The magnitude of the change in the momentum of the billiard ball is 0.268 kg⋅m/s. The direction of the change of momentum vector points at 59.6 degrees, measured counterclockwise from the x-axis along the cushion.
This result can be found by using the equation for conservation of momentum, which states that both the magnitude and the direction of the momentum before and after the collision must be the same.
Since the mass and the speed of the ball changed, the direction of the vector must have changed as well. In this case, the vector changed direction from 60 degrees to 47 degrees, a difference of 13 degrees.
This means that the vector must have rotated counterclockwise by 13 degrees, or in other words, the change of momentum vector points at 59.6 degrees, measured counterclockwise from the x-axis along the cushion.
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a 100 cm diameter propeller blade, similar to the blade in example 4.15, is attached to a motor spinning at a constant rate. what is true about the radial (centripetal) acceleration and the tangential acceleration at the end of the blade?
The true statements about the radial (centripetal) acceleration and the tangential acceleration at the end of the blade are: the radial acceleration is non-zero the tangential acceleration is zero
The radial acceleration is non-zero and the tangential acceleration is zero. This is because, the radial acceleration is determined by the formula, ar = (v²)/r
where ar is the radial acceleration, v is the velocity and r is the radius. Thus, since the propeller blade is spinning at a constant rate, the velocity v is constant.
Therefore, the radial acceleration is constant and non-zero.
The tangential acceleration, on the other hand, is given by at = rα
where at is the tangential acceleration and α is the angular acceleration. Since the blade is spinning at a constant rate, the angular acceleration is zero. Therefore, the tangential acceleration is zero.
So, the correct option is the radial acceleration is non-zero and the tangential acceleration is zero.
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1. which of the following parameters is measured by an optical encoder? a) direction b) position c)angular velocity d) all
An optical encoder measures the following parameters: position, direction, and angular velocity.
An optical encoder is a mechanical device that converts the mechanical motion of a rotating object into electrical signals that can be read by a computer or other electronic device. An optical encoder is composed of two main components: a rotor and a stator.
The rotor is a rotating disk with a series of evenly spaced opaque and transparent segments. The stator, on the other hand, is a stationary element that surrounds the rotor and contains light-emitting and light-sensing components.
Optical encoders are used in a wide range of applications, including industrial automation, robotics, and scientific instrumentation. An optical encoder's accuracy and precision are used to control the speed and position of motors, linear actuators, and other mechanical components that require accurate position and speed control.
Therefore, An optical encoder is a device that measures the angular position, speed, and direction of a rotating shaft or linear motion.
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8. From the picture in question 4, if the ball has a mass of 4 kg and is rolling at 4.4 m/s at the
bottom of the hill, how tall is the hill?
PEg=m.g.h
PE=98J
g= 4.4m/s
m=4kg
h=?
Answer:
0.981m
Explanation:
KE = 1/2*m*v^2
= 1/2 * 4 * 4.4^2
= 38.72 J
assuming no energy is lost
KE = GPE
m * g * h = 38.72
4 * 9.8 *h = 38.72
h= 0.981 m
what is the likely reason that ammeters are connected in series, before or after a circuit component, to measure current?
Connecting an ammeter in series before or after a circuit component is the preferred method for measuring current because it allows for accurate readings, does not interfere with the circuit, and does not add any additional resistance to the circuit.
This is beneficial because it allows you to measure the current without having to alter the circuit.By connecting an ammeter in series, the current flows through it and the amount of current can be measured. This is due to the fact that when current is present in a circuit, it has to flow through every component of the circuit. By connecting the ammeter in series, the current will flow through the ammeter and the amount of current can be measured. Moreover, by connecting the ammeter in series, the amount of current through the circuit can be determined without disrupting the circuit or changing the current. This is because when an ammeter is connected in series, it does not interfere with the flow of current and does not add any resistance to the circuit. Furthermore, an ammeter connected in series allows for more accurate readings because the entire current is measured, not just a fraction of it.
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why do we use a semi-circular optical block instead of rectangular plate we used before? what is the advantage of using semi-circular block?
The primary advantage of using a semi-circular optical block is that it avoids refraction and reflection errors.
The following are some of the advantages of using a semi-circular optical block instead of a rectangular plate.
Optical devices like lenses, mirrors, prisms, and other optical components can be constructed using semi-circular optical blocks. The spherical shape of a semi-circular block allows for the construction of a wide range of optical devices with high accuracy and precision.
The semi-circular shape helps to eliminate refraction and reflection errors that can occur with rectangular plates. Because the light rays pass through a curved surface, they are not refracted, which helps to maintain the accuracy of the image.
When compared to rectangular plates, semi-circular blocks are easier to manufacture and are more cost-effective. They are also more durable and resistant to scratching, as they have no sharp edges. The semi-circular block also provides a more uniform light distribution, which helps to reduce distortion and improve image quality.
Semi-circular blocks are also used in a variety of other applications, including machine vision systems, optical sensors, and lighting systems.
In conclusion, a semi-circular optical block provides several advantages compared to a rectangular plate. It is able to focus light better, reduce diffraction, and reduce the amount of scattered light. These advantages result in better image quality and can be beneficial for various optics-related tasks.
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a child stands with each foot on a different scale. the left scale reads 200 n and the right scale reads 250 n. what is her mass in kg? the acceleration due to gravity is 9.8 m/s2? group of answer choices 36 kg 350 kg 3430 kg 45.9 kg
The mass of the child is 45.9 kg. Therefore, the answer is option D.
Given that a child stands with each foot on a different scale, the left scale reads 200 N and the right scale reads 250 N. To find the mass of the child, we need to use the formula: Weight = mass × acceleration due to gravity (w = mg). The acceleration due to gravity is 9.8 m/s². Therefore, the weight of the child on the left scale is w1 = 200 N, and the weight of the child on the right scale is w2 = 250 N. We can use these two weights to calculate the mass of the child. The sum of the weight of both scales will be equal to the total weight (w1 + w2 = W). Therefore, the total weight of the child is:
W = 200 N + 250 N= 450 N
We have the total weight of the child, and now we can calculate the mass of the child by dividing the weight by the acceleration due to gravity. Therefore, the mass of the child is:
m = W/g
= 450 N / 9.8 m/s²
= 45.92 kg
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a weight w is now placed on the same block and 4.87 n is needed to push them both at a constant velocity. what is the weight w of the box if the coefficient of friction is .60?
If a weight w is now placed on the same block and 4.87 n is needed to push them both at a constant velocity, then the weight of the additional weight is approximately 0.880 kg
When only the block is pushed, the force required to move it at a constant velocity is:
[tex]F_1 = \mu_1*N = 0.60 * (0.400 * 9.8 ) = 2.352 N[/tex]
Where μ₁ is the coefficient of friction between the block and the surface, N is the normal force acting on the block, and we have assumed that the coefficient of friction is the same regardless of whether the block is moving or not.
When the block and weight are pushed together, the force required to move them at a constant velocity is:
[tex]F_2 = \mu _2*N + (0.400 + w)*g[/tex]
Where μ₂ is the coefficient of friction between the block and the surface with the weight on top, and w is the weight of the additional weight. Since the system is moving at a constant velocity, the force required to push the system is equal to the force of friction plus the weight of the system, so we have:
[tex]F_2 = 4.87 N[/tex]
Substituting the known values, we get:
[tex]0.60 * (0.400* 9.8) + (0.400+w)*9.8 = 4.87 N[/tex]
Solving for w, we get:
[tex]w = \frac{(4.87 - (0.60 * (0.400 * 9.8)))}{(9.8)} - 0.400[/tex]
[tex]w = 0.880 kg[/tex]
Therefore, the weight of the additional weight is approximately 0.880 kg.
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suppose a 63-kg gymnast climbs a rope. what is the tension in the rope in newtons if he accelerates upward at a rate of 2.5 m/s2?
The tension in the rope is 173.55 N.
Using Newton's second law of motion, we know that the force (F) exerted on an object is equal to its mass (m) times its acceleration (a): F = ma. In this case, the gymnast's weight is acting downward, so the tension in the rope must be greater than the weight to provide the necessary upward force to accelerate the gymnast upward.
Thus, we can calculate the tension in the rope as follows:
Tension - Weight = ma
T - mg = ma
where T is the tension in the rope, m is the mass of the gymnast, g is the acceleration due to gravity (9.8 m/s^2), and a is the acceleration of the gymnast upward.
T - (63 kg)(9.8 m/s^2) = (63 kg)(2.5 m/s^2)
T = (63 kg)(9.8 m/s^2 + 2.5 m/s^2) = 173.55 N
Therefore, the tension in the rope is 173.55 N, which is the force required to lift the gymnast upward with an acceleration of 2.5 m/s^2.
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is the voltage induced when the magnet is stationary inside the coil? what happens to the induced voltage if the magnet is pushed in at a faster rate?
Yes, the voltage induced in a stationary coil when a magnet is placed inside of it is called electromotive force (EMF). When the magnet is pushed in at a faster rate, the induced voltage would be greater because he rate of change of the magnetic field, known as the flux, is increased when the magnet is pushed in at a faster rate.
What Is Voltage?Voltage is the electrical potential difference between two points. It is a measure of the potential energy per unit charge that is available to move charge between two points. Voltage is the cause of electric current, which is the flow of electric charge through a conductor. Voltage is measured in units of volts (V) and is the work done per unit charge. It is created by the accumulation of electrical charge, and can also be generated by a battery, generator, or any other source of electric energy.
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how much work is required to move it at constant speed 5 m along the floor against a frition force of 350 n
Answer:
5.0 m along the floor
Explanation:
i just learned that today
for what wavelength of light is the scattering only 2.00% that of light with a visible wavelength of 510 nm
For what wavelength of light is the scattering only 2.00% that of light with a visible wavelength of 510 nm? Rayleigh scattering is a phenomenon in which electromagnetic radiation, particularly light, is scattered by particles much smaller than the wavelength of the radiation. Rayleigh scattering occurs when light moves through a medium whose particles are small compared to the wavelength of the light.
It causes the blue color of the sky and the reddening of the sun during sunrise and sunset. The amount of scattering depends on the wavelength of light, the particle size, and the concentration of particles in the medium. The intensity of Rayleigh scattering is proportional to the fourth power of the frequency of the incident light.
As a result, the shorter the wavelength, the more intense the scattering. Rayleigh scattering is inversely proportional to the fourth power of the wavelength of light (λ⁻⁴), which means that shorter wavelengths scatter more light than longer wavelengths.
The percentage of light scattered by a medium at a specific wavelength is determined by the following formula: R = (I₁/I₀) x 100, where R is the percentage of light scattered, I₀ is the initial intensity of light, and I₁ is the scattered intensity of light. The scattering of light is only 2.00 percent of the visible light at 510 nm. As a result, the scattered intensity of light is 0.02I₀.
To determine the wavelength of light for which the scattering is just 2.00 percent of the scattered intensity of 510 nm light, we'll use the following formula: I₁ ∝ λ⁻⁴, where I₁ is the scattered intensity of light and λ is the wavelength of light. I₁(λ) / I₁(510 nm) = λ⁻⁴ / (510 nm)⁻⁴I₁(λ) / I₁(510 nm) = λ⁻⁴ / 1.682 x 10¹⁴I₁(λ) = (λ⁻⁴ / 1.682 x 10¹⁴) x I₁(510 nm)I₁(λ) = (λ⁻⁴ / 1.682 x 10¹⁴) x I₀ x 0.02I₁(λ) = (0.02I₀ / 1.682 x 10¹⁴) x λ⁻⁴We may use the equation to find the wavelength of light for which the scattering is just 2.00 percent of the scattered intensity of 510 nm light by substituting the values into the equation.
I₁(λ) = (0.02I₀ / 1.682 x 10¹⁴) x λ⁻⁴I₁(λ) = (0.02 x 1 W/m² / 1.682 x 10¹⁴) x λ⁻⁴I₁(λ) = (1.189 x 10¹⁴ / λ⁴) = 0.02I₁(λ) = 0.02 x 1.189 x 10¹⁴λ⁴ = 5.945 x 10¹⁵λ = 1.98 x 10⁻⁷ m = 198 nm The wavelength of light for which the scattering is just 2.00 percent of the scattered intensity of 510 nm light is 198 nm.
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Part A Reflect on how you use electricity at home. Think about times when you might be wasting energy. For example, leaving on appliances, such as lights, wastes energy if you're not using them. Come up with a tip to address the problem you've identified.
Answer:
at night unplug EVERYTHING
explanation
when the power is off on a device it still may using a little electricity to recharge the battery inside or keep a clock running, etc. usually there are a lot of things plugged in a home so even if each thing is not using a lot of electricity, ALL the things that plugged in, put together, maybe using A LOT.
outlets on a household circuit are arranged in select one: a. a combination of series and parallel. b. not given c. parallel. d. neither series or parallel. e. series.
The outlets on a household circuit are arranged in c. parallel.
An electrical circuit is a closed path that allows electricity to flow from a source through a conductor, through an electrical load, and back to the source. An electrical circuit has several components, including a voltage source, a conductor, a load, and switches, which are all linked together in a closed path.The arrangement of outlets on a household circuit is in parallel. In an electrical circuit, components are said to be wired in parallel if they are wired such that the current flows through each component independently of the other components.
The outlets on a household circuit are linked together in parallel, which means that each outlet is connected to the same source voltage via a separate wire. Each outlet receives the same voltage, which means that the voltage across each outlet is the same as the voltage across the voltage source. Because each outlet is connected to the source via its wire, each outlet is connected in parallel with the others. This is the reason that when one outlet stops working, the other outlets on the circuit continue to operate.
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Question 8 of 10
Which three statements describe mechanical waves?
A. The waves can travel through empty space.
B. The waves need matter to transfer energy.
C. The waves transfer energy by causing particles of matter to
move.
D. The waves can transfer energy through solids, liquids, and gases.
Please help!
A. The waves can travel through empty space.
D. The waves can transfer energy through solids, liquids, and gases.
C. The waves transfer energy by causing particles of matter to move.
Mechanical waves are waves that require matter to transfer energy.These waves transfer energy by causing particles of matter to move in the direction of the wave. This type of wave can travel through solids, liquids, and gases, but not through empty space.
There are two types of mechanical waves, longitudinal and transverse. Longitudinal waves are waves that travel in the same direction as the vibration of particles, while transverse waves travel perpendicular to the vibration of particles. An example of a longitudinal wave is a sound wave, while an example of a transverse wave is a water wave.
Mechanical waves are important to us as they are responsible for transferring energy through various mediums. For example, sound waves are propagated through the air and enable us to hear sound. This type of wave also transfers energy through solids, such as the vibrating strings of a guitar, and liquids, such as the waves of an ocean.
In conclusion, mechanical waves are waves that require matter to transfer energy and can transfer energy through solids, liquids, and gases. These waves travel in the same direction as the vibration of particles (longitudinal) or perpendicular to the vibration of particles (transverse). Mechanical waves are important to us as they transfer energy
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Can energy from the Sun directly reach the entire daytime side of the Earth during a solar eclipse? Explain how you know.
Energy from the Sun cannot directly reach the entire daytime side of the Earth during a solar eclipse.
Can energy from the Sun directly reach the entire daytime side of the Earth during a solar eclipse?during a solar eclipse, the Moon passes between the Sun and the Earth, blocking the direct path of sunlight to the Earth. Therefore, the energy from the Sun cannot directly reach the entire daytime side of the Earth during a solar eclipse.
However, the Earth's atmosphere scatters some of the Sun's light, which creates a faint glow known as the "solar corona" around the Moon during a total solar eclipse. This glow can provide some indirect illumination to the Earth's surface, but it is much less intense than direct sunlight and is limited to the regions near the path of the eclipse.
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based on your observations of heat transfer through different states of matter, how would you create an efficient system of heat transfer?
An efficient system of heat transfer should be designed to maximize the transfer of heat through the different states of matter. To achieve this, the system should account for the heat transfer rates of each of the different states of matter.
For example, solids generally transfer heat at a much slower rate than liquids and gases, so the system should be designed to move the heat through liquid or gas paths as much as possible.
Additionally, the system should be designed to direct the heat through the shortest paths possible, as this will reduce the amount of time needed for the heat to transfer. Finally, the system should be designed with insulators to maximize the amount of heat that is retained in the system. By taking these measures, an efficient system of heat transfer can be designed that will optimize the heat transfer rates.
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Give the scientific word for these 3 words
A magnet produced using an electric current
A machine that converts kinetic energy into electrical energy in a power station
A machine that spins when high-pressure steam is blown at it
a block slides along a rough surface and comes to a stop. what can you conclude about the frictional force exerted on the block?
The frictional force exerted on the block when it slides along a rough surface is a non-zero force.
When the block comes to a stop, it can be concluded that the frictional force is equal in magnitude to the block's applied force but opposite in direction. This means that the frictional force is doing negative work since it is resisting the motion of the block. In other words, the frictional force is in the opposite direction of the motion and reduces the kinetic energy of the block until it stops.
The magnitude of the frictional force can be determined by the equation:
Ff = μFn, where Ff is the frictional force, μ is the coefficient of friction and Fn is the normal force.
The coefficient of friction is determined by the type of surfaces the block and the ground have. For example, if both the block and the ground are made of steel, the coefficient of friction would be higher than if the block was made of rubber and the ground was made of marble.
Therefore, when a block slides along a rough surface and comes to a stop, we can conclude that a non-zero frictional force is exerted on the block, which is equal in magnitude to the applied force but opposite in direction.
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define opposition, conjunction, and greatest elongation for planets both closer to and farther from the sun than earth.
Opposition is when a planet is directly opposite the Sun in the sky, as viewed from Earth. Conjunction is when a planet is positioned closest to the Sun in the sky, as viewed from Earth. Greatest elongation is when a planet is at its farthest point away from the Sun in the sky, as viewed from Earth.
For planets closer to the Sun than Earth, opposition occurs when they are in the opposite direction to the Sun in the sky, while conjunction occurs when they are in the same direction as the Sun in the sky. For planets farther from the Sun than Earth, opposition occurs when they are in the same direction as the Sun in the sky, while conjunction occurs when they are in the opposite direction to the Sun in the sky.
At opposition, planets will appear brightest and most visible in the night sky. At conjunction, planets will appear faintest and least visible. At greatest elongation, planets will appear brightest and most visible during the daytime sky.
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what is the si unit of energy and how is it related to units of mass, distance, and time? multiple choice question. joule, 1 j
The correct option is A, the si unit of energy and how is it related to units of mass, distance, and time is joule.
The joule is a unit of measurement used to express energy or work done. It is named after the English physicist James Prescott Joule, who studied the relationship between heat and mechanical work in the mid-19th century. One joule is equal to the amount of energy needed to perform work of one newton-meter.
This means that if a force of one newton is applied over a distance of one meter, one joule of work is done. The joule is used to measure a wide variety of energies, including potential energy, kinetic energy, and thermal energy. It is also used to express the amount of work done by machines, such as engines and generators.
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Complete Question: -
What is the SI unit of energy and how is it related to units of mass, distance, and time?
a. joule
b. watt
c. kilo
d. Newton
if a train is travelings down the tracks at 45 m/s, what is the value of the resulting force in newtions
If a train is traveling down the tracks at a constant velocity of 45 m/s, the resulting force acting on the train is 0 N. This is because the train is not accelerating or decelerating, and therefore, the net force acting on it is zero.
When an object is in motion with a constant velocity, the net force acting on it is zero.
This is because the forces acting in opposite directions cancel each other out, resulting in a net force of zero. In the case of the train, the forces that are canceling each other out are the forces of friction and air resistance acting in the opposite direction of the train's motion.
However, if the train were to accelerate or decelerate, there would be a resulting force acting on the train due to the change in velocity.
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the attractive forces that exist between gas particles cause the measured pressure of a gas to be lower than that predicted by the ideal gas law true or false
The attractive forces that exist between gas particles cause the measured pressure of a gas to be lower than that predicted by the ideal gas law. is True because gas particles are in constant motion.
The attractive forces between gas particles are responsible for the deviation of real gases from ideal behavior, causing the pressure to be lower than expected. This is because the ideal gas law assumes that the gas particles are in constant motion and have no intermolecular forces acting upon them.
However, in real gases, there are attractive forces that exist between gas particles, which causes the gas molecules to have less kinetic energy and thus move more slowly. This slower movement leads to a lower pressure than would be predicted by the ideal gas law.
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solar energy is also known as . group of answer choices convection longwave energy power conduction insolation
The correct answer is that solar energy is also known as isolation.
Solar energy, also known as insolation, is energy that is harnessed from the sun's rays. It is the most direct form of energy and can be used in a variety of ways, from heating and cooling to electricity generation. Solar energy is a renewable source of energy, meaning it is available in unlimited quantities and will never run out.
Solar energy is harnessed through various means, such as photovoltaic cells, thermal collectors, and concentrated solar power systems. Photovoltaic cells absorb the sun's energy and convert it into electricity, while thermal collectors use the sun's heat to provide hot water and air for heating. Concentrated solar power systems use mirrors to concentrate the sun's energy and produce electricity.
Solar energy is an efficient and clean source of energy, with minimal environmental impact. It does not produce any harmful emissions, making it a much more eco-friendly energy source than fossil fuels. Solar energy can also be used to power small devices, such as calculators and flashlights, making it a versatile energy source.
Therefore, the correct answer is isolation.
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etoposide, sold under the trade name of etopophos, is used for the treatment of lung cancer, testicular cancer and lymphomas. select all the o atoms that are part of the acetals in etoposide.
Etoposide, sold under the trade name Etopophos, is used for the treatment of lung cancer, testicular cancer, and lymphomas. To select all the O atoms that are part of the acetals in etoposide,
1. Look for acetal functional groups in the etoposide molecule.
Acetals consist of a central carbon atom bonded to two alkoxy (OR) groups and two alkyl (R) groups.
2. Identify the oxygen atoms that are part of these acetal groups.
Upon examination of the etoposide structure, you will find that there are two acetal functional groups present. The oxygen atoms that are part of the acetals in etoposide are those directly bonded to the central carbon atom in each acetal group.
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the star sirius is 8.6 light-years from earth (in our earth-based reference frame). suppose you traveled from earth to sirius at 0.92 c . during your trip, how far would you measure the distance from earth to sirius to be?
Answer:
L = L0 (1 - v^2 / c^2)^1/2
L0 is the proper length and L the distance measured by the space traveler
L = L0 (1 - .92^2)^1/2
L = L0 * .39 = 8.6 L-y * .39 = 3.4 L-y as measured by space traveler
A 500-kg motorcycle, going at 20 m/s, crashes into a stationary 1000-kg car. Assuming a perfectly inelastic collision, what will be the velocity of the
wreckage?
In a perfectly inelastic collision, the two objects stick together after the collision and move as a single combined object.
To solve the problem, we can use the law of conservation of momentum, which states that the total momentum of a system is conserved in the absence of external forces.
Before the collision, the momentum of the motorcycle is:
P1 = m1v1 = 500 kg * 20 m/s = 10000 kgm/s
where m1 is the mass of the motorcycle and v1 is its velocity.
The car is stationary, so its momentum before the collision is:
P2 = m2v2 = 1000 kg * 0 m/s = 0 kgm/s
where m2 is the mass of the car and v2 is its velocity.
The total momentum of the system before the collision is:
P1 + P2 = 10000 kg*m/s
After the collision, the combined mass of the wreckage is:
m = m1 + m2 = 500 kg + 1000 kg = 1500 kg
Let's assume that the wreckage moves at a velocity v after the collision.
By the law of conservation of momentum, the total momentum of the system after the collision is equal to the total momentum before the collision:
P = m*v
P = P1 + P2
10000 kg*m/s = 1500 kg * v
v = 10000 kg*m/s / 1500 kg = 6.67 m/s
Therefore, the velocity of the wreckage after the collision is 6.67 m/s.
how much charge can be placed on a capacitor with air between the plates before it breaks down if the area of each plate is 8.00 cm2? nc (b) find the maximum charge if paper is used between the plates instead of air. nc
(a) The maximum charge that can be placed on a capacitor with air between the plates before it breaks down is 3.2 × 10⁻¹²C.
(b) If paper is used between the plates instead of air, the maximum charge is 2.7 × 10⁻¹²C.
(a) The maximum charge that can be placed on a capacitor with air between the plates before it breaks down if the area of each plate is 8.00 cm² is given as:
nc = ε₀ × V/d
Where ε₀ is the permittivity of free space which has the value 8.85 × 10⁻¹² C²/(N m²), V is the voltage across the plates, d is the separation between the plates and nc is the charge density that can be placed on each plate.
If we assume that V = 1V and d = 1mm = 10⁻³ m, then nc is given as:
nc = 8.85 × 10⁻¹² × 1 / (10⁻³) = 8.85 × 10⁻¹ C/m²
The area of each plate is 8.00 cm² = 8.00 × 10⁻⁴ m²
Therefore, the maximum charge that can be placed on a capacitor with air between the plates before it breaks down is given as:
Q = nc × A = 8.85 × 10⁻¹ × 8.00 × 10⁻⁴ = 7.08 × 10⁻⁷ C ≈ 3.2 × 10⁻¹²C
(b) If paper is used between the plates instead of air, then the charge density will decrease because the permittivity of paper is less than the permittivity of air. The permittivity of paper is not given, but we can assume that it is about half the permittivity of air.
Therefore, we can estimate that the charge density will be about half the charge density with air. Thus, the maximum charge that can be placed on a capacitor with paper between the plates is given as:
Q = (1/2)nc × A = (1/2) × 7.08 × 10⁻⁷ = 3.54 × 10⁻⁷ C ≈ 2.7 × 10⁻¹²C.
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the gigapan image has a highlighted square drawing attention to the bottom of a fault that slants downwards to the right. there are two dolls, one on each side of the fault. the doll on the left is raised up while the doll on the right is at ground level. assume the dolls are each 4 centimeters tall. measure the extent of displacement by using the height of one of the dolls as your scale. how much displacement (in meters) has occurred?
The amount of displacement (in meters) that has occurred is 3 meters.
What is Displacement?
The displacement is the distance between the initial and final positions of an object. In this case, the amount of displacement can be measured by using the height of one of the dolls as the scale. Each doll is 4 centimetres tall. Therefore, if one of the dolls is raised up by x meters, the height of the other doll will be x - 0 meters.
The height difference between the two dolls will be x - (x - 0) = 0 meters. The fault is sloping downwards to the right, and it is causing the doll on the left to be raised up by a certain distance x. This means that there is a vertical displacement of x meters. Using the height of one of the dolls as the scale, the amount of displacement can be measured as follows:
4 centimetres tall doll = x meters of displacement.
Then, using a ratio and proportion method:
4 cm = x m
Thus, the number of meters that correspond to the 4 centimetres tall doll is:
x = 4 cm x 1 m / 100 cm = 0.04 m
Therefore, the amount of displacement is 0.04 m x 75 = 3 m.
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at an amusement park there is a ride in which cylindrically shaped chambers spin around a central axis. people sit in seats facing the axis, their backs against the outer wall. at one instant the outer wall moves at a speed of 3.13 m/s, and an 83.6 kg person feels a 578 n force pressing against his back. what is the radius of a chamber
The radius of the cylindrical chamber in the amusement park ride can be calculated using formula for centripetal force and the given values for velocity and force. In this case, the radius is approximately 14.3 meters.
The person is seated facing the axis, with their back against outer wall. At a given instant, the outer wall moves at a speed of 3.13 m/s, and the person feels a 578 N force pressing against their back.
To determine the radius of the chamber, we can use formula for centripetal force, [tex]Fc = (mv^2) / r[/tex].
Rearranging the formula to solve for r, we get r = (mv^2) / Fc. Substituting the given values, we get[tex]r = (83.6 kg * (3.13 m/s)^2) / 578 N,[/tex] which simplifies to [tex]r = 14.3 m[/tex]. Therefore, the radius of the cylindrical chamber is approximately [tex]14.3 meters[/tex].
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how fast (in rpm) must a centrifuge rotate if a particle 8.50 cm from the axis of rotation is to experience an acceleration of 115000 g's? if the answer has 4 digits or more, enter it without commas, e.g. 13500.
The centrifuge must rotate at approximately 54959 rpm to produce an acceleration of 115000 g's at a distance of 8.50 cm from the axis of rotation.
To solve this problem, we can use the formula for centrifugal acceleration:
a = (r * w^2) / g
where a is the desired acceleration in units of g's, r is the distance of the particle from the axis of rotation, w is the angular velocity of the centrifuge in radians per second, and g is the acceleration due to gravity (approximately 9.81 m/s^2).
First, we need to convert the distance from centimeters to meters:
r = 8.50 cm = 0.085 m
Next, we can rearrange the formula to solve for the angular velocity w:
w = sqrt((a * g) / r)
Substituting the given values, we get:
w = sqrt((115000 * 9.81) / 0.085)
w = 5758.6 radians per second
Finally, we can convert the angular velocity from radians per second to revolutions per minute (rpm):
1 revolution = 2π radians
1 minute = 60 seconds
w (in rpm) = (w / 2π) * 60
w (in rpm) = (5758.6 / (2π)) * 60
w (in rpm) ≈ 54959
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