The altitude of the satellite is 883.89 km
What is the altitude?Generally, The Rayleigh criterion for resolution states that the minimum angle, θ, between two point sources that can be resolved is given by:
θ = 1.22 * λ / D
where
λ is the wavelength of light and
D is the diameter of the lens.
The minimum distance, d, between two point sources that can be resolved is given by:
d = θ * L
where
L is the distance from the lens to the image.
Given the green lights have a wavelength of 508 nm, we can convert it to meters:
λ = 508 * 10^-9 m
Given the diameter of the lens is 49.8 cm, we can convert it to meters:
D = 49.8 cm * (1 m / 100 cm)
= 0.498 m
Using the Rayleigh criterion, we can find the minimum resolvable angle:
θ = 1.22 * λ / D
= 1.22 * 508 * 10^-9 / 0.498
= 1.24449799*10^{-6} radians
We know the lights on the satellite are spaced 1.1 m apart, so:
d = 1.1 m
Solving for the distance from the lens to the image, L:
L = d / θ
= 1.1 m / 1.24449799*10^{-6} radians
=883890.53 m
Finally, converting the distance to kilometers:
L = 883890.53 m * (1 km / 1000 m)
= 883.89 km
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A horizontal force of 3 N is exerted on an object while a vertical force of 4 n is exerted at the same time. calculate the resultant force on the object.
Answer:
resultant force = 5N
Explanation:
Answer:
5N
Explanation:
Horizontal Force = 3N
Vertical Force = 4N
Resulting force (magnitude) = √(4² + 3²)
= 5 N
According to the first law of thermodynamics, the sum of the heat gained by a system and the work done on that same system is equivalent to which of the following? (2 points) a. entropy change c. temperature change b. internal energy change d. specific heat
According to the first law of thermodynamics, the sum of the heat gained by a system and the work done on that same system is equivalent to internal energy change.
The first law of thermodynamics is based on the principle of the conservation of energy. The principle of conservation of energy states that energy cannot be created or destroyed. It can, however, be transferred from one location to another and converted to and from other forms of energy.
The first law of thermodynamics states that the total internal change of a system is the sum of the algebraic sum of the heat gained by a system and the work done on that system.
Hence, the internal energy change is the correct option.
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light traveling in air enters a material at an angle of 30 degrees with respect to the normal. the refracted beam in the material makes an angle of 15 degrees with respect to the normal. calculate the index of refraction of the material.
The index of refraction of the material is 1.93
To calculate the index of refraction (n) of the material, we can use the formula:
n = sin(angle of incidence) / sin(angle of refraction)
In this case, the angle of incidence is 30° and the angle of refraction is 15°. Therefore:
n = sin(30°) / sin(15°)
n = 1.93
So the index of refraction of the material is 1.93.
It's worth noting that in general, when the angle of incidence is smaller, the angle of refraction will be smaller as well, so the refracted beam will be closer to the normal. And the index of refraction is inversely proportional to the sine of the angle of incidence and refraction.
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I need help please mark you answers with the question Ex: Question: 1 The answer is __
thank you
The velocity of an object includes direction of the motion of an object whereas speed does not include direction. Thus, the correct options for 1, 2, 3, 4, and 5 are B, B, A, A, and B, respectively.
What is Velocity?Velocity can be defined as the directional speed of an object in the motion as an indication of the rate of change in the position of an object as observed from a particular frame of reference by the observer and as measured by a particular standard of time.
The velocity is different from that of speed as it is a vector quantity, the velocity of an object includes direction of the motion of an object whereas speed does not include direction.
Track runners cover same distance however, the winner in the race is the one who covers the particular distance in less time than other competitors.
The slowest runner in the graph is the one represented with blue color. This is because, this runner took maximum time to cover the distance.
The distance covered by the train is 300 miles in time period of 6 hours. Therefore, the speed of the train will be the distance covered by the train divided by the total time taken.
Speed of the train = 300 miles/ 6 hours
Speed of the train = 50 miles per hour.
The example of velocity is the one with the unit of length per time. From the given options, 80 miler per hour is an example of velocity as miles is the unit of length and hour is the unit of time.
Therefore, the correct options for 1, 2, 3, 4, and 5 are B, B, A, A, and B, respectively.
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Consider a case where the potential energy of two interacting molecules is E=1.3 kJ/mol. Choose all options that apply:(A) The net force on either molecule is zero.(B) The molecules are an infinite distance apart.(C) The forces between molecules are attractive.(D) The forces between molecules are repulsive.
(C) The forces between the molecules are attractive.
The simplest form of matter, molecules are made up of two or more atoms that are chemically bound. They are a chemical substance's tiniest particle that nonetheless has its chemical properties. They can be straightforward or intricate, and they come in a range of sizes and shapes. Two or three atoms make up simple molecules like oxygen or water, but thousands of atoms make up complex compounds like proteins or DNA. The boiling point, melting point, and reactivity of an object are all determined by the interactions between its molecules. The type of bonding between the atoms and the overall electric charges of the molecule determine the attractiveness or repulsion of these interactions.
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PART A
First, record some data for this comparison below.
Record your measured values of displacement and velocity for times t = 8.0 seconds and t = 10.0 in the columns below.
Next, use the measured displacment and velocity values at t = 7.0 seconds and t= 9.0 seconds to interpolate the values of displacement and velocity at t = 8.0 seconds.
Use the followinf formula to interpolate and extrapolate. Remember, x and y here represent values om the x and y axes of the graph. The x values will really be time and the y values will either be displacement (x) or velocity (vx).
(formula included in picture)
The displacement at 8.0 seconds is 19.08 m.
The velocity at 8.0 seconds is -0.06 m/s.
What is the displacement and velocity of the particle?
The displacement and velocity of the particle is calculated by applying interpolation and extrapolation.
8.0 s --------> 19.08 m
10.0 s --------> 16.81
8.0 s --------> x
(8 - 10 ) / ( 10 - 8 ) = ( 19.08 - 16.81 ) / ( 16.81 - x )
(-2 ) / ( 2 ) = ( 2.27 ) / ( 16.81 - x )
-1 (16.81 - x ) = 2.27
16.81 - x = -2.27
x = 16.81 + 2.27
x = 19.08 m
The velocity at 8.0 seconds is calculated as follows;
8.0 s ---------------> -0.06 m/s
10.0 s ---------------> -2.39 m/s
8.0 s ----------------> x
( 10 - 8 ) / ( 10 - 8 ) = ( -2.39 - - 0.06 ) / ( -2.39 - x )
1 = ( -2.33 ) / ( -2.39 - x )
-2.39 - x = -2.33
x = 2.33 - 2.39
x = -0.06 m/s
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during the collision, how significant was friction? consider that any impulse effects from friction would be based upon the magnitude of the friction and the time the friction has to act.
During the collision, friction was significant in the sense that it had an effect on the impulse of the collision.
The magnitude of the friction and the time it had to act are important factors in determining the effect of friction on the impulse of the collision.
In general, the greater the magnitude of the friction, the greater the effect on the impulse of the collision, and the longer the time that friction has to act, the greater the effect on the impulse of the collision.
Static friction occurs when the two objects in the collision are not moving relative to each other, and the magnitude of static friction depends on the surface roughness and the normal force between the two objects. The longer static friction has to act, the greater the total impulse of the collision.
Kinetic friction occurs when the two objects in the collision are moving relative to each other, and the magnitude of kinetic friction depends on the coefficient of kinetic friction between the two objects. The longer kinetic friction has to act, the greater the total impulse of the collision.
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what is the dryness fraction of the steam if wet saturated steam at 8 bar (hig = 2048 kj/kg) requires 82 kj of heat per kg of steam to completely dry it
(1996 KJ/Kg) is the dryness fraction of the steam if wet saturated steam at 8 bar which requires 82 kJ of heat per kg of steam to completely dry it.
The dryness fraction of steam can be calculated as follows:
Let's assume that the mass of steam is 1 kg. The heat required to convert the wet saturated steam to dry saturated steam is 82 kJ/kg. The total heat content of the wet saturated steam can be calculated using the enthalpy of saturated steam at 8 bar, which is 2048 kJ/kg.
So, the amount of heat that is left in the steam after removing 82 kJ of heat is
2048 kJ/kg - 82 kJ/kg = 1966 kJ/kg.
The dryness fraction of steam can be calculated as the ratio of the heat content of the dry saturated steam to the total heat content of the wet saturated steam:
Dryness fraction = Heat content of dry saturated steam / Total heat content of wet saturated steam
The heat content of dry saturated steam can be calculated from the enthalpy of dry saturated steam at 8 bar, which is often represented as hg.
So, Dryness fraction = hg / (hg + 82 kJ/kg) = hg / 1966 kJ/kg
The enthalpy of dry saturated steam at 8 bar can be obtained from steam tables, or calculated from the specific enthalpy of saturated steam and the dryness fraction using the equation:
hg = hf + xhfg
Here hf is specific enthalpy of saturated liquid at 8 bar and hfg is latent heat of vaporization at 8 bar.
Since the dryness fraction of steam can be expressed as hg / 1966 kJ/kg, we can rearrange the above equation to solve for the dryness fraction:
x = (hg / 1966 kJ/kg)
Therefore, the dryness fraction can be calculated by dividing the enthalpy of dry saturated steam by the total heat content of the wet saturated steam (1966 kJ/kg).
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two football players with mass of 75 kg and 100 kg run towards each other with a combined speed of 6 m per second and 8 m per second respectively. if they grab each other as they collide the combines speed of the two players just after the collision would be
When two objects collide and stick together, their combined speed after the collision can be calculated using the conservation of momentum principle. The principle states that the total momentum of an isolated system remains constant if no external forces act on it.
In this case, the initial momentum of the two players before the collision can be calculated as follows:
75 kg * 6 m/s + 100 kg * (-8 m/s) = 450 kg m/s
After the collision, the players stick together, and their combined speed can be calculated as follows:
Final momentum = (75 kg + 100 kg) * v
450 kg m/s = 175 kg * v
v = 450 kg m/s / 175 kg = 2.57 m/s
So, the combined speed of the two players just after the collision would be 2.57 m/s.
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Drew currently walks two miles every day after school but wants to take his workout to the next level. Which of these changes would you suggest he make to his routine to increase his stamina?
Answer:
Explanation:
Drew could run instead of walk after school.
Two objects with different masses and different velocities have the same momentum. What must be true of the velocity of the more massive object?
Answer: i think the answer is b
Explanation:
Answer:
The more massive object has a slower velocity than the lesser massive object.
Explanation:
Let M1 be the mass of the more massive object. M2 be the mass of less massive object. V1 be the mass of more massive object. V2 be the mass of less massive object. It is told that their momenta are the same. So M1V1= M2V2 or M1/M2= V2/V1.Also M1 is greater than M2.
From the equation we got M1/M2= V2/V1.
This means V2/V1 is greater than 1.
Which means V2 is greater than V1.
The object with more mass has lesser velocity than object with less mass.
Thus the answer to your problem is, The more massive object has a slower velocity than the lesser massive object.
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a student believes that such a large decrease in mechanical energy must be accompanied by at least a small decrease in momentum. how would you convince this student of the truth?
To convince the student, you can explain that mechanical energy is a scalar quantity that is the sum of kinetic and potential energy, while momentum is a vector quantity that represents the product of an object's mass and velocity.
The two are not necessarily related. A decrease in mechanical energy could occur without a change in momentum if, for example, the velocity of the object decreases while its mass remains constant, or if the potential energy increases. On the other hand, an increase in mechanical energy could occur without a change in momentum if, for example, the velocity of the object increases while its mass remains constant, or if the potential energy decreases.
The relationship between mechanical energy and momentum depends on the specific situation and the forces acting on the object, and is not determined by simple rules such as the magnitude of the change in mechanical energy.
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The concentration of enzyme for each experiment was 5.0 uM. What is the kcat for the reaction at ph 4.5 when no chloride added when compound 3 is substrate?
DIDN'T GET WRONG BUT WANTED TO BETTER UNDERSTAND
2.5E-2 s^-1
Rate for compound 3 is 125 nM/s, and rate of product formation did not vary over time for first 5 minutes implies enzyme was saturated with substate.
Kcat=Vmax/[E]= 125 nM/s/(5.0 uM)= 2.5E-2 s^-1
The kcat for the reaction of the enzyme at pH 4.5 when no chloride is added and compound 3 is the substrate is 2.5E-2 s^-1. This value is calculated using the formula Kcat = Vmax / [E], where Vmax is the maximum velocity of the reaction, and [E] is the concentration of the enzyme.
In this experiment, the concentration of the enzyme is 5.0 uM, and the rate of product formation for compound 3 is 125 nM/s. As the rate of product formation did not vary over the first 5 minutes, it can be assumed that the enzyme was saturated with substrate. Using this information, the kcat can be calculated as:
Kcat = Vmax / [E]
= 125 nM/s / (5.0 uM)
= 2.5E-2 s^-1
Therefore, the kcat for the reaction at pH 4.5 when no chloride is added and compound 3 is the substrate is 2.5E-2 s^-1.
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a wood block has a mass of 12.4 g and a density of 45.02 g/cm^3. find the volume of the block in cm^3.
Answer:
The volume of the block can be found by using the formula:
Density = Mass / Volume
Rearranging the formula to solve for volume:
Volume = Mass / Density
So,
Volume = 12.4 g / 45.02 g/cm^3
= 0.2747 cm^3
a merry-go-round is initially at rest. it accelerates constantly until its final angular speed is 10 rad/s and it completes 3 rotations in the process. what angular acceleration does the carousel have during this time?
The angular acceleration of the merry-go-round starting from rest to a velocity of 10 rad/s and completing 3 rotations is 2.67 rad/s².
Angular Acceleration is defined as the rate of change of angular velocity per unit time. It is usually expressed in radians per second square. The angular acceleration is also called rotational acceleration. The angular acceleration is expressed as, α= ΔωΔt, where Δω is the change in angular velocity and Δt is the change in time. The merry-go-round is initially at rest. So, the initial angular velocity is 0. The number of rotations completed in this process is 3 rotations. The final angular velocity is 10 rad/s. The angular displacement is( 3×2π) rad. So angular acceleration is given by the equation, a=w²/2×d=10×10/2×3×2π= 2.67 rad/s².
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an automobile traveling at 70.0 km/h has tires of 80.0 cm diameter. (a) what is the angular speed of the tires about their axles? (no response) 48.6 rad/s (b) if the car is brought to a stop uniformly in 35.0 complete turns of the tires (without skidding), what is the magnitude of the angular acceleration of the wheels? (no response) 5.37 rad/s2 (c) how far does the car move during the braking?
(a) The angular speed of the tires an automobile traveling at 70.0 km/h has tires of 80.0 cm diameter about their axles = 48.611 rad/s
(b) The magnitude of the angular acceleration of the wheels if the car is brought to a stop uniformly in 35.0 complete turns of the tires (without skidding) = 5.37 rad/s²
(c) The car moves during the braking = 87.92 m
The angular speed of the tire can be calculated using the linear velocity and radius.
We can find the remaining unknowns by using angular speed and rotational motion kinematic equations. We can calculate the distance traveled by using the formula for the length of the curve in terms of angle and radius.
The equation for angular speed:
ω = v/r
Where:
ω = angular speed
v = velocity
r = radius
70.0 km/h = 19.4 m/s
Diameter = 80 cm
Radius = 0.4 cm
Hence,
(a) the angular speed:
ω = (19.4 / 0.40)
= 48.611 rad/s
(b) the magnitude of the angular acceleration of the wheels:
θ = 35.0 x 2[tex]\pi[/tex] rad
= 219.8 rad
For rotational motion, use the third equation of motion.
ω² = ω₀² + 2[tex]\alpha[/tex]θ
Hence, the angular acceleration of the wheels:
[tex]\alpha[/tex] = (48.611)² / (2 x 219.8)
= 5.37 rad/s²
(c) the car move during the braking:
s = rθ
= 0.4 x 219.8
= 87.92 m
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what element seems poorly placed in group ia (1), the alkali metals?
The element which seems poorly placed in group ia (1), the alkali metals is hydrogen.
Methane is the most prevalent chemical element and is thought to make about 75% of the universe's mass. Numerous hydrogen atoms can be found in water, plants, animals, and, of course, people here on earth. The lightest element is hydrogen. Under normal circumstances, hydrogen is a gas made up of diatomic molecules with the formula H2. It is non-toxic, tasteless, colourless, odourless, and extremely flammable.
Alkali metals are extremely reactive, hence they are almost never encountered in nature in their elemental state instead appearing as ionic compounds (except for hydrogen).
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what is replicability in tok
Replicability in the context of the theory of knowledge (ToK) refers to the ability of a knowledge claim or scientific experiment to be repeated and produce consistent results.
In ToK, replicability is seen as an important criterion for evaluating the reliability and validity of knowledge claims. When a scientific experiment is replicated and produces consistent results, it increases the confidence that the original experiment was correctly designed and executed, and that the results accurately reflect the underlying phenomena being studied. Conversely, if a scientific experiment cannot be replicated, it calls into question the validity of the original experiment and the knowledge claims that were based on its results.
In addition to its importance in the evaluation of scientific knowledge, replicability is also a key aspect of the process of scientific inquiry. By attempting to replicate previous experiments, scientists can build on existing knowledge and add to the body of scientific evidence in support of a particular hypothesis or theory.
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A 40.0 kg projectile leaves a 2200 kg launcher with a speed of 800 m/s. What is
the recoil velocity of the launcher?
A 40.0 kg projectile leaves a 2200 kg launcher with a speed of 800 m/s. 10m/s is the recoil velocity of the launcher.
How does one calculate recoil velocity?
The recoil velocity of the launcher can be calculated using the law of conservation of momentum. According to this law, the momentum of the projectile leaving the launcher must be equal to the momentum of the recoiling launcher. Therefore, the momentum of the projectile is equal to the momentum of the launcher.
The momentum of the projectile is equal to the product of its mass and velocity:
Momentum of the projectile = 40.0 kg x 800 m/s = 32,000 kg m/s
The momentum of the launcher is also equal to the product of its mass and velocity:
Momentum of the launcher = 2200 kg x V (velocity of the launcher)
Therefore, the recoil velocity of the launcher can be calculated by solving for V:
32,000 kg m/s = 2200 kg x V
V = 32,000 kg m/s/2200 kg
V = 14.545 m/s
Therefore, the recoil velocity of the launcher is 14.545 m/s.
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part 1 of 2
An amusement park ride consists of a rotating circular platform 7.87 m in diameter from which 10 kg seats are suspended at the end of 3.3 m massless chains. When the system ro-tates, the chains make an angle of 43.5° with the vertical.
The acceleration of gravity is 9.8 m/s?
What is the speed of each seat? aswer in units of m/s.
part 2 of 2
If a child of mass 40.6 kg sits in a seat, what is the tension in the chain (for the same angle)?
Answer in units of N.
Gravity's acceleration is 9.8 m/s², The speed of each seat is 11.63 m/s.
Define acceleration of gravity?
Acceleration due to gravity is also acceleration, but acceleration is only concerned with the force of gravity, whereas acceleration is concerned with any force.
The acceleration due to gravity on any body is the acceleration with which the earth attracts the body towards itself as a result of the earth's gravitational field. The acceleration due to gravity is the acceleration with which a body moves towards the earth due to gravity.
The gravitational force between two objects is affected by the distance between their centres of mass, so the force of gravity on an object is smaller at the equator than at the poles. Because of this effect, gravitational acceleration is about 0.18% lower at the equator than at the poles.
given data:
diameter = 7.83 m
mass = 10 kg
distance = 3.3 m
angle = 43.5°
acceleration of gravity = 9.8 m/s²
for speed we will apply here formula that is express as
speed = √(Rg/tanθ ) ......................1
put here all value in equation 1 we get
here R = diameter /2 + mass × sin43.5
R = 7.83/2 + 10(0.463)
R= 8.545 m
speed = √(8.545(9.8)/tan(90-43.5) )
speed = 11.63 m/s
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a study hall is 5.4 m long and 5.7 m wide and 10. m high. if the air conditioner provides 434.7 cu ft. of air/min, how long (in minutes) will it take for the air into the room to be completely replaced once? 1 m
For the air in the room to be completely replaced once, it will take 24.85 minutes if the air conditioner provides 434.7 cu ft. of air/min.
The volume of the study hall can be calculated as
5.4 m × 5.7 m × 10 m = 308.18 cubic meters.
Converting the airflow rate of the air conditioner from cubic feet to cubic meters, we get 434.7 cu ft/min = 12.3824 m³/min.
Therefore, it would take 308.18 / 12.3824 = 24.85 minutes for the air in the room to be completely replaced once.
It's important to note that this calculation assumes ideal conditions with no air leakages, no air being added to the room, and a constant air flow rate. In reality, the actual time it takes for the air in the room to be completely replaced will depend on various factors such as air leaks, people entering and leaving the room, and variations in the airflow rate of the air conditioner.
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help me please pleass please i beg
There are three states of matter.
What are the states of matter?There are three states of matter and these are the solid, the liquid and the gas. We have to note that the way that the states of matter are found would depend on the arrangement and the movement of the particles that are in each of the states of matter as we know it.
In this case we know that the liquid and the gases are compressible but the solid is nnot compressible. The sold has a fixed shape but the liquid and the gas does not. The liquid and the solid have a definite volume but the gas does not.
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Write two ways of reducing friction
Answer:
Explanation:
The two ways of reducing friction are by:
1) applying lubricants (like oil or grease)
2) by converting static or sliding friction into rolling friction with the help of wheels or ball bearings.
a drone has a frequency of 2.11 ghz (gigahertz). what wavelength is associated with this frequency?
The wavelength of the drone which is associated with the frequency of 2.11 Ghz is 0.111 m.
λ = c / f = ( 3 x 10^8 ) / ( 2.71 x 10^8 ) = 0.111 m.
where lambda is the wavelength, c is the speed of light and f is the frequency.
What is wavelength?
The distance between repeating components of a wave, like electromagnetic waves, is known as its wavelength (e.g. light, radio waves). The Greek letter lambda is frequently used to symbolize it, and it is typically expressed in meters.
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Object A, which has been charged to +4.0 nC is at the origin. Object B, which has been charged to −8.0 nC, is at (x,y)=(0.0 cm, 2.0 cm).
What is the electric force on B due to A in component form?
What is the electric force on A due to B in component form?
The electric force on B due to A in component form is -7.2 x 10^-4N and the electric force on A due to B in component form is +7.2 x 10^-4N.
Given the charge on object A (q1) at origin = +4.0 nC
The charge on object B at (x,y) is (q2) = −8.0 nC
The position of object B = (0.0 cm, 2.0 cm).
Soo, the distance from origin to object B is (r) = 2cm = 0.02m on y-axis.
From Coulombs law, we know that Fc = kq1q2/r^2 where k is electrostatic constant = 9 x 10^9Nm^2/C^2
The electric force on B due to A in component form is Fq1q2
Then, Fq1q2 = 9 x 10^9 x (+4 x 10^-9)(-8 x 10^-9)/0.02 x 0.02
Fq1q2 = -7.2 x 10^-4N
The electric force on A due to B in component form is Fq2q1
Then, Fq2q1 = 9 x 10^9 x(-8 x 10^-9) (+4 x 10^-9)/0.02 x 0.02
Fq2q1 = 7.2 x 10^-4N
Here, the electric force on B due to A and on A due to B is same in magnitude but the direction of force changes.
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find the volume of the parallelepiped (box) determined by u, v, and w.
The volume of the parallelepiped determined by u, v, and w is| w · ( u × v)|.
In geometry, a parallelepiped is a three-dimensional figure made up of six parallelograms. Similar to a parallelogram, just like a cube is a square. The volume of the parallelepiped enclosed by a, b, and c is: Volume = area of the base and height = |a×b∥c||cosφ|=|(a×b)·c| The formula comes from the properties of the cross product. The area of the base of the parallelogram is |a×b| and the vector a×b is perpendicular to the base. The height of the cube is |c||cosφ|. Therefore, the volume of the parallelepiped determined by u, v, and w is| w · ( u × v)|.
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the meridian is a north-south line on the sky that passes through the zenith. what is the right ascension of a star that is on the meridian at midnight on the 21st of september?
The right ascension of a star that is on the meridian at midnight on September 21st is 0 hours.
The right ascension of a star that is on the meridian at midnight on September 21st can be calculated based on the position of the sun on that day and time. On September 21st, the sun is at the vernal equinox, which marks the start of spring in the Northern Hemisphere and the beginning of the astronomical year. At the vernal equinox, the sun is at the celestial equator and its right ascension is zero hours.
As the meridian is a north-south line on the sky that passes through the zenith, a star that is on the meridian at midnight on September 21st will have the same right ascension as the sun at the vernal equinox, which is 0 hours.
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april has 3 hours to spend training for an upcoming race. she completes her training by running full speed the distance of the race and walking back the same distance to cool down. if she runs at a speed of 10mph and walks back at a speed of 2mph , how long should she plan to spend walking back?
April should plan to spend walking back after 3 hours training for an upcoming race and runs at a speed of 10mph and walks back at a speed of 2mph = 30 minutes.
How to determine the time to spend walking back?First, determine the distance,
d = speed x time
The distance = 10
The speed = 2 mph
The time = (3 - x hours)
Let's say 'x' represents the amount of time spent running in hours, and 3-x represents the amount of time spent walking in hours.
Hence,
10x = 2(3 - x)
10x = 6 - 2x
12x = 6
x = [tex]\frac{1}{2}[/tex] hour
= 30 minutes
So, April should she plan to spend walking back in 30 minutes.
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a) does the work you do on a book as you lift it onto a shelf depend on the path that the book takes?
No, time has nothing to do with work. The amount of force needed to lift the book does, however, depend on how quickly you raise it because force is a function of time.
Time is not a consideration and is not included in the calculation, hence work done is independent of the path because displacement is independent of the path.
Both the height of the shelf, which determines your displacement, and the mass of the object, which you are lifting against an increasing force of gravity, are relevant.
Because the force you apply to the book is in the same direction as its displacement, lifting it is considered positive work. Inverse work is being done by gravity.
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Complete Question:
Does the work required to lift a book to a high shelf depend on how fast you raise it? Does the power required to lift the book depend on how fast you raise it? Explain.
I used up all my tries for part a and I'm honestly stuck. I know it has something to do with the conservation of energy but I can't figure it out :(
a. Find d, the initial displacement of the spring-block system (in cm).
b. Find the speed of the block when it reaches the equilibrium position. (in m/s)
c. How fast is the block moving when it reaches a position 4.00 cm to the left of its equilibrium position?
d. Assuming friction not negligible, find the coefficient of kinetic friction between the block and the surface if the block-spring system compresses 0.300 cm from the equilibrium position before stopping and moving back to the right?
Using the equation of motion:
1/2mv^2 = 1/2kx^2
where
m is the mass of the block,
v is the velocity
x is the displacement from the equilibrium position
we can find the initial displacement, d.
b. To find the speed of the block when it reaches the equilibrium position, we can use the conservation of mechanical energy.The total mechanical energy of the system is the sum of the kinetic energy and potential energy.
Initial Potential energy = 1/2kd^2
Final kinetic energy = 1/2mv^2
so,
v=sqrt(2*(1/2kd^2))/m
c. The speed of the block when it reaches a position 4.00 cm to the left of its equilibrium position will be the same as when it reaches the equilibrium position. Because the speed will be at its maximum at the equilibrium position.d. To find the coefficient of kinetic friction between the block and the surface, we can use the work-energy theorem, which states that the work done on an object is equal to the change in kinetic energy of the object.Work done = change in kinetic energy
The work done by friction is equal to the force of friction multiplied by the distance over which the force acts.
Friction force = friction coefficient * normal force
Friction force = friction coefficient * m * g
work done = friction force * distance
By putting the value of friction force and work done we can find the coefficient of kinetic friction.
Hooke's Law
Hooke's Law states that the force (F) required to extend or compress a spring by some distance x is proportional to that distance. Mathematically, it is represented as F = kx, where k is the spring constant and is unique to the spring. This relationship is only valid for small displacements, and assumes that the spring is not stretched beyond its elastic limit.
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