Susan should expect to save approximately $3,822.5 in energy bills each year by replacing her incandescent bulbs with LED bulbs.
LED bulbs are much more energy-efficient than incandescent bulbs. They use significantly less power and last much longer.
One of the ways to estimate energy savings is to calculate the difference in power consumption between an incandescent bulb and a LED bulb of the same brightness.
For example, if an incandescent bulb uses 60 watts and a LED bulb uses 10 watts to produce the same amount of light, the LED bulb will use 83% less energy than the incandescent bulb.
If we assume that each LED bulb last for an average of 25,000 hours and the incandescent last for an average of 1,200 hours and the cost of electricity is $0.13 per kWh, the savings will be:
(45 bulbs * (60-10)W/1000) * 25000hrs/yr * $0.13/kWh = $3,822.5
So, Susan should expect to save approximately $3,822.5 in energy bills each year by replacing her incandescent bulbs with LED bulbs.
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Am I doing this right? I am trying to find the current, did I even draw the circuit right?
By disassembling the circuit and connecting a "ammeter" in series (or in-line) with it, all of the electrons that are flowing through the circuit must also pass through the meter in order to measure current in the circuit.
In a circuit, how do you determine the current?The formula V = IR is something you should be aware of. By dividing the voltage by the resistance, or I = V/R, you may quickly determine the current value from the equation.By disassembling the circuit and connecting a "ammeter" in series (or in-line) with it, all of the electrons that are flowing through the circuit must also pass through the meter in order to measure current in the circuit.For domestic circuits using 120 volts, the maximum electrical flow that a circuit is intended to handle is typically 15 or 20 amps. Compared to 15-amp circuits, 20-amp circuits require bigger wires.To learn more about current refer to:
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2. the water level of a tank on a building roof is 20 m above the ground. a hose leads from the tank bottom to the ground. the end of the hose has a nozzle, which is pointed straight up. what is the maximum height to which the water could rise? what factors would reduce this height?
The maximum height of the water after coming out of the nozzle is affected is by the initial speed and the value of the
The water level of the tank on the building is 20m. The hose leads from the tank bottom to the ground and leads to the nozzle that is point to the top.
Here, we know, the energy will also be conserved because the there is o external force, so the kinetic energy at the top will be equal to the potential energy at the bottom in the ideal case.
Now, we can write,
1/2mv² = mgh
v = √(2gh)
g is the acceleration due to gravity and the h is the height of the tank.
Putting values,
v = √(2 x 10 x 20)
v = 20 m/s
Now, we can use the equation of motion,
v = √(2hg)
h = v²/2g
v is the speed of the water from the nozzle.
h = 10m.
This is because we have considered the ideal case where there is no energy loss, so water will go till a height of 10m when it comes out of the nozzle. The height rise is affected by the initial speed.
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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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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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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.
The complete question is attached.
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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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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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. 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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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 spider monkey (mass 40 kg) is frolicking through the jungle at a speed of 3. 0 m/s. All of a sudden, a panther appears and tries to eat the monkey. The monkey begins to run frantically—now he has a speed of 14. 0 m/s. How much work does the monkey do to increase its speed?
When a panther appears and attempts to eat the monkey, the monkey performs 3740 J of work to increase its speed.
What is work?Work in physics is the energy transferred to or from an object by applying force along a displacement. In its most basic form, work equals the product of force strength and distance traveled for a constant force aligned with the direction of motion. Work is the transfer of energy caused by a force acting on an object as it moves. The work done by a force on an object is calculated as the product of the magnitude of the force multiplied by the magnitude of the displacement multiplied by the cosine of the angle between them.
Here,
W=1/2mv1²-1/2mv2²
=1/2*40(14²-3²)
=3740 J
The monkey does 3740 J of work of increase its speed when a panther appears and tries to eat the monkey.
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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 1.50 v battery supplies 0.450 w of power to a small flashlight for 20.0 min. (a) how much charge (in c) does it move?
The total number of charges moved to power up the light for 20 min is 3.75 x 10¹⁹
The voltage of the battery = 1.50 V
The power supplied by the battery = 0.45 W
The flashlight will glow for 20 min
The total number of charges moved during the flashing of the flashlight can be found using the formula,
I = P/V
where I is the current
P is the power
V is the voltage supplied
We also know that,
I = Q/t
Let us substitute this equation, with the above equation, and we get
Q = Pt/V
Now, let us substitute the known values in the above equation, we get
Q = 0.45 x 20 / 1.50
= 9 / 1.50
= 6 C
Then, the number of charges is
n = Q/e
where e is the charge of an electron
n = 6 / 1.6 x 10⁻¹⁹
= 3.75 x 10¹⁹
Therefore, the number of charges moved is 3.75 x 10¹⁹
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the maximum amount of weight a jack can lift is called its
The "Load Capacity" of a jack refers to the greatest weight it can support. Maximum weight of cargo that has been authorised by the country where the vehicle was registered.
Define the term Load Capacity?We can determine the necessary minimum capacity for a trailer jack by analysing the concentration of loads in a typical trailer.
The capacity should take into consideration both the jack's responsibility to sustain the weight and the lifting mechanism's capability to lift it.The tongue of a conventional trailer is designed to support 10% to 15% of a gross trailer weight when the trailer is positioned horizontally. Take the gross trailer weight then multiply it by the number of trailer jacks required to support the trailer. 15 to determine the tongue's theoretical weight. Choose a jack with a safety margin with which you are familiar with and that can support that weight.Thus, the "Load Capacity" of a jack refers to the greatest weight it can support.
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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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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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Which of these is a benefit of desalination technology?
• A. Toxic salty residue
• B. High energy cost
• C. Fresh drinking water
O D. High financial cost
Desalination removes potentially harmful minerals and chemicals in addition to the salt that is present in your water.
What advantages does desalination technology offer? The fact that a desalination plant makes drinking water readily available to people who need it most is undoubtedly one of its main advantages.Even in countries with access to fresh water, this holds true whether there is a drought or a natural calamity.Desalination removes potentially harmful minerals and chemicals in addition to the salt that is present in your water.Physical separation of microorganisms by chemical processes is used to remove them.In addition to removing salt, desalination also gets rid of potentially dangerous metals, chemicals, and microorganisms from your water source.By physically rejecting bacteria via chemical processes, it eliminates microorganisms.To learn more about desalination technology refer
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suppose a 3000 cm3cm3 container holds 7.0 gg of nitrogen gas at a pressure of 200 kpakpa. the gas can be heated at constant pressure if a piston moves outward to let the gas expand as it's heated. alternatively, the gas can be heated at constant volume if the piston is locked in place to prevent expansion. how does the heat required for one of these processes compare to the heat required for the other process?
The gas can be heated at constant pressure if a piston moves outward to let the gas expand as it's heated. Alternatively, the gas can be heated at constant .
Define constant pressure?
The term isobaric has been derived from the Greek words “iso” and “baros” meaning equal pressure. As such, the constant pressure is obtained when the volume is expanded or contracted. This basically neutralizes any pressure change due to the transfer of heat.At constant pressure, an isobaric process occurs. The force exerted is constant since the pressure is constant, and the work done is expressed as PΔV. Heat should be delivered into the system at a specific pace if gas is to expand at a certain pressure of an isobaric expansion.Saying that the gases are at constant pressure means that the pressures do not vary with spatial position within the cylinder. Both gases occupy the entire volume, and, as you said, they exert unequal pressures. The pressure that a gas exerts within a mixture is called its partial pressure.To learn more about pressure refers to:
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a 1687 kg car is traveling down the road at 96.6 km/h. while traveling at this rate of speed, what is the kinetic energy of this vehicle in kilojoules?
The kinetic energy of this vehicle is 605.835 KJ when its mass is 1687 kg and traveling at speed of 96.6 km/h.
Given,
mass of the car, m = 1687 kg
speed, v = 96.6 km/h
we know that, Kinetic energy
KE = 1/2 mv²
But we need KE in Joule or KJ
so first we convert km/h to m/s
v = 96.6 km/h = 96.6 x (1000/3600) m/s
v = 26.8 m/s
Now,
KE = 1/2 x 1687 x (26.8)²
or KE = 605835.44 Joule = 605835.44 x 10⁻³ Kilojoule
or KE = 605.835 KJ
Therefore, the kinetic energy of this vehicle is 605.835 KJ when its mass is 1687 kg and traveling at speed of 96.6 km/h.
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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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find the time it takes the electron to travel through the region of the electric field, assuming it does not hit the side walls
The time taken by the electron is [tex]3.33*10^{-8} seconds[/tex] .
Complete question:
An electron traveling at [tex]3*10^{6} m/s[/tex] enters a 0.1 m region with a uniform electric field. Find the time it takes the electron to travel through the region of the electric field, assuming it does not hit the side walls.
(See the figure attached)
Since, no field and hence no force act on the electron along X-direction.
Hence, [tex]v_{x}[/tex] remains constant.
Now time taken = t = l/[tex]v_{x}[/tex]
Where,
l = length of field = 0.1 m
v = speed of electron = [tex]3*10^{6} m/s[/tex]
Putting this value in above equation, we get t = [tex]3.33*10^{-8} seconds[/tex] .
Electrostatics is a branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges. Electrostatic phenomena arise from the forces that electric charges exert on each other and are described by Coulomb’s law.Even though electrostatically induced forces seem to be relatively weak.To know more about electrostatics visit:
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Hermann ebbinghaus’ research would most likely predict that?
Mike would rapidly forget most of the material that he read. Dr. Ummel conducts a memory experiment where he shows a fight between two men and describes the contact as "punching" to one group and "tapping" to the other group.
What is meant by memory ?
The capacity or method for repeating or recalling what has been learnt and retained, particularly through associative mechanisms. As he got older, his memory started to fail.Sensory memory, short-term memory, and long-term memory are the three basic types of memory that are discussed.Memory is the capacity to retain and recall knowledge when necessary. Working memory, short-term memory, long-term memory, and sensory memory are the four main categories of memory.Storage refers to where long-term data is kept, whereas memory refers to where short-term data is kept. The term "memory" is most frequently used to describe the main storage on a computer, such as RAM. Information is also processed in memory.To learn more about memory refer to
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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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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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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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Marcus wants to test the effect of gravity on objects with different masses. He drops two footballs from a first-floor window, a second-floor window, and a third-floor window. In each case, he times how long it takes the footballs to reach the ground. What is wrong with his experiment’s design?
A.) The windows are not high enough to show significant differences in drop times.
B.) The drops are not repeated.
C.) It does not include objects with different shapes.
D.) It does not include objects with different masses.
Answer: (D.) It does not include object with different masses
Explanation:
It does not include objects with different masses. Therefore, option D is correct.
What is gravity?The force that pulls items toward the center of a planet or other entity is called gravity. All of the planets are kept in orbit around the sun by gravity. A universal, non-contact force, gravity. The gravitational pull of the Earth keeps everything on its surface.
All objects with mass, including our Earth, really bend and curve spacetime, which is what causes gravity to pull you toward the ground. What you experience as gravity is that curvature. If things of different masses are dropped from the same height, they will still impact the ground at the same time because Earth provides everything with the exact same acceleration.
One thing that is wrong about Marcus' experiment is that it does not include objects with different masses. Therefore, option D is correct.
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the austonian links to an external site.is the second tallest building in austin. legend says that during a cold morning in january, if you drop a rock from the top of the building, you will hear the sound of its impact seconds later. can we use this information to determine the height of the austonian? let's try!
No, we are unable to estimate the austonian's height using this information.
Its Austonian height makes it the second-tallest structure in Texas, behind The Independent, and the second-tallest all-residential structure in North America, west of the Mississippi River.
The second-tallest structure in Austin is the Austinian, which has a connection to an external site. According to a tale, if you drop a rock from the top of a building on a chilly January morning, you will hear the sound of its hit seconds later.
The 58-story Independent, which is 690 feet (210 m) tall and has 58 stories, is the tallest finished structure in the American city of Austin, Texas. After Houston and Dallas, it is the tallest skyscraper in Texas and the tallest all-residential tower west of the Mississippi River. It was completed in 2019.
height of austonian = 16[tex]t^{2}[/tex].
t = [tex]\sqrt{H}[/tex]/4.
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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 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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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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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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