The average power delivered to the train during its acceleration is 0.134 W.
The average power delivered to the train during its acceleration can be calculated using the equation P = Fv/t. The total mass of the train is 505 g, which can be converted to kilograms by multiplying by 0.001. The time it takes for the train to accelerate is 31.0 ms, which can be converted to seconds by dividing by 1000. The velocity of the train is 0.700 m/s. Using these values, the average power delivered to the train can be calculated as:
P = (505g*0.001 kg/g) * (0.700 m/s/ (31.0ms/1000s))
P = 0.134 W
The average power delivered to the train is 0.134 W. This calculation shows that the electric motor was able to deliver enough power to accelerate the train from rest to 0.700 m/s in 31.0 ms.
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an electron microscope is designed to resolve objects as small as 0.49 nm. what energy electrons must be used in this instrument?
An electron microscope is designed to resolve objects as small as 0.49 nm by using electrons as a source of illumination.
This requires electrons of high energy, typically in the range of 50 to 300 keV (kilo electronvolts). To put this into perspective, 50 keV is equivalent to 8.25 x 10^-17 Joules of energy.
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A Frisbee gets stuck in a tree. You want to get it out by throwing a 1.0-kg rock straight up at the Frisbee. If the rock’s speed as it reaches the Frisbee is 4.0 m/s, what was its speed as it left your hand 2.8 m below the Frisbee? Specify the system and the initial and final states.
Answer: The rock's speed as it left your hand was 8.8 m/s.
Explanation: The system is the rock and the Earth. The initial state is the rock at rest in your hand 2.8 m below the Frisbee. The final state is the rock hitting the Frisbee at a speed of 4.0 m/s.
Using conservation of energy, we know that the initial potential energy of the rock-Earth system is transformed into both kinetic energy and potential energy at its maximum height. Therefore, we can use the conservation of energy equation:
potential energy (initial) = kinetic energy (final) + potential energy (final)
mgh = 1/2mv^2 + mgh
where m is the mass of the rock, g is the acceleration due to gravity, h is the height that the rock has been raised, and v is the velocity of the rock.
We can solve for the initial velocity by rearranging the equation:
v = sqrt(2gh + v^2)
Plugging in the values, we get:
v = sqrt(2 * 9.81 * 2.8 + 4^2)
v ≈ 8.8 m/s
Therefore, the rock's speed as it left your hand was 8.8 m/s.
is it possible for an observer to travel fast enough so that in his system the earthquake happens also exactly now?
Yes, it is theoretically possible for an observer to travel fast enough so that in his system the earthquake happens also exactly now. This is due to the fact that time slows down as an object approaches the speed of light, a phenomenon known as time dilation.
The equation for time dilation states that the elapsed time T observed in the frame of reference of an observer travelling at velocity v is given by
[tex]T = T0 / \sqrt{(1 - v^2/c^2)}[/tex] ,
where ,T0 is the elapsed time as observed from the reference frame of an observer at rest relative to the travelling object, c is the speed of light, and v is the velocity of the travelling object. Therefore, the greater the velocity of the travelling object, the slower the elapsed time in its reference frame.
For an observer to travel fast enough so that in his system the earthquake happens also exactly now, he would need to travel at a velocity equal to or greater than the speed of light. This is impossible according to Einstein's theory of relativity, since nothing can travel faster than the speed of light in a vacuum.
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logs sometimes float vertically in a lake because one end has become water-logged and denser than the other. what is the average density of a uniform-diameter log that floats with 20.0% of its length above water?
Uneven-diameter logs that float with 20.0% of their length above water have an average density of 0.8g/cm3. The density is the proportion of weight to capacity.
An item it's far less compact that liquid may be supported up liquid water, and hence it floats. More dense objects can sink when submerged in water. Less dense logs float whereas more thick logs sink. A body can change its condition of rest or motion by the application of force
Instead of obliquely reading from either the side, read the scale stick straight from of the end of both the log. → The diameter of a log is only ever calculated within the bark. Employ a log measuring rod to determine the log's small end's "diameter from within bark," also known as "d.i.b."
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at what speed is a bicyclist traveling when his 27 inch diameter tires are rotating at an angular speed of 5p radians per second?
The bicyclist is travelling at 0.0034 miles/hour
Thus, According to the given question, His bicycle's tire is 27 inches in diameter
∴ radius = 27/2 inches. His angular speed is 5π rad/sec.
1 complete rotation is 2π rad
∴ 5π rad/sec = 5π/2π = 2.5 complete rotations/sec
∴ It will be 2.5 times 60 complete rotations per minute. = 150 rpm.
Circumference of a circle is 2πr
= 2π(27/2) inches
= 84.82 inches which is equivalent to 0.00135 miles per rotation. The tire rotates at 150 rpm
∴The distance it will cover in miles per hour is = (0.00135×150)/60 miles/hour = 0.0034 miles/hour.
Thus, The bicyclist is travelling at 0.0034 miles/hour.
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calculate the work done on the block by the spring during the motion of the block from its initial position to where the spring has returned to its uncompressed length.
The work done on the block by the spring during its move from its initial position to where the spring has returned to its uncompressed length is[tex]W = (1/2) \times k \times x^2[/tex].
We need to know the spring constant (k) and the displacement of the block (x) from its initial position to the position where the spring has returned to its uncompressed length. We can use the formula:
W = (1/2) * k * x^2
where W is the work done on the block, k is the spring constant, and x is the displacement of the block.
This formula is derived from the potential energy stored in the spring, which is given by:
U = (1/2) * k * x^2
where U is the potential energy stored in the spring.
When the block is initially at rest, the spring is compressed, and it has potential energy given by U = - (1/2) * k * x^2, where x is the initial compression of the spring.
Note that the negative sign indicates that the work done by the spring is negative, which means that the spring is doing work on the block in the opposite direction to the displacement of the block. This is because the spring force is always directed opposite to the displacement of the block.
As the block is released, the spring begins to push it back to its uncompressed length, and the block begins to move.
The work done on the block by the spring is equal to the change in potential energy of the spring, which is given by:
W = U_final - U_initial
Since the final position of the block is where the spring has returned to its uncompressed length, the final potential energy of the spring is zero. Therefore, the work done on the block by the spring is:
W = U_initial
Substituting the initial potential energy of the spring into this equation, we get:
W = (1/2) * k * x^2
Therefore, the work done on the block by the spring during its move from its initial position to where the spring has returned to its uncompressed length is given by the formula:
W = (1/2) * k * x^2
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the space station rotates in order to simulate earth's gravity - so that the normal force on an astronaut at the outer edge would be the astronaut's weight on earth. what is the period of the rotation, t (time for one complete revolution) needed to achieve this?
The space station rotates in order to simulate earth's gravity so that the normal force on an astronaut at the outer edge would be the astronaut's weight on earth. The period of rotation needed to achieve this is: 29.27 minutes
The Space Station is a microgravity environment that is constantly in freefall around the Earth, but it is not affected by gravity. As a result, the astronauts in the Space Station float and move around in the Station. However, by rotating the Space Station, a simulated gravity effect can be created that is comparable to gravity on Earth.
This is due to the centrifugal force that is generated as a result of the rotation. The period of rotation required to generate the required centrifugal force can be calculated.
The centrifugal force generated by the rotation of the Space Station is equal to the force of gravity acting on the astronauts on Earth. Therefore, the formula used to calculate the period of rotation is given:
T = 2π √(R/g)
Where T is the period of rotation, R is the radius of the Space Station, and g is the acceleration due to gravity on Earth. The value of g is 9.8m/s², and the radius of the Space Station is approximately 420 kilometers.
T = 2π √(420,000 / 9.8)
T = 1,756.22 seconds
The period of rotation of the Space Station required to generate a centrifugal force equivalent to the force of gravity on Earth is approximately 1,756.22 seconds or approximately 29.27 minutes.
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Air at atmospheric pressure of inside a of Hg is trapped availaible 760mm. container piston. The piston is so that the volume 100 km² to 150 dm³. the with a moveable pulled out slowly is increased from temperature remaining constant. What will be presture of the air?answer of this numerical?????
If the piston is positioned so that the volume is between 100 km² and 150 dm³, the air pressure within the container is 506.67 mm Hg. the from a moveable drawn out slowly while the temperature stays the same.
How do you determine air pressure?We can rewrite the equation as P = nRT/V using the ideal gas law, where PV = nRT, where P is pressure, V is volume, n is number of moles of gas, R is ideal gas constant, and T is temperature.
We can assume that n, R, and T are constants because the temperature doesn't change. Hence, we can write:
P1V1 = P2V2
P1(100) = P2 x (150)
Upon solving for P2, we obtain:
P2 = (P1 x V1) / V2
P2 = 506.67 mmHg
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how do the light-collecting area and best possible angular resolution of telescope with a 10-meter diameter mirror compare to that of a telescope with a 5-meter diameter mirror?
Angular resolution and light-collecting area:
The light-collecting area of a telescope is the amount of light that the mirror can collect. It is critical in astronomy because the brighter the star or galaxy you are looking at, the more information you can gather.
The angular resolution, on the other hand, is a measurement of the minimum angle between two stars that can be distinguished using a telescope. A high angular resolution means that you can see objects more clearly.
A telescope with a 10-meter diameter mirror has a four times larger light-collecting area and twice the best possible angular resolution compared to a telescope with a 5-meter diameter mirror. Therefore, a larger telescope will provide better images of objects in space because it gathers more light and can see more clearly.
The light-collecting area and best possible angular resolution of the telescope depending on the size of the mirror or lens used. This is why larger telescopes are better suited for astronomical observation than smaller ones.
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What is the magnitude of the applied electric field inside an aluminum wire of radius 1. 0 mm
that carries a 4. 0- A
current? [
σaluminum
= 3. 6 ×
10 7
A/(V⋅m)
]
The following formula may be used to determine how large the electric field is within the aluminium wire:
E = J/σ
E, J, and are the electric field, the current density, and the conductivity of aluminium, respectively.
where A is the wire's cross-sectional area and I is the current.
The following formula may be used to get the cross-sectional area of the wire:
A = πr^2
where r is the wire's radius.
We obtain the following by substituting the aluminum's electrical conductivity value from the problem:
E = J/σ
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if two flutists play their instruments together at the same intensity, is the sound twice as loud as that of either flutist playing alone at that intensity? why or why not?
No, the sound wouldn't be twice as loud as that of either flutist playing alone at that intensity. The increase in sound intensity would be less than twice as loud.
This is because when two sound waves coincide, the amplitude of the resulting sound wave is the sum of the amplitudes of the individual sound waves. That is, when two identical sound waves come together, they create a new sound wave that is slightly louder than the original sound wave, but not twice as loud.
Furthermore, sound intensity is affected by the distance from the sound source, and when two flutists are playing together, the sound waves produced have to travel further before they reach the listener, thus reducing the intensity of the sound.
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Compared to a landscape that develops in a cool, dry climate, a landscape that develops in a warm, rainy climate will most likely weather and erode a. Slower, so the landforms are more angular b. Slower, so the landforms are more rounded c. Faster, so the landforms are more angular d. Faster, so the landforms are more rounded
A landscape that develops in a warm, rainy climate will most likely weather and erode faster, so the landforms are more rounded.
This is because in a warm, rainy climate, there is more water available to weather and erode the landforms. The water can penetrate cracks and crevices in the rocks, dissolve minerals, and carry away sediments. Over time, this can lead to the rounding of edges and the smoothing of surfaces, resulting in more rounded landforms.
In contrast, in a cool, dry climate, there is less water available to weather and erode the landforms. This can result in slower rates of erosion and less rounding of the landforms.
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Which label identifies a rarefaction?
O A
Ов
O C
OD
In the longitudinal wave ,B represents the phenomenon of rarefaction. Rarefaction refers to the region of a sound wave where the pressure of the medium is lower than its normal value.
What is rarefaction?Rarefaction is a term used to describe a decrease in the density or pressure of a substance, such as a gas or liquid. In the context of sound waves, rarefaction refers to the region of a sound wave where the pressure of the medium is lower than its normal value, causing the particles of the medium to be spread further apart than usual.
Sound waves are composed of regions of compression and rarefaction that alternate in a regular pattern as the wave travels through a medium. In a compressional (longitudinal) sound wave, the particles of the medium are pushed together in regions of compression, while they are spread apart in regions of rarefaction. These changes in pressure and density cause the wave to propagate through the medium.
In general, rarefaction can occur in any medium, not just in sound waves. For example, in a gas, rarefaction can be caused by a decrease in pressure, temperature or density. In a liquid, rarefaction can be caused by a decrease in pressure or density. Rarefaction waves can be observed in many natural phenomena, such as atmospheric pressure waves, seismic waves, and waves on the surface of water.
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imagine you have a sensitive radio telescope and you would like to look at the sun. is it reasonable to expect that you would see it?
Yes, it is reasonable to expect that you would see the Sun with a sensitive radio telescope.
Radio waves can penetrate through the clouds and the atmosphere, so with a powerful radio telescope you can observe the Sun even on a cloudy day.
Gather the necessary components of the radio telescope, such as a dish and receiver. Point the radio telescope towards the Sun. Tune the receiver to the proper frequency. Take a look at the results from the telescope and observe the Sun.
Therefore, you can expect that you would see the Sun with a sensitive radio telescope.
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b) what happens to the reaction rate when the concentration (absorbance) of the reactants is quadrupled? determine the reaction order by solving the following equations. show a sample computation in your lab notebook.
Rate 4/ Rate 2 = [CV 4]’/[CV 2]’ <-> X = ________ Rate 5/ Rate 3 = [CV 5]’/[CV 3]’ <-> X = ________
When the concentration of the reactants is quadrupled, the reaction rate depends on the reaction order. To determine the reaction order, we can solve the given equations:
1.[tex]Rate 4 / Rate 2 = [CV 4]'^x / [CV 2]'^x[/tex]
2.[tex]Rate 5 / Rate 3 = [CV 5]'^x / [CV 3]'^x[/tex]
To find the reaction order (x), we first need to know the values of the rates (Rate 4, Rate 2, Rate 5, Rate 3) and the concentrations (CV 4, CV 2, CV 5, CV 3). Once you have these values, you can plug them into the equations and solve for x.
For example, let's say the given values are:
Rate 4 = 8, Rate 2 = 2, Rate 5 = 10, Rate 3 = 1
CV 4 = 4, CV 2 = 1, CV 5 = 5, CV 3 = 2
Now plug these values into the equations:
1.[tex]8 / 2 = (4^x) / (1^x)[/tex]
2. [tex]10 / 1 = (5^x) / (2^x)[/tex]
Solve for x:
1. [tex]4 = 4^x[/tex]
2. [tex]10 = (5^x) / (2^x)[/tex]
From equation 1, we can deduce that x = 1 (since 4^1 = 4). Thus, the reaction order is 1, which means the reaction rate is directly proportional to the concentration of the reactants. Therefore, when the concentration of the reactants is quadrupled, the reaction rate will also be quadrupled.
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what observation can you make that allows you to determine the relative magnitudes of the forces on the upper book?
Observing the reaction of the book when placed on the table, we can determine the relative magnitudes of the forces on the upper book. If the book stays in place, then the magnitude of the normal force is equal to the gravitational force. If the book slides down, then the gravitational force is greater than the normal force, and if the book slides up, then the normal force is greater than the gravitational force.
To determine the relative magnitudes of the forces on the upper book, we can observe the reaction of the book when placed on the table. If the book stays in place and does not move, then the forces on the upper book are in balance, meaning that the magnitude of the normal force is equal to the gravitational force.
To explain further, the normal force is the force that the table exerts on the book. It opposes the force of gravity, which is the force of attraction between the book and the Earth. When the normal force is equal to the gravitational force, the book is in equilibrium, meaning that it stays in place. When the gravitational force is greater than the normal force, the book slides down, and when the normal force is greater than the gravitational force, the book slides up.
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a girl weighing 455 n jumps from a tree, and her center of mass falls a vertical distance of 1.50 m. find the impulse necessary to bring her to rest.
The impulse necessary to bring her to rest is zero (0 Ns). Taking into account that the girl's momentum was maintained even as she fell, and since she started from rest, her final momentum should also be zero. So no additional push is needed beyond what gravity provides.
To find the impulse necessary to bring the girl to rest, we need to use the principle of conservation of momentum, which states that the total momentum of a system is conserved in the absence of external forces. In this case, we can assume that the girl is initially at rest, so her initial momentum is zero.
When the girl jumps from the tree, she is subject to the force of gravity, which causes her to accelerate downwards. We can use the equation for the gravitational potential energy to find the work done by gravity:
[tex]W = mgh[/tex]
Where W is the work done by gravity, m is the mass of the girl, g is the acceleration due to gravity, and h is the vertical distance that the center of mass falls.
Plugging in the given values, we get:
[tex]W = (455 N)(1,50 m)(9,81 m/s^2) \\W= 6.717,08 J[/tex]
This work done by gravity is equal to the change in kinetic energy of the girl, which can be expressed as the impulse required to bring her to rest:
J = ΔK
[tex]J= -mv[/tex]
where J is the impulse, ΔK is the change in kinetic energy, m is the mass of the girl, and v is her final velocity. Since the girl comes to a stop, her final velocity is zero, so we can simplify the equation to:
[tex]J = mv[/tex]
Plugging in the given mass and solving for the impulse, we get:
[tex]J = (455 N)(-0 m/s) \\J = 0 Ns[/tex]
Therefore, the impulse necessary to bring the girl to rest is zero.
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first you walk 5.38 m in a direction 35.0 degrees north of east. then you walk 8.50 m in a direction 60.0 degrees south of east. what is your total displacement for this trip, both magnitude and direction?
The total displacement for this trip is 10.50 m in a direction 25.0 degrees south of east.
The total displacement for this trip can be calculated by first breaking the trip into its two components and then combining the two.
First, you walked 5.38 m in a direction 35.0 degrees north of east. This can be written in vector form as <5.38, 35.0>.
Second, you walked 8.50 m in a direction 60.0 degrees south of east. This can be written in vector form as <8.50, -60.0>.
To find the total displacement, we can add the two vectors together: <5.38, 35.0> + <8.50, -60.0> = <13.88, -25.0>. This means that the total displacement is 13.88 m in a direction 25.0 degrees south of east.
We can also calculate the magnitude of the displacement by using the Pythagorean theorem: d = √(5.38² + 8.50²) = 10.50 m. This means that the total magnitude of the displacement is 10.50 m.
In summary, the total displacement for this trip is 10.50 m in a direction 25.0 degrees south of east.
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every atom (other than hydrogen and helium) that you see around us, making up everything including the earth, is literally group of answer choices from the big bang star stuff, from stars
Every atom other than hydrogen and helium that we see around us is actually the result of nucleosynthesis, a process of nuclear fusion in stars that creates heavier elements.
During nucleosynthesis, two hydrogen atoms collide and form helium, which is then subjected to intense pressures and temperatures that allow the helium to fuse into heavier elements such as,
oxygen, nitrogen, and carbon. This process repeats until the heavier elements that form the core of stars, like iron and nickel, are created.
The process of fusion is ongoing and eventually the star runs out of fuel and explodes in a supernova, releasing the material that was created within it.
This material is then scattered across the universe, eventually forming clouds of gas and dust that coalesce to create planets, moons, and other bodies, including Earth.
All of the atoms that make up our planet, from oxygen to iron, are the direct result of this process, which began in the big bang and continues to the present day.
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a student exerts a horizontal force of 40.0 n with her hand and pushes a 10.0 kg box a distance of 2.0 m across a frictionless floor. calculate the magnitude of the work done by the student. group of answer choices 40.0 j 60.0 j 80.0 j 100.0 j
The magnitude of the work done by the student is 80.0 J. Option c is correct.
The work done by the student can be calculated using the formula,
W = Fd cos(theta)
where W is the work done, F is the force exerted, d is the distance moved, and theta is the angle between the force vector and the displacement vector.
In this problem, the force exerted by the student is a horizontal force of 40.0 N, and the box is moved a distance of 2.0 m across a frictionless floor. Since the force and displacement vectors are in the same direction (horizontal), the angle between them is 0 degrees, so cos(theta) = 1. Therefore, we can calculate the work done as,
W = (40.0 N)(2.0 m) cos(0) = 80.0 J
Hence, option c is correct choice.
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What velocity of a body will you obtain from the position vs.
time graph for the following data: position from origin is 0 m, 10
m, 20 m, 30 m and 40 m at instants 0 s, 1 s, 2 s, 3 s, 4 s?
Answer:10 m/s
Explanation:
what is the purpose of wires in a circuit? why do we use wires to connect power supplies to resistors or other objects on a circuit board? why can't we just use power supplies and resistors?
The purpose of wires in a circuit is to provide a path for electric current to flow.
We use wires to connect power supplies to resistors or other objects on a circuit board because these objects do not have a direct electrical connection. If we did not use wires, electric current would not flow from the power supply to the resistor or other object.
Wires are essential components in a circuit because they provide the pathway for electricity to flow from one component to another. Without wires, the flow of electric current would be impossible, and a circuit would not work.In a circuit board, power supplies are connected to resistors and other objects using wires.
The power supply provides the voltage, while the resistor or other object provides the resistance. By connecting the power supply to the resistor or other object using wires, we create a complete circuit. Without wires, the power supply and resistor would be unable to communicate with each other, and the circuit would not function properly.
In conclusion, wires are an essential component of a circuit. They provide a pathway for electric current to flow, allowing power supplies and resistors to communicate with each other and create a complete circuit.
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true or false: energy is the capacity to do work and work is anything that involves moving matter against an opposing force.
The given statement "Energy is the capacity to do work and work is anything that involves moving matter against an opposing force" is TRUE. Energy is the capacity to do work, which is defined as any action that requires the application of a force to move matter. This includes tasks such as lifting a book, pushing a door open, or running.
Energy refers to the capacity of a physical system to perform work. Energy is generally used to complete tasks, such as moving an object from one location to another, heating up or cooling down a material, or lighting up a room. Work is defined as the transfer of energy to an object via a force applied to the object over a given distance, as per the statement. Work is usually identified as the displacement of an object through a force applied to it in the direction of its displacement against an opposing force.Energy and work are two distinct but interrelated concepts in physics. Energy is the capacity to perform work, and work is the transfer of energy from one object to another through a force acting over a distance. Energy and work are both expressed in joules (J), the unit of energy in the International System of Units (SI).
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65. a 150-w lightbulb emits 5% of its energy as electromagnetic radiation. what is the radiation pressure on an absorbing sphere of radius 10 m that surrounds the bulb?
The radiation pressure on an absorbing sphere of radius 10 m that surrounds the lightbulb is approximately 3.98 x 10^-13 Pa.
The radiation pressure on an absorbing sphere can be calculated using the formula,
P = (2 * I) / c
where P is the radiation pressure, I is the intensity of the radiation, and c is the speed of light.
First, we need to calculate the intensity of the radiation emitted by the lightbulb. The energy emitted per second by the lightbulb is 150 W, and 5% of this energy is emitted as electromagnetic radiation. Therefore, the energy emitted as radiation is,
E = 150 W * 0.05 = 7.5 W
The intensity of the radiation is the power per unit area, and can be calculated by dividing the energy emitted per second by the surface area of a sphere with a radius of 10 m,
I = E / (4 * pi * r^2) = 7.5 W / (4 * pi * 10^2 m^2) = 5.98 x 10^-5 W/m^2
Now we can calculate the radiation pressure, P = (2 * I) / c = (2 * 5.98 x 10^-5 W/m^2) / 3 x 10^8 m/s = 3.98 x 10^-13 Pa
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how much work is done lifting a 15 pound object from the ground to the top of a 30 foot building if the cable used weighs 2 pounds per foot
The amount of work required to lift a 15 pound object from the ground to the top of a 30 foot building if the cable used weighs 2 pounds per foot is 1050 foot-pounds.
In order to solve the problem, we can use the formula W = Fd. where, W is the work done, F is the force required and d is the distance covered by the object while being lifted or moved.
So, we have to first calculate the force required to lift the object. Let us assume the force required is F, then
F = weight of object + weight of cable
F = 15 + 2 * 30
F = 75 pounds
Therefore, the force required to lift the object is 75 pounds. Now, we can calculate the work done as follows:
W= Fd
W = 75 * 14
W = 1050 foot-pounds
Therefore, the amount of work required to lift a 15 pound object from the ground to the top of a 30 foot building if the cable used weighs 2 pounds per foot is 1050 foot-pounds.
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a space traveler weighs 682 n on earth. what will the traveler weigh on another planet whose radius is 3 times that of earth and whose mass is 2 times that of earth?
The traveler's weight on another planet whose radius is 3 times that of Earth and whose mass is 2 times that of Earth is 21.647 N
The following is the solution to the given problem:
Mass and gravity are related to one another. Gravity is generated by the planet's mass, and the magnitude of the gravitational force is determined by the mass of the planet on which the object is situated, as well as the mass of the object.
Mass, distance, and gravity are all factors that influence the gravitational force. Mass is directly proportional to the gravitational force and inversely proportional to the square of the distance from the gravitational force's center.
Here is the formula: Force of gravity = G(M1M2)/d²where, G is the gravitational constant 6.67 x 10^{-11} N(m/kg)^2, M1 is the mass of the first body, M2 is the mass of the second body, d is the distance between the centers of two bodies.
On earth, the traveler weighs 682 N. On another planet whose radius is 3 times that of Earth and whose mass is 2 times that of Earth, we have to calculate the traveler's weight.
Mass of Earth is 5.972 × 10^24 kg2,
Radius of Earth is 6.371 x 10^63.
The mass of the planet whose radius is 3 times that of Earth and whose mass is 2 times that of Earth.
Mass of the planet = 2 x mass of Earth = 2 x 5.972 × 10^24 kg = 1.1944 × 10^25 kg4.
The radius of the planet whose radius is 3 times that of Earth,
Radius of the planet = 3 x radius of Earth = 3 x 6.371 x 10^6 m = 1.9113 × 10^7 m5.
The distance between the two planets.
Distance between two planets = radius of planet + radius of Earth
= 1.9113 × 10^7 m + 6.371 x 10^6 m
= 2.54813 x 10^7 m
= 2.54813 x 10^10 cm.
Putting all the values in the formula.
Force of gravity = G (M1 M2) / d²
Where, Mass of the traveler on the other planet is m.
Mass of the Earth is M1 = 5.972 × 10^24 kg.
Mass of the other planet is M2 = 2 x 5.972 × 10^24 kg = 1.1944 × 10^25 kg.
Radius of the Earth is r1 = 6.371 x 10^6 m.
Radius of the other planet is r2 = 3 x 6.371 x 10^6 m = 1.9113 × 10^7 m.
Distance between the two planets is d = 2.54813 x 10^10 cm.682
= G (M1 M2)/d²
G = 6.674 × 10^-11 N m² / kg²
Force of gravity on other planet = G(mM2)/r² where m is the mass of the traveler on the other planet
= 6.674 × 10^-11 × (m × 1.1944 × 10^25)/(1.9113 × 10^7)²
Weight on another planet = force of gravity on another planet × mass of the traveler on another planet
= (6.674 × 10^-11 × (m × 1.1944 × 10^25)/(1.9113 × 10^7)²) × m
= 21.647 N (approximately)
Therefore, the traveler's weight on another planet whose radius is 3 times that of Earth and whose mass is 2 times that of Earth is 21.647 N (approximately).
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the acceleration of a super-vehicle is proportional to the difference between 240 km/h and the velocity of this sports car. if it can accelerate from rest to 120 km/h in one second, what speed can it reach from rest in three seconds?
The speed that the car can reach from rest in three seconds is 79.73 km/hr.
The acceleration of a super-vehicle is proportional to the difference between 240 km/h and the velocity of this sports car.
Initial speed u = 0 km/hr,
Final speed v = ? t
Time t = 3 s,
Velocity at a particular time = v,
Acceleration = proportional to the difference between 240 km/h and the velocity of this sports car Given acceleration is proportional to the difference between 240 km/h and the velocity of this sports car
So, a ∝ (240 - v)To find constant of proportionality k, Let's assume acceleration when velocity is 0 is 100m/s² when t=1sWhen v=0, a=k(240 - 0) = 240k ⇒ 100=k(240 - 0) = 240k ⇒ 100=k
Therefore acceleration is a=100(240-v)When t=3 seconds, u=0km/hr, v=? and a=100(240-v)Using the formula, v=u+atWe get, v = u + at=0+(100(240 - v)) * 3v = 24000 - 300v⇒ 301v = 24000⇒ v = 79.73 km/hr
Therefore, the speed that the car can reach from rest in three seconds is 79.73 km/hr.
Note: While solving these types of questions, we should try to find out the constant of proportionality and then substitute the values to get the result.
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if the sun is located at one focus of earth's elliptical orbit, the earth is at the other focus. question 20 options: true false
a sample of paramagnetic material is located very close to a bar magnet, in a region in which the field of the magnet appears almost uniform over small distances. if the magnet is kept in the same location but rotated in a counter-clockwise direction so that the sample is no longer in the quasi-uniform region of the magnetic field, how will the sample respond?
When a sample of paramagnetic material is moved out of the quasi-uniform region of a magnetic field, it will experience a torque and tend to align with the magnetic field, but the magnetization may be weaker and less stable due to the non-uniform field.
The paramagnetic materials are also affected by :
When a paramagnetic material is placed close to a bar magnet in a region where the magnetic field appears almost uniform, the material aligns itself with the direction of the magnetic field lines. This happens because the material is weakly attracted to the magnetic field due to its paramagnetic properties.However, if the magnet is rotated in a counter-clockwise direction, the magnetic field lines near the paramagnetic material will no longer be uniform. As a result, the material will no longer be able to align itself with the magnetic field lines and will experience a torque instead. The torque will cause the material to rotate until it aligns itself with the new direction of the magnetic field lines.This phenomenon is similar to how a compass needle behaves when it is placed near a magnet. When the magnet is rotated, the compass needle will also rotate until it aligns itself with the new direction of the magnetic field lines.The paramagnetic material will align itself with the magnetic field lines when the field is uniform, but when the field is no longer uniform due to the rotation of the magnet, the material will rotate until it aligns itself with the new direction of the magnetic field lines.
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a 300n force is applied to a bolt by a wrench at 180 degrees. the length of the wrench is 0.2m. what is the torque? justify your answer.
Torque is the rotational force acting on an object due to a force applied at a certain distance away from its pivot point. Since the force is 300N and the wrench is 0.2m away from the pivot point, the torque is 300N * 0.2m, which equals 60Nm.
The torque is the result of the force applied by a wrench multiplied by the length of the wrench. In this case, the force applied is 300N and the length of the wrench is 0.2m, so the torque is 60Nm (300N x 0.2m = 60Nm). Justification of this answer can be seen using the definition of torque. Torque is defined as the product of the magnitude of the force applied, and the distance from the force to the axis of rotation. In this case, the force of 300N is being applied at 180 degrees, so the distance from the force to the axis of rotation is 0.2m (the length of the wrench). Therefore, the torque is equal to the force multiplied by the distance, which is 60Nm (300N x 0.2m = 60Nm).
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