (2.016 g Hydrogen) / (18.01 g/mol H2O).
1.054 g sample divided by 0.436 g of carbon and 0.037 g of hydrogen yields 0.581 g of oxygen.
Now locate moles by using molar masses.
0.436 grams of carbon with a molecular weight of 12.01 = 0.0363 mol C
0.0367 mol H for 0.037 grams of hydrogen and 0.0363 mol O for 0.581 grams of oxygen
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The complete question should be:
In combustion analysis, a 1.054-g sample of maleic acid yields 1.599g of CO29 and 0.327g of H20.
When 0.609g of maleic acid dissolved in 25.00g of glacial acetic acid, the freezing point drops by 0.82 degrees C Maleic acid does not ionize in glacial acidic acid, which has a freezing point depression constant of Kf=3.90*c/m.
In a titration experiment, a 0.4250-g sample of maleic acid is dissolved in water and requires 34.03ml of 0.2152 M KOH for its complete neutralization.
The pH of 0.215g of maleic acid in 50.00mL of the aqueous solution is found to be 1.80.
Determine the empirical formula for maleic acid. Enter the atoms in order of C, H, and O.
the maximum lift-to-drag ratio of the world war i sopwith camel was 7.7. if the aircraft is in flight at 2250 ft when the engine fails, how far can it glide in terms of distance measured along the ground?
The far that can it glide in terms of distance measured along the ground is 38,500 ft.
Given that,
World War I Sopwith Camel was 7.7.
If the aircraft is in flight at 5000 ft when the engine fails.
Based on the above information, the calculation is as follows:
[tex]\begin{aligned}& \frac{\text { lift }}{d r a g}=\frac{\text { Distance }}{\text { height }} \\& 7.7=\text { Distance } \div 5500\end{aligned}[/tex]
So, the distance is 38,500 ft.
Distance is a measurement of how far away two things or locations are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common use.
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1. What is Fad,x, the x-component of the force exerted by the infinite wire on segment ad of the loop?2. What is Fbc,x, the x-component of the force exerted by the infinite wire on segment bc of the loop?.3. What is Fnet,y, the y-component of the net force exerted by the infinite wire on the loop?
The Fad,x, the x-component of the force exerted by the infinite wire on segment AD of the loop is 2.39 X 10⁻⁸ N. The Fbc,x, the x-component of the force exerted by the infinite wire on segment BC of the loop is 9.56 X 10⁻⁹ N. The Fnet,y, the y-component of the net force exerted by the infinite wire on the loop is zero.
1. The Fad,x, the x-component of the force exerted by the infinite wire on segment AD of the loop =
= Fad,x = u₀i₁i₂H / (2πL)
= Fad, x = [ (4π X 10⁻⁷)(0.672)(0.256) X (0.25) ] /2π X 0.36
= Fad,x= 2.39 X 10⁻⁸ N
2. The Fbc,x, the x-component of the force exerted by the infinite wire on segment BC of the loop =
= Fbc,x = u₀i₁i₂H / (2π) X (L+W)
= Fbc,x = (4π X 10⁻⁷)(0.672)(0.256)((0.25)/2π X (0.36+0.54)
= Fbc,x = 9.56 X 10⁻⁹ N
3. The Fnet,y, the y-component of the net force exerted by the infinite wire on the loop =
= Fnet,y = 0, since force acting on perpendicular wire is zero.
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you are a passenger on a spaceship. as the speed of the spaceship increases, you would observe that the length of your spaceship is: [a] getting shorter. [b] getting longer. [c] not changing.
As the speed of the spaceship increases, we, as passengers, would notice that the length of your spaceship does not change.
Astronauts do not notice their speed any more than do passengers on a commercial aircraft once they are traveling in orbit at a constant speed of roughly 16,150 mph (26,000 kph). A spaceship is a form of artificial satellite used for a wide range of tasks such as communications, Earth observation, meteorology, navigation, space colonization, planetary exploration, and cargo and person transfer. All spacecraft, with the exception of single-stage-to-orbit rockets, require a launch vehicle to enter space (carrier rocket).
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FILL IN THE BLANK. the electric field inside the dome of a highly-charged van de graaff generator is _________.
The electric field inside the dome of a highly-charged van de graaff generator is ZERO.
Van de Graaff generators are electrostatic generators and partial accelerators that store direct current on a hollow sphere by creating a strong electric field. With a potential difference of up to 5 megavolts, it is a partial accelerator.
The dome of the Van de Graaff generator is a hollow spherical. The electric field within a hollow conductor will be zero in a charged state due to electrostatic shielding.The scenario is comparable to that of an electric field or a hollow conductor conveying current.There is no static energy in an uncharged state to create an electric field on the dome. It is because there could be a loss on the dome's surface.know more about electric field here
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6. focus on concepts, question 6 five hockey pucks are sliding across frictionless ice. the drawing shows a top view of the pucks and the three forces that act on each one. the forces can have different magnitudes (f, 2f, or 3f), and can be applied at different points on the puck. only one of the five pucks could be in equilibrium. which one?
The figure (4) is said to be in equilibrium with the force 2F in the centre and F on the top and bottom of the hockey puck.
For a body to be in equilibrium, the net force acting on the body and the net moment acting on the body must be zero.
Let us consider the net force acting on the body of pucks (force toward positive direction is positive and force towards negative direction is negative).
For puck 1, net force = 3F - F -2F = 0
For puck 2, net force = 2F + F - F = 2F
For puck 3, net force = F + 2F - F = 2F
For puck 4, net force = F + F - 2F = 0
For puck 5, net force = 3F - F - 2F = 0
In puck 1 and puck 5, net torque about the centre mass is not zero.
In puck 4, net torque about the centre mass is zero.
Thus, puck 4 is said to be in equilibrium.
The question is incomplete. The figure is missing in the question. It is attached in the below attachment.
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if the strings are made of the same material, how would you expect the diameters of the lowest and highest strings to compare?
The correct option is B) [tex]d_{low} = 4d_{high}[/tex].The diameter of the lowest string is four times that of the highest string.
Because frequency is inversely proportional to the square root of mass density, the low string's mass density would be 16 times greater. The radius would increase by 4 times as a result.
If the diameter is same, the mass is same and the speed is 1/4 times due to the square root sign in the denominator. The frequency is 1/4 times because the wavelength is constant.
The relationship between frequency and diameter of a string is given by,
[tex]f=\frac{1}{L*d} \sqrt{\frac{4T}{\rho \pi}}[/tex]
Where,
L = length of the string
d= diameter of the string
T= tension of the string
[tex]\rho[/tex] = density of the string
Given, that the lengths of the strings are same; tension of the strings are same and as the string are of same material then the density of the strings are also same.
Thus, the frequency is inversely proportional to the string diameter.
f = 1/d
So, if
[tex]4f_{low} = f_{high}[/tex]
Then,
[tex]d_{low} = 4d_{high}[/tex]
Thus,the diameter of lowest string is 4 times the diameter of highest string.
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Your question is incomplete, here is the complete question
The 6 strings on a guitar all have about the same length and are stretched with about the same tension.The highest string vibrates with a frequency that is 4 times that of the lowest string.
If the strings are made of the same material, how would you expect the diameters of the lowest and highest strings to compare?
[tex]A.\ d_{low}=2d_{high}\\\\B.\ d_{low}=4d_{high}\\\\C.\ d_{low}=16d_{high}[/tex]
1.10 g of an unknown compound reduces the freezing point of 75.22 g benzene from 5.53 to 4.92 ∘c.
The molar mass of the compound will be 123 g/mole
The ratio between the mass and the amount of substance in any sample of a chemical compound is known as the molar mass in chemistry.
How to determine a compound's molar mass
Calculate the number of atoms in each element in the compound using the chemical formula.
Add up the atomic weights of all the elements in the complex and multiply the result.
Calculate the total and convert it to grams per mole.
Change in freezing point, [tex]\delta T_f = K_f \times m[/tex]
where Kf=Cryoscopic constant=5.12 degree C for Benzene
m=molality
[tex]\delta T_f=5.53-4.92=0.61[/tex] degree C
[tex]m=\frac{\detlaT_f}{K_f}=\frac{0.61}{5.12}=0.119[/tex] mol/kg
Molality=wt(solute)/(MW(solute)*kg of solvent)
[tex]0.119=\frac{1.10}{(MW \times 0.07522)}\\\\MW=123\:g/mol[/tex]
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The complete question should be:
1.10 g of an unknown compound reduces the freezing point of 75.22 g benzene from 5.53 to 4.92 ºC. What is the molar mass of the compound?
suppose our sun suddenly becomes a black hole (a very hypothetical situation, and our sun will not end its life as black hole :)). what would happen to the planets? group of answer choices
Suppose our sun suddenly becomes a black hole (a very hypothetical situation, and our sun will not end its life as black hole). Planets would also mugged up by the gravitational pull of black hole i.e. sun black hole.
A black hole is an area of spacetime where gravity is so intense that no electromagnetic wave, not even light, has the energy to escape. According to general relativity theory, a compact enough mass can bend spacetime into a black hole. The event horizon is the line beyond which there is no escape. Despite having a significant impact on the outcome and circumstances of an object traversing it, general relativity states that it lacks any locally observable characteristics. A black hole behaves in many ways like a perfect black body since it does not reflect light. Furthermore, event horizons are expected to release Hawking radiation according to the quantum field theory in curved spacetime. When large stars end their lives and collapse, black holes of stellar mass are created. A black hole can expand by absorbing mass from its surroundings after it has created. It is possible for supermassive black holes to absorb additional stars and merge with other black holes to produce masses of millions of solar masses (M). Most galaxies' centers are believed to contain supermassive black holes. Through its interactions with other stuff and electromagnetic radiation like visible light, black holes can be detected.
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Consider an R-L circuit with a DC voltage source, as shown in the figure. This circuit has a current 1, when t <0. At t=0 the switch is thrown removing the DC voltage source from the circuit. The current decays to I(t) at time t AA VVV R A.) What is the power, Pr(t), flowing into the resistor, R, at time t? Express your answer in terms of I(t) and R. B.) What is the power flowing into the inductor? Express your answer as a function of R and I(t).
The power, the resistor and time is I²₀R e-2Rt/L and - I₀²R e-2Rt/L .
Work rate or energy delivery time is expressed as W/t, where W is the quantity of work completed or energy delivered, and t is the time interval.
A passive electrical device with two terminals that controls or limits the flow of electricity across electrical circuits. The main function of a resistor is to lower the voltage and reduce the current flow in a specific area of the circuit.
a) L di/dt + iR = 0 -Rt/L
= I = I₀ e
At t=0. I = I₀
= Pr = I²R = I₀ R e = -2Rt/t
= Pr (t) = I²₀R e-2Rt/L
b) Energy of inductor = 1/2 L I²
= 1/2 L I₀² e-2Rt/L
Power, Pl (t) = dE/dt
= d/dt (1/2 LI₀² e-2Rt/L)
= 1/2 t I₀² ( e-2Rt/L) e-2Rt/L
Pl (t) = - I₀²R e-2Rt/L
Therefore, the power, the resistor and time is I²₀R e-2Rt/L and - I₀²R e-2Rt/L .
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what would happen to the relative amount of uv radiation that the sun would emit if its temperature increased
Risks. Sunburn is a sign of short-term overexposure, while premature aging and skin cancer are side effects of prolonged UV exposure.
Risks. Premature ageing and skin cancer are side consequences of continuous UV exposure, whereas sunburn is a symptom of short-term overexposure. If eye protection is not used, UV exposure raises the risk of potentially blinding eye illnesses. UV radiation overexposure can cause major health problems, including cancer.
The amount of UV radiation is unrelated to the temperature. The position of the sun in the sky is mostly to blame for variations in UV levels between summer and winter. UV radiation is often impacted by changes in the stratospheric ozone and global climate change. More UVB (the higher-frequency, more dangerous kind of UV) may now reach the Earth's surface due to a decrease in stratospheric ozone.
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an arrow is shot straight up in the air at an initial speed of 10.2 m/s. after how much time will the arrow heading downward at a speed of 5.8 m/s? assume the magnitude of g
10.2 m/s is the initial speed of an arrow as it is launched straight up into the air. The arrow will be heading downward at a speed of 5.8 m/s after 1.63s
The arrow's steady downward acceleration once it leaves the bow is equivalent to the g of free fall. The amount of time needed for the velocity to change from an initial value of 10.2 m/s, assuming that upward is the positive direction
Given initial speed of arrow (u) = 10.2m/s
Final speed of arrow (v) = -5.8m/s (opposite in direction)
Since going downward gravity acts upon the arrow (g) = 9.8m/s
where g is the gravitational acceleration
time taken to move downward = t
We know that t = v-u/a = v-u/g
t = -5.8-10.2/-9.8 = -16/-9.8 = 1.63s
Hence time taken for the arrow to move downward is 1.63s
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you are trying to open a door that is stuck by pulling on the doorknob in a direction perpendicular to the door. if you instead tie a rope to the doorknob and then pull with the same force, is the torque you exert increased?
No; the rope doesn't change the moment arm so the torque you exert won't increase.
In physics, a force is a power that can change the motion of an item. A force could purpose an object with mass to alternate its pace. Pressure also can be described intuitively as a push or a pull. A force has both value and path, making it a vector quantity.
A pressure is either a push or a pull and it affects our each day lives because without force, people might not be capable of open and near stuff or lift up our arms or legs .
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describe how the electrostatic force between two charges changes when the distance between those two charges is tripled
The square of the separation distance is inversely correlated with the electrostatic force. F is therefore nine times smaller, or one-ninth the original value, if d is three times larger.
Coulomb's Law states that the force exerted between two charged objects is inversely related to their square of distance. As a result, if the distance is tripled, the force will be nine times weaker. The force between two charges is inversely proportional to the square of the distance between them and directly proportional to the product of the charges. The force between the two charges will therefore treble if the charge on q1 is tripled while the other charge and distance remain constant.
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if the surface temperature of the sun were to drop by a factor of 2.0, the power impinging on the earth would decrease by a factor of
If the surface temperature of the sun were to drop by a factor of 2.0, the power impinging on the earth would decrease by a factor of 8 times.
The quantity of energy transferred or transformed per unit of time is known as power. It is a mechanically accepted quantity. The watt, or one joule per second, is the unit of power in the International System of Units. Power is also referred to as activity in ancient writings. A scalar quantity is power. Power is related to other factors; for instance, the power required to move a ground vehicle is equal to the product of the vehicle's velocity, traction force on its wheels, and aerodynamic drag. A motor's output power is calculated by multiplying its torque output by the angular velocity of its output shaft. Energy divided by time represents the dimension of power. The watt (W), which equates to one joule per second, is the unit of power in the International System of Units (SI). Another popular unit of measurement is horsepower (hp), which is equivalent to a horse's power; one mechanical horsepower is equal to around 745.7 watts. Ergs per second (erg/s), foot-pounds per minute (fpm), dBm (a logarithmic measurement in relation to 1 milliwatt), calories per hour (cal/h), BTU per hour (BTU/h), and tons of refrigeration are other units of power.
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how did galileo's discovery of the phases of venus support the copernican view of a sun-centered universe?
Because Venus changes phases just like our Moon, it therefore orbits its light source (the Sun). support Copernican theory. constructed the telescope in 1609.
Galileo turned his gaze to Venus, the brightest object in the sky aside from the Sun and Moon. By observing the phases of Venus, Galileo was able to ascertain that Venus orbited the Sun, and not the Earth, as was commonly believed at the time.
Galileo was curious about the Sun and used his telescope to study it in detail. Galileo pointed his telescope at the Sun, unaware that looking at his own stars would impair his eyesight. He discovered that the Sun has sunspots that appear dark in color.
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stone is dropped from the edge of a roof, and hits the ground with a velocity of -165 feet per second. how high (in feet) is the roof?
Stone is dropped from the edge of a roof, and hits the ground with a velocity of -165 feet per second. 165 feet high is the roof.
Velocity is the direction at which an object is moving and serves as a measure of the rate at which its position is changing as seen from a specific point of view and as measured by a specific unit of time (for example, 60 km/h northbound). In kinematics, the area of classical mechanics that deals with the motion of bodies, velocity is a fundamental idea. A physical vector quantity called velocity must have both a magnitude and a direction in order to be defined. Speed is the scalar absolute value (magnitude) of velocity; it is a coherent derived unit whose quantity is measured in metres per second (m/s or m/s1) in the SI (metric system). In contrast to "5 meters per second east," which is a vector, "5 meters per second," for instance, is a scalar. In order to stress the difference between the instantaneous velocity and average velocity, velocity is defined as the rate of change of location with regard to time. The average velocity of an object, or the constant velocity that would produce the same resultant displacement as a variable velocity in the same time interval, v(t), over some time period t, may be required in various applications.
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question 1 of 30 next questionunsaved change moving to the next question prevents changes to this answer.question 1 during distillation, what is the placement of the bulb of the thermometer?
The process of distillation involves selectively boiling and condensing to separate the volatile components of a liquid mixture.
Both partial and total separation may result from this procedure. A large range of commercial processes, including the creation of alcohol and kerosene gasoline, use distillation. It is crucial to suspend a drop of condensate from the thermometer during a distillation because this promotes steady distillation and maintains a constant temperature.Since the bulb of the thermometer is in contact with both the vapour and liquid that are entering the condenser, a higher temperature will be recorded if it is situated below the opening to the condenser than if it is put close to the aperture.
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how is momentum related to the pressure exerted by a gas? explain on the molecular level, considering the behavior of molecules.
The momentum is p = m v . You can see from the equation that momentum is at once proportional to the object's mass (m) and velocity (v).
Therefore, the extra an object's mass or the extra its velocity, the extra its momentum.From equation (1), whilst the common velocity of the fueloline is increased, the momentum of the fueloline will growth too.
This will make the stress exerted via way of means of the fueloline will increase too. And, whilst the quantity of the molecules is increased, this could growth the full mass of the fueloline and the momentum of the fueloline will growth too.
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the volume of a speherical baloon is increasing at a constant rate of 100cm^3/s. how fast is the baloon's radius increasing when its diamter is 50 cm g
The diameter is increasing at a rate of [tex]\frac{1}{200\pi }[/tex]cm/g
We know the volume of the balloon is increasing at a rate of 100cm3/s
This is expressed as:
[tex]\frac{dv}{dt} =100[/tex]-----(1)
The volume of a sphere is given by:4/3πr^3
The formula gives volume in terms of the radius, not the diameter, so we will halve the diameter to get the radius.
Radius = 100:
We need to find:[tex]\frac{dr}{dt}[/tex]
Since we don't have t in our equation, we will be differentiating implicitly. We can use the chain rule for this:
[tex]\frac{dV}{dt} =\frac{dV}{dr} .\frac{dr}{dt}[/tex]--------(2)
We already know [tex]\frac{dV}{dt} =100[/tex]
100=dV/dr.dr/dt
To find dV/dr we differentiate :
V=4/3πr3
dV/dr(4/3πr3)
=4πr2
∴100=4πr2⋅dr/dt
Dividing:
100/4πr2=dr/dt
The radius is 100, so:
100/4π(100)2=dr/dt
dr/dt=1/400π
We need the diameter, so:
2⋅1/400π=1/200π
Thus, The diameter is increasing at a rate of 1/200πcm/s.
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