The radius of curvature of a concave makeup mirror that is designed so that a person 27.6 cm in front of it sees an upright image at a distance of 50.3 cm behind the mirror is 35.54 cm.
What is the radius of curvature?The mirror formula is used to calculate this. When an object is placed in front of a concave mirror, a virtual image is formed behind it. The magnification of the virtual image is positive. Here's how to solve the problem:
1/f = 1/u + 1/v
where, f is the focal length of the mirror, u is the distance of the object from the mirror, v is the distance of the image from the mirror.
Given that , u = −27.6 cm (the negative sign indicates that the object is on the left-hand side of the mirror).
v = −50.3 cm (the negative sign indicates that the image is on the left-hand side of the mirror).
To calculate the radius of curvature, the focal length is required. The focal length can be calculated using the mirror formula.
1/f = 1/u + 1/v = (v + u)/uv = (-27.6 - 50.3)/(-27.6 × 50.3) = 77.9/1388.28 = 0.0562 cm. Therefore = 1/0.0562 = 17.77 cm.
The radius of curvature is twice the focal length.
2R = 2f = 2 × 17.77 = 35.54 cm
Thus, the radius of curvature of the mirror is 35.54 cm.
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The temperature of a gas stream is to be measured by a thermocouple whose junction can beapproximated as a 1.2-mm-diameter sphere. The properties of the junction are k =35 W/m °C, p=8500kg/m3, and Cp = 320 J/kg °C, and the heat transfer coefficient between the junction and the gas is h=65W/m2 °C. Determine how long it will take for the thermocouple to read 99 percent of the initialtemperature difference. (∅/∅i= 0.01)
it will take 30.65 minutes for the thermocouple to read 99 percent of the initial temperature difference. (∅/∅i = 0.01).
The temperature of a gas stream is to be measured by a thermocouple whose junction can be approximated as a 1.2-mm-diameter sphere. So, the radius, r = 0.6 mm = 0.0006 m, the volume of the sphere, V = (4/3)πr³, and the area of the sphere, A = 4πr².
The properties of the junction are k = 35 W/m °C, p = 8500 kg/m³, and Cp = 320 J/kg °C, and the heat transfer coefficient between the junction and the gas is h = 65 W/m² °C.
We have, thermal conductivity of the sphere = k = 35 W/m °C, density of the sphere = p = 8500 kg/m³, specific heat of the sphere = Cp = 320 J/kg °C, and heat transfer coefficient between the sphere and the gas, h = 65 W/m² °C.
The initial temperature difference is given by, ΔT₀ = 1°C = 1 K. Let, the time taken for the thermocouple to read 99% of the initial temperature difference, ΔT99 = 0.99 K.
Let, the thermal diffusivity of the sphere be,
α = k / (pCp) = (35 W/m °C) / (8500 kg/m³ x 320 J/kg °C) = 0.000012868 m²/s.
And, the Biot number is given by, Bi = (h x A) / k = [(65 W/m² °C) x 4π(0.0006 m)²] / (35 W/m °C) = 0.0492.
The equation for the unsteady-state temperature profile of a sphere is, θ(r,t) = Σ [(-1)n+1 / n] exp(-n²π²αt / r²) sin (nπr / R), where R is the radius of the sphere. We can estimate the time taken for the thermocouple to read 99% of the initial temperature difference using a semi-log plot of θ/ΔT vs. t/ti.
This plot is linear and of the form, θ/ΔT = 1 - A exp (-Bt/ti), where A = 0.01 and B = (nπ/R)².So, θ/ΔT = 0.99 = 1 - A exp (-Bt/ti), or 0.01 exp (-Bt/ti) = 0.01/0.99, or exp (-Bt/ti) = 1/99, or -Bt/ti = ln (1/99), or t/ti = ln (99).
Therefore, the time taken for the thermocouple to read 99% of the initial temperature difference is, ti = t / ln (99) = (0.000012868 m²/s) (0.6 mm)² / (35 W/m °C) ln (99) = 1838.98 s or 30.65 minutes.
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if we are going to put a 36,000 btu/hr water heater and 120,000 furnace btu/hr ( both cat i appliances) in mechanical room that is 10' x 10' x 10' in size, what is the volume of space in the mechanical room?
The volume of the mechanical room is 1000 cubic feet
To calculate the volume of space in a mechanical room, given that a 36,000 btu/hr water heater and 120,000 furnace btu/hr (both cat i appliances) will be installed in a 10' x 10' x 10' room size, use the following formula:
Volume = Room Length x Room Width x Room Height
The volume of space in the mechanical room is given as follows:
Volume = 10' x 10' x 10'
Volume = 1000 cubic feet (cu ft)
Therefore, the volume of space in the mechanical room is 1000 cubic feet (cu ft).
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Complete the following sentence.
A diameter is also a...
Answer:
A diameter is also a double of radius
The net force on a current loop whose face is perpendicular to a uniform magnetic field is zero, since contributions to the net force from opposite sides of the loop cancel. However, if the field varies in magnitude from one side of the loop to the other, then there can be a net force on the loop. Consider a square loop with sides whose length is a , located with one side at x=b in the xy plane (see the figure).(Figure 1) A magnetic field is directed along z , with a magnitude that varies with x according to B= B 0 (1− x /b )
If the current in the loop circulates counterclockwise (that is, the magnetic dipole moment of the loop is along the z axis), find an expression for the x , y , and z projections of the net force on the loop.
Express your answers in terms of the variables I , a , b , and B0
The net force on a current loop when its face is perpendicular to a varying magnetic field will not be zero.
The x, y, and z projections of the net force on the loop can be expressed in terms of the variables I, a, b, and B0.
For the x-component of the force, it can be expressed as:
Fx = I a B0 (2x/b^2)
For the y-component of the force, it can be expressed as:
Fy = 0
For the z-component of the force, it can be expressed as:
Fz = -I a B0 (1-x/b)
Where
I is the current in the loop, a is the length of the sides of the loop, b is the x coordinate of the loop, and B0 is the magnitude of the magnetic field.Learn more about force : brainly.com/question/12785175
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you are designing a spacecraft to a giant planet. which planet is your spacecraft going to study, and what is it going to learn about the planet?
A spacecraft is a vehicle that can travel into space. The spacecraft can be used to study other planets, asteroids, and comets in our solar system. Spacecraft has the ability to collect data, take photographs, and make measurements about the planets and other space objects.
What can you learn about a planet?With a spacecraft, scientists can learn a lot about planets. Some of the things that can be learned include the following:
The chemical composition of the planet's surface and atmosphere.The geology of the planet, such as mountains, valleys, and other features.How the planet rotates, and how long it takes to complete one rotation.The planet's weather patterns and climate, such as temperature and wind speeds.The planet's magnetic field, and how it interacts with the solar wind.The planet's moons and rings, and how they interact with the planet.In conclusion, with a spacecraft, scientists can learn a lot about planets. Information about a planet can vary depending on the planet.
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a tennis ball is dropped from 1.0 m, bounces off the ground, and rises to 0.85 m. what kind of collision occurred between the ball and the ground?
Answer:
Inelastic collision
Explanation:
In the question, it states that when the ball bounced off the ground, it lost 0.15m. This means that it yielded some kinetic energy. Which is an inelastic collision.
When the price of radios decreases 5%, quantity demanded increases 5%. The price elasticity of demand for radios is ________ and total revenue from radio sales will ________.
Price elasticity of demand for radios is 1 and total revenue from radio sales will remain constant.
Price elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in price. Using this formula, we can calculate the price elasticity of demand for radios as follows:
Price elasticity of demand = (percentage change in quantity demanded) / (percentage change in price)
Given that when the price of radios decreases by 5%, quantity demanded increases by 5%.So, the percentage change in quantity demanded = 5% and the percentage change in price = -5%. (Because price has decreased by 5%.)Price elasticity of demand = (5% / -5%) = -1.The negative sign indicates that the demand is elastic. However, the question asks for a positive value, so we take the absolute value of -1.Price elasticity of demand = 1.
Therefore, the price elasticity of demand for radios is 1.When the price elasticity of demand is equal to 1, it means that the demand is unit elastic. This implies that the percentage change in quantity demanded is equal to the percentage change in price. If the price of radios decreases by 5% and the quantity demanded increases by 5%, it means that the total revenue from radio sales will remain constant. In other words, the increase in quantity demanded is exactly offset by the decrease in price, resulting in the same total revenue.
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a 6.96 nc charge is located 1.90 m from a 3.86 nc point charge. find the magnitude of the electrostatic force, in nano newtons, nn, that one charge exerts on the other.
The magnitude of the electrostatic force, in nano newtons, nn, that one charge exerts on the other is 57.54 nN.
The question needs to find out the magnitude of the electrostatic force, in nano newtons (nn), that one charge exerts on the other. Let us understand the given data before starting the solution.
Given data:
Charge 1 (q1) = 6.96 nCCharge 2 (q2) = 3.86 nCDistance between charges (r) = 1.90 mFormula used:
We use Coulomb's law to find the electrostatic force between the two charges.
Coulomb's Law
F = (k*q1*q2)/r²
Where,
F is the force between the charges,q1 and q2 are the two charges separated by a distance r,k is the Coulomb constant which is equal to 9 x 10⁹ Nm²/C²Let us substitute the given values in the above formula.
F = (9 * 10⁹) * (6.96 * 10⁻⁹) * (3.86 * 10⁻⁹) / (1.90)²F = 57.54 nN (nano newtons)Therefore, the magnitude of the electrostatic force, in nano newtons, nn, that one charge exerts on the other is 57.54 nN.
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what device is used to shunt transient current to ground in the event of an indirect lightning strike?
In the event of an indirect lightning strike, a Surge Protection Device (SPD) is used for shunting transient current to the ground. An SPD is a protective device that limits the voltage supplied to an electrical system by either blocking or shorting to ground any unwanted voltages above a safe threshold. This can help protect against damage from transient current, a short, high-energy burst of electricity.
A surge protector is an electrical device that protects electronic devices from power surges and other electrical disturbances. The device will shield the equipment that is plugged into it from the spikes that are present in an electrical supply.The term “surge protector” is frequently used in reference to a category of products that is also known as a “transient voltage suppressor.” This name provides insight into how these devices work. They suppress transient voltage, which is a sudden surge of voltage that is brief in nature
.How do surge protectors work?
Surge protectors work by preventing transient voltage spikes from reaching sensitive electrical equipment. These devices typically consist of a metal oxide varistor, which is a component that is used to divert any unwanted voltage away from sensitive electronics and toward a grounded element.The varistor is connected to a metal oxide varistor, which is responsible for conducting the unwanted voltage away from the equipment and toward the ground. Surge protectors will reduce voltage to a safe level by grounding the unwanted voltage. Surge protectors are used to protecting a wide range of electronic devices, including computers, audio equipment, and video equipment.
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Transient current refers to an electrical current that flows for a brief period. Transient currents are caused by temporary changes in voltage, such as those caused by electrical discharges, power outages, and other events. Surge currents are another name for transient currents, and they are often used interchangeably.
A lightning strike is an electrical discharge from the atmosphere to the earth's surface. Thunderstorms, which are associated with lightning, are the most frequent natural cause of the electrical discharge. A lightning bolt can produce extremely high voltages and currents, posing a significant threat to electrical systems and the people who operate them.
A surge protector is a device that is intended to protect electrical devices from voltage spikes, surges, and other power fluctuations. Surge protectors work by shunting transient currents to the ground in the event of an indirect lightning strike. They can also be used to safeguard against other types of power surges, such as those caused by power outages, grid switching, and other issues. Surge protectors are often utilized in industrial and commercial settings, as well as in homes.
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suppose a clay model of a koala bear has a mass of 0.195 kg and slides on ice at a speed of 0.65 m/s. it runs into another clay model, which is initially motionless and has a mass of 0.36 kg. Both being soft clay, they naturally stick together. What is their final velocity?
The final velocity of the two clay models after they stick together is 0.23 m/s.
To calculate this, we use the conservation of momentum equation:
Final Momentum = Initial Momentum
m₁v₁+ m₂v₂ = (m₁ + m₁) x v
Where m₁ and v₁ are the mass and velocity of the first object, and m₂ and v₂ are the mass and velocity of the second object.
Given question:
m₁ = 0.195kg
v₁ = 0.65m/s
m₂ = 0.36kg
v₂ = 0
Applying the given values:
m₁v₁+ m₂v₂ = (m₁ + m₁) x v
0.195kg x 0.65m/s + 0.36kg x 0 = (0.195kg + 0.36kg) * v
0,126 = 0.555v
v = 0,23 m/s
Thus, their final velocity is 0.23 m/s.
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Complete the following statement: The sum of the magnitudes of the currents directed into a junction Select one: a. is divided equally among the number of lines directed out of the junction. b.equals the current that is directed along one of the lines out of the junction. c. is greater than the total current directed out of the junction. d. equals the sum of the magnitudes of the currents directed out of the junction.
By kirchoff rule ,The sum of the magnitudes of the currents directed into a junction equals the sum of the magnitudes of the currents directed out of the junction. Therefore, the correct option is d, which says that the sum of the magnitudes of the currents directed into a junction equals the sum of the magnitudes of the currents directed out of the junction.
How does a junction work?A junction is a point where two or more lines meet. The current flowing into the junction must be the same as the current flowing out of it. The current will divide into various branches at the junction. The sum of the current entering the junction equals the sum of the current exiting the junction. Therefore, the current through one branch must be subtracted from the current through the other branch when calculating the current through each branch.The law of conservation of charge says that charge is neither created nor destroyed. Thus, the sum of the charges that flow into a junction must equal the sum of the charges that flow out of it, according to Kirchhoff's junction rule.The Kirchhoff's junction rule states that the sum of the currents into a junction must equal the sum of the currents leaving the junction. When two or more resistors are connected in a circuit, they share the current flowing through the circuit in the same direction, and the current is split into two or more branches.
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Light of 630 nm wavelength illuminates two slits that are 0.25 mm apart. FIGURE EX33.5 shows the intensity pattern seen on a screen behind the slits. What is the distance to the screen?
The distance to the screen from the two slits is 4.0 meters
Distance is the total distance traveled by an object over a specific time interval.
The distance can be calculated using the equation d = λ/(2a), where
d is the distance to the screen, λ is the wavelength of the light (630 nm in this case), and a is the separation of the two slits (0.25 mm in this case).Plugging these values in, we get: d = 630 nm / (2 * 0.25 mm) = 4.0 m. The distance to the screen from the two slits is 4.0 meters, as seen in Figure EX33.5.
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imagine swinging a ball in a circle at the end of a string. if the string that holds the ball breaks, what causes the ball to move in a straight line path?
When a ball is swung in a circle at the end of a string, it is constantly changing direction due to the force acting on it. This force is called the centripetal force, which is provided by the tension in the string.
When the string holding the ball breaks, there is no longer any force acting on the ball to keep it moving in a circular path. As a result, the ball moves in a straight line path in accordance with Newton's first law of motion, which states that an object at rest will remain at rest or an object in motion will continue to move in a straight line path at a constant speed unless acted upon by an external force.
In this case, the external force was the tension in the string, which was providing the centripetal force to keep the ball moving in a circular path. Once the string broke, the ball no longer experienced any centripetal force, and thus continued to move in a straight line path.
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You know your mass is 70 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 76 kg. What is the magnitude of the acceleration of the elevator? Express your answer using two significant figures.
The magnitude of the acceleration of the elevator is approximately 0.84 m/s².
When you stand on a bathroom scale in an elevator, it says your mass is 76 kg. Your actual mass is 70 kg.
Thus, the apparent weight of an object on the scale is the product of the object's mass and the net force acting on it. The scale reads a greater mass because of the upward force the elevator floor exerts on you.
The magnitude of the acceleration of the elevator is provided by the following formula:
The magnitude of the acceleration of the elevator = F_net/m,
where F_net is the net force on the object and m is the object's mass.
Since your actual mass is 70 kg and the scale measures an apparent mass of 76 kg, the net force acting on you is the difference between the apparent weight and the actual weight, which is given by
F_net = (76 kg - 70 kg) by × 9.8 m/s²
= 58.8 N
Thus, the magnitude of the acceleration of the elevator is: the magnitude of the acceleration of the elevator
= F_net/m = 58.8 N/70 kg
≈ 0.84 m/s²
Therefore, the magnitude of the acceleration of the elevator is approximately 0.84 m/s².
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an early submersible craft for deep-sea exploration was raised and lowered by a cable from a ship. when the craft was stationary, the tension in the cable was 5500 n . when the craft was lowered or raised at a steady rate, the motion through the water added an 1800 n drag force.
Part A
What was the tension in the cable when the craft was being lowered to the seafloor?
Express your answer to two significant figures and include the appropriate units.
Part B
What was the tension in the cable when the craft was being raised from the seafloor?
Express your answer to two significant figures and include the appropriate units.
Part A: When the craft is being lowered, the tension in the cable is 6387 N
Part B: When the craft is being raised, the tension in the cable is 5227 N
The weight of the craft will be equal to the force of gravity acting on it, which can be calculated using the mass of the craft and the acceleration due to gravity (g = 9.81 m/s²).
Therefore, the tension in the cable when the craft is being lowered is:
Tension = weight + drag force
Tension = (mass x g) + drag force
Tension = (unknown mass x 9.81 m/s²) + 1800 N
Tension = (unknown mass x 9.81) + 1800 N
Part A When the craft is stationary, the tension in the cable is 5500 N. This means that the weight of the craft is equal to the tension in the cable when it's not moving,
Solving for the mass:
5500 N = (mass x 9.81) + 0 N
mass = 5500 N / 9.81 m/s²
mass = 560.3 kg
Now we can substitute the mass into the expression for tension when the craft is being lowered:
Tension = (mass x 9.81) + 1800 N
Tension = (560.3 kg x 9.81 m/s²) + 1800 N
Tension = 6387 N
Therefore, the tension in the cable when the craft is being lowered to the seafloor is 6387 N.
Part B: When the craft is being raised at a steady rate, the tension in the cable will be equal to the weight of the craft minus the drag force due to the motion through the water.
Using the same mass of the craft that we calculated in Part A, we can calculate the tension in the cable when the craft is being raised:
Tension = weight - drag force
Tension = (mass x g) - drag force
Tension = (560.3 kg x 9.81 m/s²) - 1800 N
Tension = 5227 N
Therefore, the tension in the cable when the craft is being raised from the seafloor is 5227 N.
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the sun is shining on james and has created a shadow that is 8 feet long what is the distance from his head to his shadow
The distance from James's head to his 8-foot long shadow is 8 feet.
To find this, we can use the simple triangle relationship: opposite side (the shadow) is equal to the hypotenuse (the distance between James's head and his shadow) times the cosine of the angle formed by the sun's rays.
The distance from James's head to his shadow can be calculated using trigonometry. The tangent function can be used for this purpose.
To calculate the distance from James's head to his shadow, follow these steps:
Firstly, draw a right triangle with one of its angles adjacent to James's head and the other adjacent to the base of the shadow. The hypotenuse of the triangle is the line between James's head and the tip of the shadow.
Let x be the distance from James's head to the base of the shadow. The hypotenuse is the square root of (x^2 + 8^2).
Use the tangent function to find the value of x. tan(angle) = opposite/adjacent. In this case, the angle is the angle of elevation of the sun, which can be determined from the time of day and the location.
If the angle is not known, it can be assumed to be 45 degrees. tan(45) = opposite/adjacent.
The opposite side is 8, so: x = 8/tan(45) = 8/1 = 8 feet.
Therefore, the distance from James's head to his shadow is 8 feet.
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Part A A canoe is designed to have very little drag when it moves along its length. Riley, mass 62 kg, sits in a 21 kg canoe in the middle of a lake. She dives into the water off the front of the canoe, along the axis of the canoe. She dives forward at 1.7 m/s relative to the boat. Just after her leap, how fast is she moving relative to the water? Express your answer with the appropriate units Value Units Submit Request Answer ▼ Part B Just after her leap, how fast is the canoe moving relative to the water? Express your answer with the appropriate units. (c)EValue Units
The speed of Riley relative to the water is 1.7 m/s. and the speed of canoe relative to the water is 0 m/s.
How fast is Riley moving relative to the water?The equation needed to solve the problem is the following:
Final Velocity = Initial Velocity + (Acceleration × Time)
The steps to solve for speed of Riley are the following:
Mass of Riley = 62 kg
Mass of canoe = 21 kg
Speed of leap relative to the boat = 1.7 m/s
By using the equation for conservation of momentum (also known as the center of mass formula):
m₁v₁ + m₂v₂ = (m₁ + m₂)vf
Solve for the unknown variable: vf = (m₁v₁ + m₂v₂) / (m₁ + m₂)
Plugging in the values given, you get: vf = (62 kg × 1.7 m/s) / (62 kg + 21 kg) = 1.2 m/s
Therefore, Riley is moving at 1.2 m/s relative to the water.
Velocity of the canoe relative to the water can be determined by using the equation for conservation of momentum (also known as the center of mass formula):
m₁v₁ + m₂v₂ = (m₁ + m₂)vf
v₂ = [(m₁ + m₂)vf - m₁v₂] / m₂
Plugging in the values given, you get: v₂ = [(62 kg + 21 kg) × 1.2 m/s - 62 kg × 1.7 m/s] / 21 kg = 0 m/s
Therefore, the canoe is not moving relative to the water.
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A ball of mass, m is thrown straight up and rises h after leaving your hand, it momentarily stops. Acceleration due to gravity g is downward. Ignore air resistance. Part A (5 points): If the ball is the system, and the Earth is the surroundings, what is the change in potential energy, ΔUsys of the system, and what is the work done, Wsurr by the surroundings ? Δ Usys = 0; Wsurr = -mgh Δ Usys = mgh; Wsurr = -mgh Δ Usys = mgh; Wsurr = 0 Δ Usys = 0; Wsurr = 0 Δ Usys = -mgh; Wsurr = 0
the correct answer is option (C). If the ball is the system, and the Earth is the surroundings, the change in potential energy, ΔUsys of the system is mgh, and the work done, Wsurr by the surroundings is 0. Therefore.
In this case, the ball is hurled straight up, reaching a height of h before briefly coming to a stop. We assume the ball to be the system and the Earth to be the surroundings in order to calculate the change in potential energy of the system and the work performed by the surroundings. The system's change in potential energy is mgh because the ball's gravitational potential energy grows as it ascends to a height of h. Yet, because the environment is not subjected to any labour from the ball during its rise and descent, there is no work done by the environment.
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What is the difference between point to point encryption and end-to-end encryption?
Point-to-point encryption and end-to-end encryption are two distinct cryptographic approaches. Both these methods offer data security but in different ways.
The difference between point to point encryption and end-to-end encryption is as follows:
Point-to-point encryption
Point-to-point encryption (P2PE) protects payment card data from the time it is swiped to the point it is encrypted. It encrypts card data before it enters a merchant's system, keeping it secured until it is sent to the payment processor. The data is then decrypted and transmitted through the processing network to the card issuer for approval. P2PE prevents any attempts to intercept the card data while it's in motion from the terminal to the payment processor.
End-to-end encryption
End-to-end encryption (E2EE) involves encrypting data from the point of origin to its final destination. End-to-end encryption secures the entire data transmission process from client to server. It encrypts the data at the source, such that the data is protected throughout its journey. Therefore, end-to-end encryption is mainly used in messaging and communication apps like WA, etc.
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The prelab required you to use the impedance method to calculate the steady-state amplitude and phase (in degrees) of vc to an input vs = cos(2phi ft) where f-1000 Hz (ω = 2phif). The results from the prelab are . Ao=_____Phase, φ =_____degrees
The steady-state amplitude Ao = 50.03 degrees and phase, φ = -88.7 degrees by using the impedance method.
The given equation for vs is:
vs = cos(2phi ft) ...[1]
where, f = 1000 Hz,
therefore ω = 2φf
ω= 2000π radians/s
Let's find the impedance of the circuit elements.
The impedance of the resistor is R.
The impedance of the capacitor is:
Zc = 1/(jωC)
The impedance of the inductor is:
ZL = jωL
As the capacitor and resistor are connected in series, their total impedance is:
ZC+R = R + 1/(jωC) ...[2]
Now, as the inductor is connected in parallel with the combination of R and C, the total impedance of the circuit is:
Ztotal = (ZC+R) || ZL...[3]
Ztotal = (R + 1/(jωC)) || jωL
Ztotal = 1/[(1/R) + j(1/ωC - ωL)]...[4]
Comparing the real and imaginary parts of the equation [4],
we get, 1/R = √{(1/ωC - ωL)^2} ...[5]and
1/ωC - ωL = 0
or
ωL = 1/ωC ...[6]
From equation [5],
we get, R = 1/√{(1/ωC - ωL)^2} ...[7]
The magnitude of the input voltage Vs is 1 volt.
The amplitude of the steady-state output voltage, Vc is given by:
Voc = Ao x 1VoltA0
Voc = R/ZtotalA0
Voc = R/1/[(1/R) + j(1/ωC - ωL)]A0
Voc = R(1/R) + jR(1/ωC - ωL)A0
Voc = 1 + jR(1/ωC - ωL) ...[8]
From equation [6],
we get: L = 1/(ωC)
L = 1/(2π x 1000)
L = 1.59 x 10-7 H
Substituting L in equation [6],
we get: ωL = ωC
ωL = 1/2π x 1000 x 1.59 x 10-7
ωL = 0.1Ω
From equation [7], we get: R = 1000 Ω
Substituting the value of R and ωL in equation [8],
we get: A0 = 1 + j1000(1/2π x 1000 x 1.59 x 10-7 - 0.1)
A0 = √{(1^2) + (-50.03)^2}
A0 = 50.03 degrees
Let φ be the phase of the output voltage with respect to the input voltage.
Therefore, we have: tanφ = -50.03φ = -88.7 degrees
Therefore, Ao = 50.03 degrees and φ = -88.7 degrees.
Answer: Ao = 50.03 degrees, φ = -88.7 degrees.
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(Figure 1) shows a collision between three balls of clay. The three hit simultaneously and stick together. Assume that m = 60 g and v = 2.9 m/s. ⬤↘ m 40 m/s, and 45°
←⬤ v 30 g
↑
⬤ 20 g and 2.0 m/s
Part A What is the speed of the resulting blob of clay? Express your answer with the appropriate units. V = ? Part B What is the movement direction of the resulting blob of clay? Express your answer in degrees below the horizontal. θ = ?
The speed of the resulting blob of clay is 20.99 m/s and the direction is 45.82⁰ below the horizontal.
Given :
Masses of balls of clay:
m₁ = 60g,
m₂ =20g,
m₃ = 30g.
Speed of balls of clay :
v₁ = 40m/s,
v₂= 2m/s,
v₃ = 2.9m/s
we can write the speed in vector form as :
υ₁ = 40( x + y)/ √2 m/s,
υ₂ = 2 y m/s,
υ₃ = 2.9 (-y) m/s, where x and y are unit vectors in perpendicular directions.
During a collision, the momentum remains conserved. Hence using the conservation of total momentum we can calculate the final speed of the resulting bob clay.
Using conservation of momentum,
initial momentum = final momentum
m₁υ₁ + m₂υ₂ + m₃υ₃ = (m₁+m₂+m₂)υ,
where υ = final velocity of clay blob.
Putting all the values in the above equation,
60 × 40( x + y)/ √2 + 20×2 y+30 ×2.9 (-y) = (60+20+30) υ
on solving the above equation, we get
υ = 14.63 x + 15.06 y
The magnitude of the final speed will be equal to √(14.63²+ 15.06²)
Final speed= 20.99 m/s.
and
Angle = tan⁻(15.06/14.63)
Angle = 45.82⁰ below the horizontal.
Therefore, the speed of the resulting blob of clay is 20.99 m/s and the direction is 45.82⁰ below the horizontal.
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If the change in internal energy = 1714J, specific
heat capacity = 49J/°C/kg, and mass = 38kg,
what is the temperature change experienced?
Give your answer to 2 decimal places.
Answer:
0.92°C
Explanation:
C = change in Q/m × change in T
so
change in T = change in Q/C ×m
C= 49
m= 38
change in Q= 1714
then
= 1714/49 × 38
= 1714/1862
= 0.92°C
rounded off to 2 d.p
i measure an emission line in the lab at 500.7 nm. the same line in a star (now being absorbed) has wavelength 502.8 nm. what can i say about this star? group of answer choices it has a large parallax it has unusually strong spectral lines it is moving away from me it is moving towards me
The star is moving away from you. This is indicated by the fact that the observed wavelength (502.8 nm) is longer than the laboratory wavelength (500.7 nm), which is consistent with the Doppler effect caused by the star moving away from the observer.
What is Doppler effect?
The Doppler effect, named after Austrian physicist Christian Doppler, is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is commonly observed with sound waves, but can also occur with light waves and other types of waves. When the observer is moving towards the source of the wave, the frequency and wavelength appear to increase, resulting in a higher pitch. When the observer is moving away from the source of the wave, the frequency and wavelength appear to decrease, resulting in a lower pitch or longer wavelength.
What is wavelength?
Wavelength is the distance between two consecutive points in a wave that are in phase, or at the same point in their cycle. It is usually represented by the symbol lambda (λ) and is measured in units of distance, such as meters or nanometers.
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shown below is a small particle of mass 25.0 g that is moving at a speed of 9.3 m/s when it collides and sticks to the edge of a uniform solid cylinder. the cylinder is free to rotate about its axis through its center and is perpendicular to the page. the cylinder has a mass of 0.460 kg and a radius of 9.3 cm, and is initially at rest. what is the angular velocity of the system after the collision?
A small particle of mass 25.0 g that is moving at a speed of 9.3 m/s when it collides and sticks to the edge of a uniform solid cylinder. The cylinder is free to rotate about its axis through its center and is perpendicular to the page. the cylinder has a mass of 0.460 kg and a radius of 9.3 cm, and is initially at rest. The angular velocity of the system after the collision is 55.7 rad/s.
The angular velocity of the system after the collision is determined by the conservation of angular momentum. This law states that the total angular momentum of an isolated system remains constant; if a system has an initial angular momentum of 0, any change in angular momentum must be balanced by a corresponding change in the rotational speed of the system.
In this case, the initial angular momentum of the system is 0 since the cylinder is initially at rest. After the collision, the mass of the small particle can be considered to be moving in a circular path with a radius of 9.3 cm. This means the final angular momentum of the system is equal to the linear momentum of the particle times the radius of the cylinder: 25.0 g x 9.3 cm x 9.3 m/s = 21.0 kg m2/s.
The final angular velocity of the system is then equal to the total angular momentum divided by the total moment of inertia of the system: 21.0 kg m2/s / (0.460 kg x (9.3 cm)2) = 55.7 rad/s.
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what happens to the domains of an object when it becomes magnetized?
When an object becomes magnetized, the domains within the object align themselves in a particular direction. A domain is a small region within a magnetic material that behaves like a tiny magnet, with its own north and south poles.
In an unmagnetized object, these domains are randomly oriented, so their magnetic fields cancel each other out and the material as a whole has no net magnetic field. When an external magnetic field is applied to the material, the magnetic domains become aligned with the external field, resulting in a net magnetic field for the material. If the external field is strong enough, it can overcome the random orientation of the domains and cause them to align in the direction of the external field. Once the domains are aligned, the object will retain its magnetism even after the external magnetic field is removed. This is because the domains will remain in their aligned state until another external magnetic field is applied to the object and causes them to realign.
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a boy coasts down a hill on a sled, reaching a level surface at the bottom with a speed of 7.2 m/s. if the coefficient of friction between the sled's runners and snow is 0.055 and the boy and sled together weigh 540 n, how far does the sled travel on the level surface before coming to rest?
The boy coasts down the hill on the sled and reaches a level surface with a speed of 7.2 m/s. The coefficient of friction between the sled's runners and the snow is 0.055, and the boy and sled together weigh 540 N. To determine how far the sled will travel on the level surface before coming to rest, we need to calculate the distance using the formula Distance = (Speed x Time) - (1/2 x Acceleration x Time2). We can determine the time it takes for the sled to come to rest using the equation Speed = (Friction x Normal Force) / Mass. So, Speed = (0.055 x 540N) / 540N = 0.055 m/s. Time = 7.2/0.055 = 130.9 seconds. We can then calculate the distance as Distance = (7.2 x 130.9) - (1/2 x 0.055 x 130.92) = 927.9 m. Therefore, the sled will travel 927.9 m before coming to rest.
The boy and sled weigh 540 N. A boy coasts down a hill on a sled, reaching a level surface at the bottom with a speed of 7.2 m/s. The coefficient of friction between the sled's runners and snow is 0.055. How far does the sled travel on the level surface before coming to rest?
The distance traveled by the sled on the level surface before coming to rest is 72.22 meters.
What is friction?
Friction is a force that opposes motion. It is the friction between the sled's runners and the snow that causes the sled to stop. The formula for frictional force is:f = μN where f is the frictional force, μ is the coefficient of friction, and N is the normal force, which is equal to the weight of the sled and boy since they are on a level surface. The normal force is given by: N = m*g where m is the mass of the sled and boy and g is the acceleration due to gravity, which is equal to 9.81 m/s^2.
How far does the sled travel on the level surface before coming to rest?
The sled will travel a certain distance, d, before it stops. The distance, d, is given by:d = (v^2 - u^2) / 2fwhere v is the final velocity, u is the initial velocity (which is 7.2 m/s), and f is the frictional force. The frictional force is f = μN = μmgSubstituting the given values:d = (7.2∧2 - 0∧2) / (2*0.055*540*9.81)d = 72.22 meters. Therefore, the sled will travel 72.22 meters on the level surface before coming to rest.
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Studying a spectrum from a star can tell us a lot. All of the following statements are true except one. Which statement is not true?The total amount of light in the spectrum tells us the star's radius.We can identify chemical elements present in the star by recognizing patterns of spectral lines that correspond to particular chemicals.Shifts in the wavelengths of spectral lines compared to the wavelengths of those same lines measured in a laboratory on Earth can tell us the star's speed toward or away from us.The peak of the star's thermal emission tells us its temperature: hotter stars peak at shorter (bluer) wavelength
All of the following statements are true about studying spectrum from a star except the statement that "The total amount of light in the spectrum tells us the star's radius."
It is possible to identify chemical elements present in the star by recognizing patterns of spectral lines that correspond to particular chemicals. In other words, we can determine which elements are present in a star by analyzing the spectrum of the light it emits. This is because every chemical element has a unique spectrum of energy that it emits.
The wavelength shifts of spectral lines compared to the wavelengths of those same lines measured in a laboratory on Earth can tell us the star's speed toward or away from us. This is known as the Doppler effect, and it enables astronomers to calculate how fast a star is moving relative to Earth. For example, if the spectral lines are shifted towards the blue end of the spectrum, it means that the star is moving towards us.
On the other hand, if the spectral lines are shifted towards the red end of the spectrum, it means that the star is moving away from us.The peak of the star's thermal emission tells us its temperature: hotter stars peak at shorter (bluer) wavelengths. This is because the hotter an object is, the more energy it radiates, and the shorter the wavelength of that radiation. Therefore, the peak of the thermal emission spectrum provides an indication of the star's temperature.
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Using the heat of vaporization of benzene, 395 J/g, calculate the grams of benzene that will condense at its boiling point if 8.44 kJ is removed.
Considering the heat of vaporization of benzene, the mass that will evaporate, at the boiling point, if 8.44 kJ/g of heat is extracted is 21.36 g.
Given the heat of vaporization of benzene, 395 J/g and the heat removed, 8.44 kJ, we can determine the mass of benzene that condenses by converting the heat removed to J/g as follows:
Qv = 8.44 kJ/g · 1000 J / 1 kJ = 8440 J/g
Hence, mass of benzene that condenses can be found by dividing the heat removed by the heat of vaporization as shown:
mass = heat removed / heat of vaporization
m = 8440 J/g / 395 J/g
m = 21.36 g
Therefore, 21.39 g of benzene will condense at its boiling point if 8.44 kJ is removed.
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Can we use our brainly points.
What did the triangle say to the circle?
Your pointless
Answer:
i actually giggled at that oml.
Explanation:
that was good
the diagram below shows four cannons firing shells with different masses at different angles of elevation. the horizontal component of the shell's velocity is the same in all four cases. in which case will the shell have the greatest range if air resistance is neglected? (a) cannon a (b) cannon b only (c) cannon c only (d) cannon d
The diagram below shows four cannons firing shells with different masses at different angles of elevation. the horizontal component of the shell's velocity is the same in all four cases. The case will the shell have the greatest range if air resistance is neglected is (a) cannon a
The cannon which would have the maximum range if air resistance is neglected is given by the expression R = (V²/g)sin(2θ). The horizontal component of velocity is the same for all four shells, Vx = Vcosθ. Where R is the range, V is the velocity, g is the gravitational acceleration, θ is the angle of projection, and Vx is the horizontal component of the velocity. The diagram below shows four cannons firing shells with different masses at different angles of elevation.
For the maximum range, we need to take the angle of projection to be 45°. The mass of the shell is not a consideration since it doesn't affect the time of flight or the range of the shell.Therefore, the maximum range is given by the highest value of V²sin(2θ)/g. As sin(90) = 1, sin(0) = 0, sin(30) = 1/2, sin(45) = √2/2, sin(60) = √3/2, sin(70) = 0.94, the maximum value of sin(2θ) is obtained when θ = 45°.For all four cannons, the horizontal component of velocity, Vx = Vcosθ, is the same. Therefore, the maximum range is obtained for Cannon A when air resistance is neglected. Therefore, the correct answer is (a) Cannon A.
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