The cubic term increases the work needed to compress an ideal spring by: 66.67 percent.
How does the cubic term affect the work done in compressing an ideal spring?The work required to compress an ideal spring is given by the equation W = (1/2)kx².
The cubic term, which is usually ignored in the linear force-extension equation, is introduced into the equation for work done because the spring's potential energy increases non-linearly as it is compressed.
The equation for work done on an ideal spring that takes into account the cubic term is:
W = (1/2)kx² + (1/3)kx³.From the above equation, it can be seen that the work done is increased by the cubic term.
The question is asking by what percentage the cubic term increases the work done over what would be needed to compress an ideal spring without the cubic term.
Here is the calculation: If we take out the cubic term from the above equation, we get W = (1/2)kx².
So the difference is (1/3)kx³, which is the contribution of the cubic term to the work done.
The percentage increase is given by:(0.333kx³ / 0.5kx²) x 100% = 66.67%
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What is the quantum physics observer paradox?
Answer:
“The paradox means that if quantum theory works to describe observers, scientists would have to give up one of three cherished assumptions about the world,” said Associate Professor Eric Cavalcanti, a senior theory author on the paper.
nflate a balloon at room temperature. leave the inflated balloon in the refrigerator overnight. what happens to the balloon? explain
When inflating a balloon at room temperature and leaving the inflated balloon in the refrigerator overnight, it will deflate.
А bаlloon will deflаte when we inflаte а bаlloon аt room temperаture аnd then leаve the inflаted bаlloon in the refrigerаtor overnight becаuse the molecules in а bаlloon аre very energetic, аnd when they аre heаted up, they move fаster аnd further аpаrt from eаch other.
When we put а bаlloon in а refrigerаtor, it cools down, аnd the molecules inside it lose some of their energy. This meаns thаt they move more slowly аnd аre closer together, so the pressure inside the bаlloon decreаses аnd the bаlloon deflаtes.Therefore, the bаlloon deflаtes becаuse the pressure inside the bаlloon decreаses аs the bаlloon cools down.
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what is the schwarzschild radius for the black hole at the center of our galaxy if it has the mass of 4 million solar masses?
The Schwarzschild radius for the black hole at the center of our galaxy is approximately 11.8 billion meters, or about 7.3 million miles.
What is Schwarzschild radius ?The Schwarzschild radius is a measure of the size of the event horizon of a black hole, which is the boundary beyond which nothing, not even light, can escape.
The formula for the Schwarzschild radius is:
r = 2GM/c²
where;
r is the Schwarzschild radius, G is the gravitational constant, M is the mass of the black hole, andc is the speed of light.For a black hole at the center of our galaxy with a mass of 4 million solar masses, we can calculate its Schwarzschild radius as:
r = 2G M / c²
= 2 x 6.6743 × 10⁻¹¹ m³ kg⁻¹ s⁻² x 4 million x 1.98847 × 10³⁰ kg / (299792458 m/s)²
= 1.18 × 10¹⁰ meters
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Grandma Dynamite accelerates her bus from a dead start to 90 m/sec in just 12 seconds. What is her acceleration?
The acceleration in this instance is 7.5 meters per second square, which is a measure of the ratio of change in velocity with regard to time.
In physics, acceleration is the rate at which the velocity of an entity changes in relation to time. According to Newton's Second Law, the sum of all forces operating on an object results in its acceleration. Meter per second squared (m s2) is the measure of acceleration used in the SI system. Accelerations add according to the parallelogram law because they are vector variables (they have a magnitude and direction). The calculated net force is a vector that is equivalent to the product of the object's acceleration and mass, both of which are scalar quantities.
We are given:- initial velocity (u) = 0m/s
Final Velocity (v)= 90m/s
Time= 12s.
Therefore the acceleration is:-
90/12= 7.5 m/s^2.
Hence the acceleration is 7.5m/s^2.
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A student places a transparent semicircular block on a sheet of paper and draws
around the block. She directs a ray of light at the centre of the flat edge of the block.
Figure 1 shows the path of the ray through the block.
Figure 1
incident ray
centre of the flat
edge of the block
transparent
semicircular block
emergent ray \ sheet of paper
[foya}(4] State why the emergent ray does not change direction as it leaves the block.
[1 mark]
The emergent ray does not change direction as it leaves the block because it is traveling perpendicular to the flat surface of the semicircular block.
What is an emergent ray?An emergent ray is described to be a refracted beam that originates from a medium or channel after refraction.
It is known that when light passes from one medium to another at a particular angle, it changes direction due to refraction, which is caused by a change in the speed of light as it travels through different media.
If light passes through a flat surface at a perpendicular angle, there is no change in speed or direction, so the emergent ray travels in a straight line without bending or changing direction.
But in this scenario, the incident ray is directed towards the center of the flat edge of the block, it enters the block perpendicular to the flat surface and emerges from the block at the same angle and direction as the incident ray, without any refraction or change in direction.
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a 500 g rock slides across an ice covered pond and strikes a 725 g object that is at rest. is it possible for both objects to be at rest after the collision?
Yes, it is possible for both objects to be at rest after the collision. This type of collision is known as an elastic collision.
In an elastic collision, both kinetic energy and momentum are conserved. Kinetic energy is the energy that an object possesses due to its motion. In a perfectly elastic collision, the kinetic energy is completely conserved, meaning that it is transferred from one object to another. Momentum is the product of an object's mass and velocity.
In an elastic collision, momentum is conserved.To solve this problem, we can use the conservation of momentum. According to the principle of conservation of momentum, the total momentum of a system of objects is conserved if there is no external force acting on the system. In this case, both objects are on the same surface and are only subjected to the frictional force of the surface.
The momentum of the rock before the collision can be calculated as: p1 = m1v1 = 0.5 kg × 3 m/s = 1.5 kg m/s.The momentum of the object at rest before the collision can be calculated as:p2 = m2v2 = 0.The total momentum of the system before the collision is:p1 + p2 = 1.5 kg m/s.The momentum of both objects after the collision is zero, so the total momentum of the system after the collision is also zero.
Therefore: p1' + p2' = 0.p1' is the momentum of the rock after the collision, and p2' is the momentum of the object at rest after the collision. Since the total momentum of the system is conserved, we can write: p1' + p2' = p1 + p2.0.5 kg × v1' + 0.725 kg × v2' = 1.5 kg m/s.
The two unknown velocities can be solved using the two equations: p1 + p2 = p1' + p2' and 0.5 kg × v1' + 0.725 kg × v2' = 1.5 kg m/s.
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if loads are connected in parallel do they have the same voltage
Answer:
Yes
Explanation:
A parallel circuit has two or more paths for current to flow through. Voltage is the same across each component of the parallel circuit. The sum of the currents through each path is equal to the total current that flows from the source.
how far away is the screen in meters, if a slide is placed 110 mm from the lens and produces a sharp image?
The distance of the screen from the lens is: 0.055 meters
Given the distance of slide from the lens = 110 mm, we need to find the distance of screen from the lens in meters.
According to the lens formula,1/f = 1/v - 1/u
Where, f is the focal length of the lens
v is the distance of the image from the lens
u is the distance of the object from the lens
In this case, the slide is acting as an object and the screen is the image produced by the lens.
Since the image produced is sharp, we can assume that the lens is able to produce a real image.
Hence, v is negative. u = -110 mm = -0.11 m
Using the given formula, we have: 1/f = 1/v - 1/u
Putting v = -v and solving for v, we get:v = -u*f / (u - f)
Putting in the values of u = -0.11 m and f = 40 mm = 0.04 m, we get: v = -(-0.11)*(0.04) / (-0.11 - 0.04) = 0.055 m
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The period of a wave is 0.044s. How many cycles will the energy source make in 22s?
Answer:
The number of cycles can be calculated by dividing the total time by the period:
Number of cycles = Total time / Period
In this case, the period is 0.044 s and the total time is 22 s, so:
Number of cycles = 22 s / 0.044 s = 500
Therefore, the energy source will make 500 cycles in 22 seconds.
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you are running around a track at 5 km/h and then you increase your speed to 10 km/h. by what factor did you increase your kinetic energy?
As a result, when you raised your speed form 5 km/h into 10 km/h, you increased the kinetic energy from a factor of 4.03.
What exactly is kinetic energy?The energy of motion is kinetic energy, which can be observed in the motion of an object or subatomic particle. All particles & moving objects contain kinetic energy. When something moves, whether it's a person walking, an baseball flying through the air, an piece of bread falling out of a table, or charged particles inside an electric field, it has kinetic energy.
What are the four forms of kinetic energy?Radiant, thermal, acoustic, electrical, and mechanical kinetic energy are the five main categories.
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Part B Object A has a mass m and a speed v, object B has a mass m/2 and a speed 4u, and object C has mass 3m and a speed v/3. Rank the objects according to the magnitude of their momentum Rank from smallest to largest. To rank items as equivalent, overlap them. Reset Help Smallest momentum Largest momentunm Object A Object C Object B The correct ranking cannot be determined. Submit My Answers Give Up
Smallest momentum: Object B, Object A, Object C.
Largest momentum: Object C, Object A, Object B.
Momentum is defined as the product of mass and velocity, p = mv. Comparing the three objects, we can calculate their momentum as follows,
Object A: p = mv
Object B: p = (m/2) x (4u) = 2mu
Object C: p = (3m) x (v/3) = mv
From these equations, we can see that Object B has the smallest momentum since it has the lowest mass and speed. Object A has a larger momentum than Object B but smaller than Object C, which has the largest momentum due to its large mass. Therefore, the correct ranking from smallest to largest momentum is Object B, Object A, Object C.
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consider a flow with a pressure and temperature of 1 atm and -3.15 oc. a pitot tube is inserted into the flow and measures a total pressure of 1.129 atm. what is the velocity [m/s] of the flow?
The velocity is approximately 23.28 m/s of a given a pressure and temperature of 1 atm and -3.15°C, and a total pressure of 1.129 atm measured by a Pitot tube.
The velocity of the flow can be calculated using Bernoulli's equation, which relates the pressure, density, and velocity of a fluid in a steady flow.
The Bernoulli's equation states that:
[tex]P + (1/2) * \rho* v^2=constant[/tex]
where P is the pressure,
ρ is the density,
v is the velocity, and
constant is a constant along a streamline.
Assuming that the fluid is an ideal gas, the density can be calculated using the ideal gas law:
[tex]P * V = n * R * T[/tex]
where V is the volume,
n is the number of moles,
R is the gas constant, and
T is the temperature.
Rearranging the ideal gas law to solve for density, we get:
[tex]\rho= (P * M) / (R * T)[/tex]
where M is the molar mass of the gas.
Substituting the given values, we get:
[tex]\rho= (1 * 0.02897) / (8.314 * (273.15 - 3.15)) = 1.225 kg/m^3[/tex]
where the temperature is converted to Kelvin by adding 273.15.
The velocity can be calculated using the formula:
[tex]v = {((2 * (P_t - P)) / \rho)}[/tex]
where [tex]P_t[/tex] is the total pressure measured by the Pitot tube.
Substituting the given values, we get:
[tex]v = \sqrt{((2 * (1.129 - 1)) / 1.225)} = 23.28 m/s[/tex]
Therefore, the velocity of the flow is approximately 23.28 m/s.
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A grasshopper jumps into the air. As it rises into the air, the grasshopper slows down and loses kinetic energy.
Because the grasshopper’s kinetic energy is decreasing, what else occurs?
a circuit in a home provides power to a light fixture. the homeowners want to use a compact fluorescent bulb instead of an incandescent bulb. compact fluorescent bulbs can produce as much light as incandescent bulbs but with less energy. how is this possible?(1 point) responses fluorescent bulbs have been designed to put out more energy than they receive. fluorescent bulbs have been designed to put out more energy than they receive. fluorescent bulbs produce other forms of energy, too, including heat. fluorescent bulbs produce other forms of energy, too, including heat. energy is destroyed when it passes through an incandescent bulb. energy is destroyed when it passes through an incandescent bulb. incandescent bulbs produce other forms of energy, too, including heat. incandescent bulbs produce other forms of energy, too, including heat.
A circuit in a home provides power to a light fixture. The homeowners want to use a compact fluorescent bulb instead of an incandescent bulb. compact fluorescent bulbs can produce as much light as incandescent bulbs but with less energy because: it makes them a more cost-effective choice over time.
The homeowners want to use a compact fluorescent bulb instead of an incandescent bulb. Compact fluorescent bulbs can produce as much light as incandescent bulbs but with less energy. Fluorescent bulbs have been designed to put out more energy than they receive. This makes them a more efficient light source than incandescent bulbs.
Unlike incandescent bulbs, fluorescent bulbs produce less heat and use less electricity. Fluorescent bulbs produce light by exciting mercury vapor. The mercury vapor emits ultraviolet light, which is converted into visible light by a phosphor coating on the bulb's interior. This process uses less energy than an incandescent bulb, which produces light by heating a filament until it glows.
Fluorescent bulbs can also last much longer than incandescent bulbs, which makes them a more cost-effective choice over time. Overall, fluorescent bulbs are a more efficient and environmentally friendly choice for lighting compared to incandescent bulbs.
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which is greater? the annual energy usage of the earth, or the energy released by the sun in 1 second?
The energy released by the sun in one second, also known as the solar luminosity, is much greater than the annual energy usage of the earth.
The solar luminosity is estimated to be about 3.8 x 10^26 watts, while the total energy usage of the earth is estimated to be around 157,481 terawatt-hours per year, or about 18 x 10^12 watts. This means that the energy released by the sun in just one second is many orders of magnitude greater than the total energy used by all human activities on earth in a year. The sun's enormous energy output is what drives most of the physical and biological processes on our planet.
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the magnitude of the electric field in an em wave is doubled. what happens to the intensity of the wave?
"When the magnitude of the electric field in an EM wave is doubled, the intensity of the wave increases by a factor of 4."
The intensity (I) of an electromagnetic wave is given mathematically as,
I = (1/2) ε₀ c E²
where,
ε₀ is the electric constant
c is the speed of light
E is magnitude of the electric field
An electromagnetic wave's intensity will increase by a factor of four if the electric field's magnitude doubles.
I' = (1/2)ε₀c(2E)² = 4(1/2)ε₀ c E² = 4 I
Electromagnetic waves are waves that are usually produced by oscillating electric and magnetic fields. An electromagnetic wave is a combination of electric and magnetic fields that oscillate perpendicularly to each other and to the direction of wave propagation. Light, microwaves, X-rays, and radio waves are the examples of electromagnetic waves.
The power transferred per unit area by an electromagnetic wave is said to be the intensity of the wave. The magnitude of the electric field in an EM wave is connected with its intensity.
Thus, as the magnitude of the electric field in an EM wave is doubled, the intensity of the wave becomes four times of the value.
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For a given mass of a gas at a constant temperature, if the volume,′ V′ becomes three times then pressure P will become: a. 3Pb. P/3c. 3P/Td. 9P
According to Boyle's law, the pressure of a gas is inversely proportional to its volume at constant temperature. The correct answer is Option: (b).
If the volume of a gas at a constant temperature becomes three times larger, the pressure of the gas will decrease to the one-third of its initial value. Thus, the correct answer is Option: (b) P/3. This relationship can be mathematically represented as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the new pressure and volume, respectively. Therefore, if V2 = 3V1, then the P2 = P1/3.
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determine the vertical acceleration of the cylinder with a weight wa = 53 lb for each of the two cases. neglect friction and the mass of the pulleys. the acceleration is positive if up, negative if down
The given question states that we have to determine the vertical acceleration of the cylinder with a weight wa = 53 lb for each of the two cases. Neglect friction and the mass of the pulleys.
The acceleration is positive if up, negative if down. What is the formula for acceleration? Acceleration is defined as the rate of change of velocity of an object with respect to time. The formula for acceleration is given by a=Δv/Δt, where a = acceleration (m/s²)Δv = change in velocity (m/s)Δt = change in time (s)To calculate the vertical acceleration of the cylinder, we can use the formula for force, which is given by F = ma, where F = force (N)m = mass (kg)a = acceleration (m/s²) Now, we will calculate the mass of the cylinder using the given weight of wa = 53 lb.1 lb = 0.453592 kg Therefore, wa = 53 lb = 24.0409 kg For the first case, the weight is acting downwards on the cylinder. Therefore, the force on the cylinder can be calculated as F = ma F = 24.0409 kg × 9.8 m/s²F = 236.03 N Now, we can use this force to calculate the acceleration of the cylinder. a = F/ma = 236.03 N/24.0409 kg a = 9.8 m/s²Therefore, the vertical acceleration of the cylinder for the first case is 9.8 m/s², which is positive as it is upwards. For the second case, the weight is acting upwards on the cylinder.
Therefore, the force on the cylinder can be calculated as F = maF = 24.0409 kg × 9.8 m/s²F = 236.03 N Now, we can use this force to calculate the acceleration of the cylinder. a = F/ma = 236.03 N/24.0409 kga = -9.8 m/s²Therefore, the vertical acceleration of the cylinder for the second case is -9.8 m/s², which is negative as it is downwards.
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the spacing between atomic planes in a solid is of similar length-scale to the wavelength of which type of electromagnetic radiation? the spacing between atomic planes in a solid is of similar length-scale to the wavelength of which type of electromagnetic radiation? visible light radio waves gamma rays infrared radiation ultraviolet light x-rays
The spacing between atomic planes in a solid is of a similar length scale to the wavelength of X-rays.
X-rays have a very short wavelength, typically on the order of 0.1 to 10 nanometers, which is similar in length scale to the spacing between atomic planes in a solid. This makes X-rays ideal for studying the structure of crystals and other materials, as they can be diffracted by the regularly spaced planes of atoms in a crystal lattice, producing a diffraction pattern that can be analyzed to determine the crystal structure.
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PLEASE PLEASE PLEASE HELP ME ANSWER THIS QUESTION!
What atoms are found in CO2?
CO2 contains one carbon atom and two oxygen atoms.
C stands for carbon
O for oxygen
A diver does 8000 J of work against gravity to climb a diving board. if he weighs 800N
1. calculate the height of the board above the ground.
The height of the board above the ground is 10 m. see the section below for calculation
Calculation of DistanceWe know that the expression for distance is given as
Work = Force x Distance
Substituting into then expression above we have
8000 J = 800 N x Distance
Making distance subject of formula we have
Distance = 8000 J / 800 N
Distance = 10 m
Distance is a measure of how far two points are from each other. For example, if a person were to walk 10 meters, the distance they have traveled is 10 meters.
Distance can also refer to the amount of work done by a certain force, such as when lifting an object. In this case, the work done is measured in units of Joules, and the force in Newtons. The distance is then calculated by dividing the work done by the force. Therefore, distance is a measure of how far two points are from each other, as well as a measure of the amount of work done by a certain force.
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for a point on the rim of the flywheel, what is the magnitude of the tangential acceleration after 2.00 s of acceleration?
Explanation:
We can use the formula for tangential acceleration:
a_t = r * α
where a_t is the tangential acceleration, r is the radius of the flywheel, and α is the angular acceleration.
To find the angular acceleration, we can use the formula:
θ = 1/2 * α * t^2
where θ is the angular displacement, t is the time, and α is the angular acceleration.
Rearranging this formula to solve for α, we get:
α = 2θ / t^2
Substituting in the given values, we get:
α = 2 * (2π) / (2.00 s)^2
Simplifying, we get:
α = 1.57 rad/s^2
Substituting this into the formula for tangential acceleration, along with the given radius of the flywheel, we get:
a_t = (0.274 m) * (1.57 rad/s^2)
Simplifying, we get:
a_t = 0.431 m/s^2
Therefore, the magnitude of the tangential acceleration of a point on the rim of the flywheel after 2.00 s of acceleration is approximately 0.431 m/s^2.
question two pieces of silk have an electric charge after being rubbed on a piece of amber. what will happen when the two silk pieces are brought close together?
When two pieces of silk that have been rubbed on a piece of amber are brought close together, they will experience electrostatic attraction.
The electrostatic attraction is because the rubbing of the amber transfers electrons from the amber to the silk pieces, which creates a net positive charge on one piece and a net negative charge on the other. This results in the positive charge being attracted to the negative charge and the two pieces of silk being attracted to each other. This is due to the electric forces of attraction between particles with opposite charges.
This attraction can be seen through the "Leyden Jar" experiment, where two pieces of glass and two pieces of silk that have been rubbed on a piece of amber are placed on either side of the Leyden Jar. When the two pieces of silk are brought close together, an electric spark is observed. This is a result of the attraction of the opposite charges.
In conclusion, when two pieces of silk that have been rubbed on a piece of amber are brought close together, they will experience electrostatic attraction due to the electric forces of attraction between particles with opposite charges.
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when a hammer thrower releases her ball, she is aiming to maximize the distance from the starting ring. assume she releases the ball at an angle of 47.9 degrees above horizontal, and the ball travels a total horizontal distance of 33.6 m. what angular velocity must she have achieved (in radians/s) at the moment of the throw, assuming the ball is 1.16 m from the axis of rotation during the spin?
In order to throw the ball to a distance of 33.6\ m, the hammer thrower must achieve an angular velocity of 15.7 rad/s.
We need to find the velocity of the ball at release. We can use the equations of projectile motion to relate the horizontal distance traveled by the ball to its initial velocity and angle of release. The horizontal distance is given by:
[tex]d = (V^2\times sin(2\theta))/g[/tex]
where d is the horizontal distance, V is the initial velocity, g is the acceleration due to gravity, and θ is the angle of release.
Given horizontal distance d = 33.6\ m and θ = 47.9°
Substituting the given values, we get:
[tex]33.6 m = (V^2sin(2\times47.9^o))/9.8\ m/s^2[/tex]
Solving for V, we get:
V = 18.21 m/s
Now, to find the angular velocity we can use the formula
[tex]\omega = V/r[/tex]
[tex]\omega=18.21/1.16\ rad/s[/tex]
[tex]\omega = 15.705\ rad/s[/tex]
Therefore, the angular velocity the hammer thrower must have achieved at the moment of the throw is [tex]15.705\ rad/s[/tex].
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an object sits in front of a converging lens 27.2 cm away from it. if the image of the object is formed 68.3 cm on the opposite side of the lens, what is the focal length of the lens?
The focal length of the lens, in which the image is formed on the opposite side of the object- 68.3cm away from it, is -68.5cm.
The formula for finding the focal length of a lens is:
1/f = 1/di + 1/do
where f is the focal length of the lens, di is the distance from the lens to the image and do is the distance from the lens to the object.
In this case, di = -68.3 cm (since the image is formed on the opposite side of the lens), and do = 27.2 cm. Plugging these values into the formula gives:
1/f = 1/-68.3 + 1/27.2
Simplifying this equation gives:
1/f = -0.0146
Multiplying both sides by -1 gives:
-1/f = 0.0146
Dividing both sides by 0.0146 gives:
f ≈ -68.5 cm
The negative sign indicates that the lens is a diverging lens rather than a converging one. If you want to find the focal length of a converging lens, you should get a positive value for f.
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atmospheric drag is proportional to density. how does the magnitude of atmospheric drag change over a solar cycle at 100 km altitude?
Therefore it isn't nearly the same 100 km above the tropics as it is 100 km above the poles. The atmosphere will receive more direct sunlight throughout the course of a year, heat up, causing its density to decrease.
What is magnitude in physics?Magnitude is simply "distance or amount" in the context of physics. In terms of motion, it shows the either the absolute or relative size, direction, or movement of an item. It is used to describe something's size or scope. Magnitude in physics often refers to a size or amount.
Is magnitude a scalar or a vector?Scalars only have magnitude, but vectors also include direction. It might be confusing because magnitude happens for both physical quantities and vectors. For scientists, certain quantities—like speed—have extremely specific meanings. Speed is the scalar magnitude of a velocity vector, according to definition.
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a red laser pointer has a wavelength of 650 nm . the laser beam leaves the laser through a 1.0- mm -diameter aperture. what would be the width of the laser beam after traveling from the earth to the moon, 384,000 km away?
A red laser pointer with a wavelength of 650 nm has a width of 3,205,524 km that leaves the laser through a 1.0-mm diameter aperture.
Let's first figure out the diameter of the beam. We know that the aperture of the laser pointer is 1.0 mm in diameter. So, the diameter of the beam leaving the laser is also 1.0 mm.
In this case, we can assume that the laser beam spreads out uniformly in all directions as it travels from Earth to the Moon. Therefore, the diameter of the beam would increase linearly with distance from the source. This increase in diameter is determined by the divergence angle of the beam.
In this case, we can use the following formula to determine the beam diameter after it has traveled a certain distance:
D = D₀ + 2 * L * tan(θ/2)
where D is the diameter of the beam at distance L from the source, D₀ is the diameter of the beam at the source, λ is the wavelength of the light, and θ is the divergence angle of the beam.
As we do not know the divergence angle, we need to make an assumption about it. For a typical laser pointer, the divergence angle can be anywhere between 0.1 and 1 degree. We'll assume a divergence angle of 0.1 degrees, which is on the low end of the range.
Substituting the values we know into the formula, we get:
D = D₀ + 2 * L * tan(θ/2) = 1.0 mm + 2 * 384,000 km * tan(0.1/2) = 3,205,524 km.
The width of the laser beam after traveling from the Earth to the moon, 384,000 km away is 3,205,524 km.
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(I) A cyclist and her cycle have a total mass of 85kg. Calculate the combined kinetic energy of the cyclist and cycle when travelling at a speed of 12m/s.
(ii) The kinetic energy of the cyclist and cycle increases at an average rate of 180 joules per second. Calculate the time it takes to gain this energy.
The combined kinetic energy of the cyclist and cycle is 6120 J. It takes 34 seconds for the kinetic energy of the cyclist and cycle to increase by 6120 J at a rate of 180 J/s.
What is the kinetic energy equation?Kinetic energy has the following formula: K.E. (= 1/2 m v2, where m is the object's mass and v is its square velocity. The kinetic energy is measured in kilograms-meters squared for every second squared if the mass is measured in kilogrammes and the velocity is measured in metres per second.v
f =12× 15= 310 m/s
The initial velocity is given asv i =6× 5= 35 m/s
The increase in kinetic energy is given as,
ΔKE= 21 m(v f −v i2 )= 21 ×90(( 310 ) 2 −( 35 ) 2 )=375J
Thus, the increase in kinetic energy is 6120J
What is kinetic energy combined?Total mechanical energy is represented by the sum of potential and kinetic energy. The energy an object has as a result of its motion or position is known as mechanical energy. Kinetic energy is the energy of motion, and potential energy is the energy in position or shape.
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Find the acceleration (in m/s^2) of a car that travels from rest, to a velocity of 60 m/s in a distance of 212.0 ft.
A. 32 m/s^2
B. 27.9 m/s
C. 27.9 ft/s^2
D. 27.9 m/s^2
Show the work for determining the acceleration of the car...show symbolic solution then numerical solution.
As the units for acceleration are metres per second squared, we must first convert the distance from feet to metres. We know that 3.28084 feet are equal to 1 metre, so we can calculate: 212.0 feet (1 m / 3.28084 ft) = 64.6218 m.Hence, the car's total distance travelled was 64.6218 metres.
What is the acceleration of a car travelling down a straight road that goes from 0 to 100 km/h in 10 seconds in terms of m/s2?How quickly does a car travelling along a straight road accelerate to reach 100 km/h in 10 seconds? 6 m/s.
What is a body starting at rest's acceleration A in MS 2?The acceleration a (in ms 2) of a body, starting from rest varies with time t (ins) following the equation a= 3t+4.
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A hydroelectric power plant needs to provide 9.8•10^9 J of electricity every hour. The efficiency of the power plant is 90% The water falls 40m to the turbine.
A) What is the power output of the power plant in watts?
B) What is the actual power that must be supplied by the water to produce this power?
C) How much water must pass through the power plant’s turbine every second in order to provide this amount of power?
According to the information, the power output of the power plant is 2.44998 x 10^6 W, and the amount of water that must pass through the power plant’s turbine every second in order to provide this amount of power is 6.9497 x 10^3 kg/s.
How to find the power output of the power plant in watts?A) To find the power output of the power plant in watts, we can use the formula:
Power output = Efficiency x Power inputwhere the power input is the energy input per unit time, which in this case is the energy provided per hour. We need to convert this to Joules per second (Watts). So:
Power input = 9.8 x 10^9 J/hour = 2.7222 x 10^6 J/sNow we can plug in the given efficiency:
Power output = 0.9 x 2.7222 x 10^6 J/s = 2.44998 x 10^6 WTherefore, the power output of the power plant is 2.44998 x 10^6 W.
How much power must be supplied by the water?The actual power that must be supplied by the water to produce this power can be found by using the formula:
Power input = Power output / EfficiencyWe can use the value of the efficiency already given, so:
Power input = 2.44998 x 10^6 W / 0.9 = 2.7222 x 10^6 WTherefore, the actual power that must be supplied by the water to produce this power is 2.7222 x 10^6 W.
C) To find out how much water must pass through the power plant’s turbine every second in order to provide this amount of power, we need to use the formula:
Power input = mass flow rate x g x hwhere mass flow rate is the amount of water flowing per second, g is the acceleration due to gravity (9.81 m/s^2), and h is the height of the water fall (40m).
We can rearrange the formula to solve for the mass flow rate:
mass flow rate = Power input / (g x h)mass flow rate = 2.7222 x 10^6 W / (9.81 m/s^2 x 40m) = 6.9497 x 10^3 kg/sTherefore, the amount of water that must pass through the power plant’s turbine every second in order to provide this amount of power is 6.9497 x 10^3 kg/s.
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