Research demonstrates that group problem-solving produces superior results. If they have a team player behind them, people are more inclined to take calculated risks that result in innovation.
How do you develop into a productive team member?See how you can be a great team member in these seven ways.Respect Your Due Dates. You must be trustworthy if you want the respect of your coworkers.Be receptive.Respect the working styles of others.Working as a team promotes the development of the individual, boosts job satisfaction, and lessens stress. Be upbeat and do your best to assist people. Everyone will appreciate your cooperation and willingness to put in a lot of effort, even your boss.
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a pith ball has a shortage of 1.85 x 10^17 electrons. what is the net charge on this ball in coulombs?
The net charge on the pith ball in coulombs when the number of electrons is specified is calculated to be 2.96 × 10⁻² C.
Given that, number of electrons = 1.85 × 10¹⁷
We know the charge on electron as, e = 1.6 × 10⁻¹⁹ C
The relation between charge and number of electrons is known to be,
Q = n e
where, Q is charge
n is number of electrons
e is charge on electron
After putting the values into the equation above, we have,
Q = 1.85 × 10¹⁷ × 1.6 × 10⁻¹⁹ = 2.96 × 10⁻² C
Thus, the net charge is calculated to be 2.96 × 10⁻² C.
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A person kicks a rock off a cliff horizontally with a speed of 21m/s. If the height of the cliff is 85 meters, find Time and range
The time spent in the air by the rock is 4.2 seconds.
The range of the of the rock's motion is 88.2 m.
What is the time of motion of the rock?
The time spent in the air by the rock is its time of motion and it is calculated as follows;
t = √ ( 2h / g )
where;
h is the height of fallg is acceleration due to gravityt = √ ( 2 x 85 / 9.8 )
t = 4.2 seconds
The range of the of the rock's motion is calculated as follows;
x = vt
x = 21 m/s x 4.2 s
x = 88.2 m
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C) The man raises his body a vertical distance of 0. 63 m to go from stage 1
to stage 2. Calculate the work done by the man. Use your answer to part
(b)Use the equation: work done = force x distance
The work done by the man in lifting his body is 493.92J.
What is work done?
When an object is moved over a specific distance by an external force, the quantity of energy transferred to it is called work. The quantity of energy transmitted to an object through work is referred to as the work done on the thing. Since the man raises his body a vertical distance of 0.63m to go from stage 1 to stage 2 he is doing work against gravity. So, the work done in this case is given by W=mgh where m is the mass of the body, g is the acceleration due to gravity and h is the height raised by the body.
Now, according to the question
Mass of the man=80Kg
Height raised by the man=0.63m
Acceleration due to gravity=9.8
On substituting the values in the given formula, we get the work done as
W=80×9.8×0.63
W=493.92J
Therefore, the work done by the man is 493.92J.
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g if the prism is surrounded by a fluid, what is the maximum index of refraction of the fluid that will still cause total internal reflection within the prism?1
Therefore, the highest fluid index of refraction at which we can still produce entire internal reflection is 1.34.
What occurs when light is refracted?A wave bends when it reaches a medium with a different speed, which is known as refraction. When light travels through a slow medium after traveling through a fast medium, the light ray is bent in the direction of the boundary between the two media.
Explain to children what refraction is.When light travels from one material to another and changes direction or bends, this is known as refraction. When light strikes water, for instance, it refracts after passing through the air. This may cause a straw in a glass of water to seem twisted at the surface.
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the equator is characterized by relatively high or low pressure aloft
The equator is characterized by relatively low atmospheric pressure aloft.
What is equator?The equator is a large circle that surrounds Earth and sits on a plane perpendicular to its axis, everywhere being equally far from the geographic poles.
This geographic, or terrestrial, Equator separates Earth's Northern and Southern hemispheres and serves as the fictitious reference line on the planet's surface from which latitude is calculated; in other words, it is the line at latitude 0°.
In hotter equatorial regions, the air above expands, gets less dense, and rises. At this latitude, this causes a low pressure band to form.
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a bullet is fired straight up and takes 14.8 s to reach its peak. determine how high the bullet goes and its initial velocity (magnitude
The bullet goes up to the height of 1074.6 m, and its initial velocity was 145.2 m/s, If the bullet takes 14.8 sec to reach its peak.
Time taken by the bullet to reach its peak, t = 14.8 sec
Velocity after 14.8 sec, v = 0
Let the initial velocity, = u
Acceleration working on the bullet, a = -g = -9.81 m/s²
By the first equation of motion,
v = u + at
0 = u - 9.81 × 14.8
u = 145.2 m/s
Let the highest peak reach by the bullet is h meter, then by using the second equation of motion,
h = ut + 0.5at²
h = (145.2 × 14.8) + 0.5(-9.81)(14.8)²
h = 1074.6 m
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what is meant by intensity of sound 6.81 times as great as the intenstiy of another sound. relative the the quieter sound, what is the intensity level
The energy of the first sound is 6.81 times bigger than the energy of the second sound, or 6.81 times stronger than the intensity of another sound.
Its intensity is the term used to describe how loud a sound is to an individual. Loudness cannot be quantified objectively since everyone perceives loudness differently. Following is a description of the relative characteristics of the acoustic signal, audio intensity, and sound intensity. The kinetic energy of the mass of air is created by the combination of the source's increasing amplitude and the vibrating surface.
The formula for sound intensity is acoustic power divided by the normal area to the propagation direction.
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a person throws a rock straight up into the air. at the moment it leaves the person's hand it is going 29 mph. when the rock reaches its peak, how fast is it going and what is the magnitude and direction of its acceleration? ignore air drag. express your answer using appropriate mks units.
In a downward direction, the magnitude of the acceleration is negative and velocity is zero.
What is acceleration?The rate of change in velocity is defined as acceleration.The rate at which speed changes with time, in terms of both speed and direction.If a factor or an object moves in a straight line, it is said to be extended.The acceleration of the Earth is always downward.As a result, when an object is launched upward, its acceleration is directed downward.If the object is moving downward, so is the acceleration.Here,
The object would cease to move at the maximum height, and thus the velocity of the object at the peak of motion would be seen to be zero. In this case, the acceleration would be negative.To learn more about acceleration refer to :
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2. 4 A stellar atmosphere consists almost entirely of hydrogen. Assume that 50% of the hydrogen molecules are dissociated into atoms and that the pressure is 100 Pa. Given that the binding energy of the hydrogen molecule is 4. 48 eV, estimate the temperature
The estimated temperature in the stellar atmosphere is T = 4.48 / 8.62 x 10^-5 * ln([H2]/4) .
To estimate the temperature of a stellar atmosphere consisting almost entirely of hydrogen, we can use the concept of dissociation equilibrium. When a gas is in equilibrium, the rate of formation of molecules from atoms is equal to the rate of dissociation of molecules into atoms. The dissociation equilibrium constant (Kd) is given by the ratio of the concentration of atoms to the concentration of molecules, at a given temperature and pressure.
In this case, it is given that 50% of the hydrogen molecules are dissociated into atoms, so the concentration of atoms is half the concentration of molecules. The pressure is also given as 100 Pa.
The dissociation equilibrium constant (Kd) can be calculated using the following equation:
Kd = [H]^2 / [H2]
Where [H] is the concentration of atomic hydrogen and [H2] is the concentration of molecular hydrogen.
The equilibrium constant can also be related to the binding energy of the hydrogen molecule (E) and the temperature (T) using the following equation:
Kd = e^(-E/kT)
Where k is the Boltzmann constant.
By combining the above two equations:
[H]^2 / [H2] = e^(-E/kT)
And since we know that [H] = [H2]/2
[H2]/4 = e^(-E/kT)
Now we can solve for T:
T = -E/k * ln([H2]/4)
Given that the binding energy of hydrogen molecule is 4.48 eV and k = 8.62 x 10^-5 eV/K.
T = 4.48 / 8.62 x 10^-5 * ln([H2]/4)
The pressure is not used in the above calculation. The temperature is related to the binding energy and the dissociation equilibrium constant which is dependent on the concentration of the hydrogen molecules and atoms.
It is important to note that the above calculation is a rough estimate and the temperature of a stellar atmosphere can be affected by many other factors such as radiation, convection, and other chemical reactions.
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the ability to do activities for more than a few minutes is
The ability to do activities for more than a few minutes is called aerobic ability.
Endurance is the ability to maintain an activity for extended periods of time and usually refers to aerobic ability. For example, children can play actively for hours. We need this ability to perform repetitive activities of daily living, such as stirring food while cooking, using a hair dryer to dry our hair, or walking up steps.
Recreational and job-related activity also often require a high level of endurance. Local muscle endurance is best defined as the ability to resist muscular fatigue and demonstrate how a given type of contraction can be sustained, typically measured in terms of the number of repetitions.
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a baseball is thrown vertically into the air with a velocity v, and reaches a maximum height h. at what height was the baseball moving with one-half its original velocity? assume air resistance is negligible.
At the height of 3h/4 meter, the velocity of the baseball will be half of its original velocity v, if it reaches a maximum height h.
Maximum height reached by the baseball, = h
The velocity of the ball at maximum height v₁ = 0
Initial velocity, = v
by the 3rd equation of motion, v₁² = v² - 2gh
0 = v² - 2gh
v² = 2gh
Now let the height at which the velocity will be half of the original velocity = h₁
Then by the 3rd equation of motion,
(v/2)² = v² - 2gh₁
2gh₁ = v² - v²/4 = 3v²/4
h₁ = 3v²/8g
We know v² = 2gh, So
h₁ = 3(2gh)/8g = 3h/4 m.
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how did they control a camera on the moon to perfectly follow the lunar lander as it descended from the surface
To control a camera on the moon to perfectly follow the lunar lander as it descended from the surface, engineers used a combination of tracking systems and software.
First, they used a tracking camera to monitor the descent of the lander. This camera was mounted in a fixed position, and was able to track the movement of the lander in real-time.
Additionally, engineers used software to calculate the exact trajectory of the lander and to calculate the corresponding camera movements. This allowed the camera to perfectly follow the lunar lander as it descended from the surface.
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a conducting sphere with an interior cavity has been given a charge of 2.0 nc. what is the charge on the inner surface of the sphere?
The charge on the inner surface of the sphere is +2nC because the charge on the interior cavity is 2.0nC.
A law that connects the distribution of electric charge to the resulting electric field is known as Gauss's law, commonly referred to as Gauss' flux theorem.
In its integral form, it asserts that the flux of the electric field out of any closed surface, regardless of how that charge is distributed, is proportional to the electric charge enclosed by the surface. In situations where symmetry requires uniformity of the field, it may be possible to determine the electric field throughout a surface encompassing any charge distribution despite the fact that the law alone is insufficient to do so.
When there is no such symmetry, Gauss's law, which states that the electric field divergence is proportional to the local density of charge, can be applied in its differential version.
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does sound travel faster in warm air or in cold air? in humid air or dry air?
In warm air, sound travels more quickly than in cold air. Since the speed of sound is directly inversely proportional to the square root of the air's absolute temperature, the speed of sound rises with temperature.
Additionally, dry air travels faster than humid air for sound. The speed of sound is slightly affected by humidity, with sound traveling slightly slower in more humid air. This is due to the fact that airborne water vapor has the ability to slow down sound waves by absorbing some of their energy.
What is moisture?The amount of water vapor in the air is measured by humidity. At a given temperature, it is typically expressed as a percentage of the maximum amount of water vapor that the air can hold.
It is said that the air has a humidity of 100 percent when it is saturated. Any additional water vapor will condense into liquid or solid form (such as dew, fog, clouds, or precipitation) because the air cannot hold any more water vapor at this point. The air can hold more water vapor and is less likely to reach 100% humidity as the temperature rises.
Specific humidity or mixing ratio, which is the ratio of the mass of water vapor in the air to the mass of the air as a whole, is another way to measure humidity.
The weather and climate can be significantly affected by humidity. High humidity can cause clouds to form and precipitation to fall. It can also make the air feel hotter. Low humidity can make the air feel cooler, make it dry, and make wildfires more likely. The human body is also affected by humidity; low humidity can dry out the skin and nasal passages, while high humidity can make it difficult to cool down and can exacerbate respiratory issues.
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. A stuntman rode his motorcycle for seven straight hours on the wall of a large vertical cylinder.
His average speed was 45 km/hr. Suppose that in a time of 30 seconds, he increases his speed
steadily from 8.3 m/s to 11.7 m/s while circling inside the cylindrical wall. How far does he
travel in the time interval in meters?
He travels a distance of 300 m in that time interval.
What is the distance that he travels?We know that we can be able to obtain the time that he travelled if we use the formula that applies to the average speed. In this case we are told in a time of 30 seconds, he increases his speed steadily from 8.3 m/s to 11.7 m/s.
Thus;
distance = Average speed/Time
Distance = (8.3 + 11.7/2) * 30
Distance = 300 m
We can see that he would move through a distance of well about 300m as the velocity is increasing as shown here.
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a proton orbits just at the surface of a charged sphere of radius 4.43 cm. if the speed of the proton is 3.22 x105 m/s, what is the charge on the sphere?
The charge on the sphere is found to be 1.5 x 10⁻¹⁵ C.
The proton is orbiting the surface of the charged sphere of radius 4.43 cm and the speed of the proton is 3.22 x 10⁵m/s. The charge on proton is 1.6 x 10⁻¹⁹ C and the mass of the proton is 1.67 x 10⁻²⁷ kg.
Now,
For revolving,
Electrostatic forces = Centripetal force
KQq/r² = Mv²/r
Here,
R is the radius of the orbit,
Q and q are the charges of the sphere and the proton,
M is the mass of the proton.
Putting values,
9 x 10⁹ x Q x 1.6 x 10⁻¹⁹/0.0443 = 1.67 x 10⁻²⁷ x 3.22 x 10⁵
Q = 1.5 x 10⁻¹⁵ C
So, the charge on the sphere is 1.5 x 10⁻¹⁵ C.
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Two objects fall from an apartment window sill at the same time. Object 1 lands on the sidewalk in 3.6 seconds. Object 2 lands on the sidewalk in 3.3 seconds. What can be concluded about the objects?
Answer:
Object 1 has more surface area than Object 2.
Explanation:
Even if both objects are falling at the same rate due to gravity, air will usually always mess with the 'speed' of an object (I hope that makes sense, I'm not the best at explaining things but Object 1 has more surface area than Object 2 IS correct).
Because of this, regardless of their mass, all objects descend in free fall at the same speed.
Why do all objects fall with the same acceleration?Because of this, regardless of their mass, all objects descend in free fall at the same speed.We frequently refer to this ratio as the acceleration of gravity because it results in a 9.8 m/s/s acceleration of any item placed in the 9.8 N/kg gravitational field at the surface of the Earth.Even if items of different masses are thrown from the same height, they will all accelerate at exactly the same rate due to Earth's uniform acceleration.Things that are heavier fall to the ground more quickly.A heavy object will hit the ground first if you drop it with a light thing.This is an artificial query.All objects fall equally, as I recall from physics.To learn more about same acceleration refer
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An electron acquires 3. 45×10−16 J of kinetic energy when it is accelerated by an electric field from plate A to plate B.
a. What is the potential difference between the plates?
b. Which plate is at the higher potential? Plate A or Plate B
The potential difference between the plates is 2156V Plate B has the higher potential because the electron moves from A to B as it acquire its own kinetic energy.
Given kinetic energy of electron (KE) = 3.45×10^−16 J
The electron is accelerated from plate A to plate B by an electric field.
We know kinetic energy = charge of electron x potential difference.
So, KE = -qV where q = 1.6 x 10^-19C which is charge of electron.
-3.45×10^−16 = -1.6 x 10^-19 x V
V = 3.45×10^−16/1.6 x 10^-19 = 2156V
Sine the potential difference is positive we can say that plate B has higher potential that plate A.
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two point charges are separated by a distance of 60.0 cm. the numerical value of one charge is twice that of the other. each charge exerts a force of magnitude 85.0 n on the other. 1) find the magnitude of the charge with a smaller magnitude.
The magnitude of the charge with a smaller magnitude is 2.42 × 10⁴ Coulomb. The result is obtained by using the formula for electrostatic force.
What is the formula for electrostatic force?The formula for electrostatic force is
F = kq₁q₂/r²
Where
F = electrostatic force (N)k = Coulomb's constant (9 × 10⁹ Nm²/C²)q₁ and q₂ = charges (C)r = distance between the charges (m)Two point charges are separated.
We have
r = 60 cm = 0.6 mq₁ = 2q₂F = 85 NFind the smaller magnitude of the charge!
The smaller magnitude of the charge is q₂.
We use the formula above to find q₂.
F = kq₁q₂/r²
85 = (9×10⁹)2q₂q₂/(0.6)²
85 = (18×10⁹)q₂²/0.36
q₂² = (18×10⁹)/(85×0.36)
q₂² = (18×10⁹)/30.6
q₂² = 5.88 × 10⁸
q₂ = √(5.88 × 10⁸)
q₂ = 2.42 × 10⁴ Coulomb
Hence, the smaller magnitude of the charge is 2.42 × 10⁴ Coulomb.
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a box of mass 50.0 kg fell from a shelf to the floor 2.00 m below. when the box hit the floor, one corner was crushed while the box came to rest in 0.05 s. what was the average net force applied to the box while it came to rest?
The net force applied by to the box is 6264.2 N, if the mass of the box is 50.0 kg and it comes to rest in 0.05 second.
Free fall height of the box, h = 2.0 m
Free fall velocity of the box just before touching the ground, v = √(2gh)
= √(2×9.81×2) = 6.264 m/s
Final velocity or the box after 0.05 sec, = 0
Time to stop, t = 0.05 sec
We know that the applied force is equal to the rate of change of momentum.
F = m(v-u)/t
F = 50 × (6.264-0)/0.05 = 6264.2
So, F = 6264.2 N
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what did Zhou artisans discover
Iron production was mastered by Zhou craftsmen.
Zhou artisans: what are they?The Zhou dynasty was one of the greatest in Chinese history, and among its many achievements were the artisans who discovered how to make iron. Iron became a common material for agricultural equipment, which was revolutionary for the Chinese people and extremely beneficial for agriculture. Everything became lot easier, quicker, and more efficient as a result.
The Zhou dynasty, which followed the Shang dynasty, was the longest to rule China.
Artisans are individuals who create handicrafts.
What made the Zhou Dynasty famous?Agriculture, education, military planning, Chinese literature, music, philosophical schools of thought, social stratification, as well as political and religious advancements, all benefited from the Zhou Dynasty's considerable cultural contributions.
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a merry-go-round rotates at the rate of 0.27 rev/s with an 85 kg man standing at a point 2.2 m from the axis of rotation. what is the new angular speed when the man walks to a point 0 m from the center? consider the merry-go-round is a solid 67 kg cylinder of radius of 2.2 m. answer in units of rad/s.
The new angular speed of the merry go round after the man came to the point 0m on the merry go round will be 1.37 rev/s.
The merry go round is rotating at the speed of 0.27 rev/s with a man of mass 85 kg on it at a pint of 2.2 m form he center of the axis of rotation.
We have to find the new speed of the merry go round when the person walk to the center of the circle.
The mass and radius of the merry go round are given to be 67 kg and 2.2m.
Using the conservation of momentum as the system is not under any external force,
Initial momentum = final momentum
I₁W₁ = I₂W₂
I₁ and W₁ are initial moment of inertia and angular speed, I₁ and W₁ are final moment of inertia and angular speed.
Putting values,
(85+67)(2.2)₂0.27 = (67)W₂
1.34 rev/s = W₂
So, the final angular speed is 1.34 rev/s.
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A spring has a constant of 2000 N/m. If 1000 kg is placed on the spring
how far in meters will it compress?
The compression in the spring will be 4.9m
What is spring force?
The force needed to compress or extend a spring attached to an object is known as the spring force. A spring exerts an equal and opposite force on a body when the object exerts a force on it. It always acts to bring mass back to its equilibrium. Spring force exerted by the spring on the body is given by = where k is the spring constant of the spring x is the compression or extension caused in the spring. To find the x we can use this formula.
Now, according to the question we have
Spring constant=2000N/m
Mass attached to the spring=1000Kg
On substituting the values in the above formula, we get the compression as
F=kx
mg=kx
1000×9.8=2000×x
x=4.9m
Therefore, the compression in the spring is 4.9m
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After landing on Mars, you drop a marker from the door of your landing module and observe that it takes 2.1 ss to fall to the ground. When you dropped the marker from the module door on Earth, it took 1.3 ss to hit the ground.
What is the magnitude of the acceleration due to gravity near the surface of Mars?
The magnitude of the acceleration due to gravity near the surface of Mars is[tex]2*d / 4.41s^2[/tex].
How to calculate acceleration?To calculate the acceleration due to gravity near the surface of Mars, we can use the equation:
d = 1/2 * a * t^2
Where d is the distance fallen, a is the acceleration due to gravity, and t is the time taken to fall.
We know that on Earth, the marker took 1.3s to fall to the ground and on Mars it took 2.1s. We also know that the distance fallen is the same on both planets, since the marker was dropped from the same height. Therefore, we can set the distance fallen equal on both planets and use the equations above to solve for the acceleration due to gravity on Mars:
d = 1/2 * a_Earth * (1.3s)^2 = 1/2 * a_Mars * (2.1s)^2
a_Mars = 2d / (2.1s)^2
a_Mars = 2d / (4.41s^2)
Where d is the distance fallen and a_Earth = 9.8 m/s^2 is acceleration due to gravity on Earth.
Therefore, the magnitude of the acceleration due to gravity near the surface of Mars is [tex]2*d / 4.41s^2[/tex]
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a rock with mass of 7.45 kg is thrown straight up with a force of 497 n gravity is 9.81 what is the net acceleration of the rock
The net acceleration working on the rock is 56.9 m/s² in upward direction, if the mass of the rock is 7.45 kg and the force applied on it is 497 N.
The upward force applied on the rock, F = 497 N
Mass of the rock, M = 7.45 kg
Acceleration due to gravity, g = 9.81 m/s²
We know force = Mass × Acceleration
Acceleration produced in the rock due to the force applied, a = 497/7.45
= 66.71 m/s²
Acceleration due to gravity is working downward, so net acceleration working on the rock, = 66.71 - 9.81 = 56.9 m/s²
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if the radius of a planet is larger than that of earth by a factor of 7.01, how much bigger is the volume of the planet than earth's?
The radius of a planet is 7.01 times of earth's. The volume of the planet is 344.47 times bigger than the volume of earth.
Let's assume that the shape of both planets are perfect spheres. The volume of a sphere is given by:
V = 4/3 πr³
Where r is the radius.
Hence, the volume is directly proportional to r³, or:
V ∝ r³
Let:
r_p = radius of the planet
r_e = radius of earth
Then,
r_p = 7.01 r_e
Using direct proportionality:
V_p : V_e = r³_p : r³_e
V_p : V_e = (7.01 r_e)³ : r³_e
V_p : V_e = 344.47 : 1
V_p = 344.47 V_e
Therefore, the volume of the planet is 344.47 times bigger than earth's.
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indicate which beam scenario will have better resolution- temporal resolution- 10cm sector size, scanning at 18cm or 7cm sector size, scanning at 13cm?
The beam scenario with a 7cm sector size and a scanning rate of 13cm will have better resolution.
This is because the more modest sector size considers a more engaged beam, and the faster scanning rate takes into account more information to be gathered in a more limited measure of time. This results in a higher-resolution image.
In the first scenario, the temporal resolution is 10cm sector size and scanning at 18cm. In this scenario, the sector size is 10cm, which means that the beam is 10cm wide.
The scanning rate is 18cm per second, which means that the beam scans 18cm in one second. The slower scanning rate in this scenario will result in a lower temporal resolution because less data are being collected in the same amount of time.
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if the string breaks when its tension exceeds 22.5n, what is the maximum speed the object can have at the bottom of the path
If the string is at the breaking point at the bottom of the circle, then the speed of the object at this point is 7.82m/s.
The force transferred through a rope, string, or wire when pushed by forces acting from opposite sides is referred to as tension. The tension force is applied along the entire length of the wire and exerts an equal amount of strain on the bodies at each end. Every physical object that comes into contact with another one applies some sort of force.
At the bottom of the circle,
Let the maximum speed will be V.
It is given when the string breaks its tension exceeds 22.5N
it means, T=22.5N
now, we know,
In a Circular path,
⇒ [tex]\frac{mV^2}{r} = T-mg[/tex]
⇒ [tex]V^{2}=\frac{r}{m}(T-mg)[/tex]
⇒ [tex]V^{2}=r(\frac{T}{m} -g)[/tex]
⇒ [tex]V=\sqrt{r(\frac{T}{m} -g)}[/tex]
According to the question,
m = 0.275KG, r = 0.850m and T = 22.5N
Putting the values, We get,
⇒ [tex]V=\sqrt{(0.850)(\frac{22.5}{0.275}-9.80 )}[/tex]
⇒ [tex]V=7.82m/s[/tex]
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The complete question is:
A 0.275 Kg ball wings in a vertical circular path on a string L=0.850m long. If the string breaks when its tension exceeds 22.5N, what is the maximum speed the ball can have at the bottom before that happens?
a galaxy has a b-k color of 3.2 magnitudes, where b refers to blue wavelengths and k refers to infrared wavelengths. what is the new b-k color if the luminosity of the galaxy at blue wavelengths rises by a factor of 100, without any change in the luminosity at k wavelengths? [
The b-k colour of a galaxy is a measure of the difference in brightness between the galaxy at blue (b) wavelengths and infrared (k) wavelengths. If the luminosity of the galaxy at blue wavelengths rises by a factor of 100, without any change in the luminosity at k wavelengths, the new b-k colour will be different.
We can use the following equation to calculate the new b-k colour:
b-k = -2.5 * log(Lb/Lk)
Where Lb and Lk are the luminosity of the galaxy at blue and infrared wavelengths, respectively.
Given that the luminosity at blue wavelengths has increased by a factor of 100 and the luminosity at k wavelengths has remained unchanged, the new b-k colour can be calculated as:
b-k = -2.5 * log(100*Lb/Lk) = -2.5 * log(100) + b-k = -2.5 * 2 + 3.2 = -0.8 + 3.2 = 2.4
Therefore, the new b-k colour of the galaxy is 2.4 magnitudes.
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The maximum horizontal distance a boy can throw a ball is 50 m. Assume he can throw
with the same initial speed at all angles. How high does he throw the ball when he throws
it straight upward?
(Hint: At what angle should the boy throw the ball to get furthest distance?]
The height the ball reaches when the boy throws the ball up in the air is 12.6m.
Given the maximum horizontal distance a boy can throw a ball (s) = 50m
The initial speed of the ball = um/s
The maximum height reached = ym
The motion in vertical direction is given as:
y = ut1 + 1/2at1^2 where v is the speed in vertical direction and a is the acceleration and t1 is the time taken to travel upward distance.
s = 0 + gt^2/2 then t = √2s/g = √2 x 50/9.8 = 3.18s
We know that as the velocity is same at any point in distance travelled distance = speed x time = 50m
So t1 = t/2 as it covers half time when reached maximum height.
The velocity (v) = gt = 9.8 x 3.18 = 31.164m/s
The maximum height reached (y) = vt1 + 1/2gt1^2 where t1 - t/2
y = vt/2 + 1/2g(t/2)^2
y = 50/2 + 1/2(9.8)(3.18/2)^2
y = 12.6m
Hence the maximum height the ball can be thrown is 12.6m.
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