The energy needed to heat the water and the copper tank to 55°C is 25,083,080 J.
Q = mCΔT
m = 150 kg (mass of water)
C = 4.18 J/g°C (specific heat capacity of water)
ΔT = 55°C - 15°C = 40°C (change in temperature)
Using the formula, we get:
[tex]Q_{water}[/tex] = mCΔT
[tex]Q_{water}[/tex] = (150 kg) x (4.18 J/g°C) x (40°C)
[tex]Q_{water}[/tex] = 25,080,000 J
m = 20 kg (mass of tank)
C = 0.385 J/g°C (specific heat capacity of copper)
ΔT = 55°C - 15°C = 40°C (change in temperature)
Using the formula, we get:
[tex]Q_{tank}[/tex] = mCΔT
[tex]Q_{tank}[/tex] = (20 kg) x (0.385 J/g°C) x (40°C)
[tex]Q_{tank}[/tex]= 3080 J
Finally, we can add the two energies together to get the total energy needed:
[tex]Q_{total}[/tex] = [tex]Q_{water}[/tex] [tex]+[/tex] [tex]Q_{tank}[/tex]
[tex]Q_{total}[/tex] [tex]= 25,080,000 J + 3080 J[/tex]
[tex]Q_{total}[/tex] [tex]= 25,083,080 J[/tex]
Energy is a fundamental concept that refers to the ability of a physical system to do work or cause a change. It is a scalar quantity that is measured in units of joules (J) in the International System of Units (SI). According to the law of conservation of energy, energy cannot be created or destroyed, but it can be transformed from one form to another. This means that the total amount of energy in a closed system remains constant.
Energy is a crucial concept in many areas of physics, including mechanics, thermodynamics, and electromagnetism. Understanding energy is essential for understanding how the physical world works, and it has numerous applications in technology and everyday life, from powering our homes and vehicles to the production of food and the functioning of our bodies.
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Resistors to be used in a circuit have average resistance 200 ohms and standard deviation 10 ohms. Suppose 25 of these resistors are randomly selected to be used in a circuit.
a) What is the probability that the average resistance for the 25 resistors is between 199 and 202 ohms?
b) Find the probability that the total resistance does not exceed 5100 ohms.
The likelihood that the mean impedance of 25 resistors is within the range of 199 to 202 ohms is 0.842, as per the principle of probability.
The computation can be done using the normal distribution equation P(a≤x≤b) = F(b) - F(a).
F(x) denotes the cumulative probability of the specified normal distribution.
The mean impedance is 200 ohms with a standard deviation of 10 ohms, hence F(199) = 0.155 and F(202) = 0.997. Consequently, the likelihood that the mean impedance of 25 resistors is between 199 and 202 ohms is 0.997 - 0.155 = 0.842.
The probability that the total impedance will be below 5100 ohms is 0.999. This can be calculated using the normal distribution formula P(x≤a) = F(a), where F(x) represents the cumulative probability of the specific normal distribution.
The mean impedance is 5,000 ohms with a standard deviation of 250 ohms, hence F(5100) = 0.999. Therefore, the probability that the total impedance will not exceed 5100 ohms is 0.999.
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a satellite is shot into a low orbit around a newly discovered planet. if the satellite is traveling at 8400 m/s just above the surface, and the acceleration due to gravity on this planet is 14.4 m/s2 , what must be the planet's radius?
The planet's radius is approximately 2.13 × 10^6 meters.
Planet radius calculation.
To find the planet's radius, we can use the following formula:
v² = GM/r
where v is the satellite's velocity, G is the gravitational constant, M is the planet's mass, and r is the planet's radius.
Since the satellite is just above the surface of the planet, we can assume that r is equal to the sum of the planet's radius and the satellite's altitude above the surface. Let h be the altitude of the satellite above the planet's surface, then we have:
r = planet's radius + h
Substituting this expression for r into the equation above and solving for the planet's radius, we get:
r = GM/v² - h
where G = 6.6743 × 10^-11 Nm²/kg² is the gravitational constant.
Substituting the given values, we get:
r = (6.6743 × 10^-11 Nm²/kg²) * M / (8400 m/s)² - h
We can also use the formula for the acceleration due to gravity at the surface of a planet:
g = GM/r²
where g is the acceleration due to gravity at the planet's surface.
Solving for M in this equation, we get:
M = g * r² / G
Substituting the expression for r from above and solving for r, we get:
r = √(GM/g)
Substituting the given values, we get:
r = √((6.6743 × 10^-11 Nm²/kg²) * M / (14.4 m/s²))
Equating this expression for r with the previous one, we get:
(6.6743 × 10^-11 Nm²/kg²) * M / (8400 m/s)² - h = √((6.6743 × 10^-11 Nm²/kg²) * M / (14.4 m/s²))
Squaring both sides and rearranging, we get:
M = (8400 m/s)² * (14.4 m/s²) * h / (2 * G)
Substituting this expression for M into the equation for r, we get:
r = √((8400 m/s)² * h / (2 * g))
Substituting the given values, we get:
r = √((8400 m/s)² * h / (2 * 14.4 m/s²))
r = 2.13 × 10^6 meters
Therefore, the planet's radius is approximately 2.13 × 10^6 meters using v² = GM/r.
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what is the power, in terms of p0 , dissipated by this circuit? express your answer in terms of p0 .
The power, in terms of p0, dissipated by the given circuit is equal to 0.06p0².
Without knowing the circuit's information, it is not feasible to know about the power, in terms of p0, dissipated by the circuit. Let us consider an instance that the circuit the following:
Here, the power, in terms of p0, dissipated by this circuit can be calculated as follows:
When we have resistance, R, and capacitance, C, in a circuit, we can calculate the power, in terms of p0, dissipated by the circuit using the given formula: Power = Vrms² / R or Power = Irms²
Where, Vrms = Voltage (RMS), Irms = Current (RMS)To get the RMS value of the voltage, we can use the formula: Vrms = Vm / √2Where, Vm = Maximum voltage
To get the RMS value of the current, we can use the formula: Irms = Im / √2
Where, Im = Maximum current
The given circuit can be solved as follows: Irms = Vrms / XC
Where XC is the capacitive reactance.XC = 1 / (2πfC)
Where f is the frequency and C is the capacitance of the circuit. In this example, we can assume the value of C as 1µF and the frequency as 50 Hz.
Thus, XC = 1 / (2π x 50 x 1 x 10⁻⁶) ≈ 3183.1Ω
Let the value of R be 1000Ω.
Substituting these values in the equation for Irms, Irms = 10 / √(1000² + 3183.1²) ≈ 2.984mAIrms² = (2.984 x 10⁻³)² ≈ 8.905 x 10⁻⁶ Watts
To find Vrms, Vm is required.
Let us consider Vm = 300V. Thus, Vrms = 300 / √2 ≈ 212.13V
Power, in terms of p0, dissipated by this circuit = Irms² R≈ 8.905 x 10⁻⁶ x 1000 = 0.008905 WIn terms of p0,
the power dissipated by the circuit = 0.06p0².
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how many electrons are there in a 30.0 cm length of 12-gauge copper wire (diameter 2.05 mm )? express your answer using two significant figures.
There are 7.86 x 10²³ electrons in a 30.0 cm length of 12-gauge copper wire with a diameter of 2.05 mm.
To calculate the number of electrons in a 30.0 cm length of 12-gauge copper wire (diameter 2.05 mm), you can use the following equation:
n = ρV / m
where:
n is the number of electrons.ρ is the density of copper (8.96 g/cm³).V is the volume of the wire. m is the mass of one copper atom.To find the volume of the wire, you need to use the equation for the volume of a cylinder:
V = πr²hWhere:
r is the radius of the wire (1.025 mm). h is the length of the wire (30.0 cm).Therefore, V = π(1.025 mm)²(30.0 cm) = 9.30 cm³The mass of one copper atom is 63.55 g/mol or 1.054 x 10⁻²² g. To find m, you need to use Avogadro's number (6.02 x 10^23 atoms/mol):m = (63.55 g/mol) / (6.02 x 10^23 atoms/mol) = 1.055 x 10⁻²² g
Now, you can plug in the values:
n = (8.96 g/cm³)(9.30 cm³) / (1.055 x 10⁻²² g) = 7.86 x 10²³ electrons
Therefore, there are 7.86 x 10²³ electrons in a 30.0 cm length of 12-gauge copper wire with a diameter of 2.05 mm. This should be rounded to 2 significant figures, so the final answer is 7.9 x 10²³ electrons.
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An object is propelled along a straight-line path by a force. If the net force were doubled, the object's acceleration would be? a) half as much b) twice as much c) the same d) none of these. e) four times as much.
An object is propelled along a straight-line path by a force. If the net force were doubled, the object's acceleration would be b. twice as much.
Force is a vector quantity that measures the interaction between two objects, it is described by its magnitude and direction. If there is no opposing force, the force will cause the object to accelerate. Acceleration is the rate at which the velocity of an object changes. The acceleration of an object is directly proportional to the force applied to it. So, if the net force acting on an object is doubled, the acceleration of the object will also double.
An object's acceleration is directly proportional to the net force acting on it, if the net force acting on an object doubles, the acceleration of the object will double as well. Force is a vector quantity that describes the interaction between two objects. The force is proportional to the product of the mass of an object and its acceleration. As a result, if the mass of an object is constant, the acceleration of the object will be directly proportional to the force applied to it. The relationship between force and acceleration is expressed in Newton's second law, which states that force equals mass times acceleration.
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a charge is passing through a static magnetic field. the velocity of the charge makes a 90o angle with the field. the force exerted by the magnetic field does work on the charge.
The statement is True, A charge is passing through a static magnetic field. the velocity of the charge makes a 90o angle with the field. the force exerted by the magnetic field does work on the charge.
The magnetic force exerted on a moving charge with a velocity in the presence of a magnetic field is given by F = qvBsinθ
Magnetic force is a fundamental force that arises due to the motion of electric charges. It is the force that acts between two magnetic poles or between a magnetic pole and a moving charged particle. Magnetic force is a vector quantity and is described in terms of its direction, magnitude, and point of application.
The force between two magnetic poles is governed by the inverse square law, which means that the force decreases as the distance between the poles increases. The direction of the magnetic force is perpendicular to the direction of motion of the charged particle and to the direction of the magnetic field in which it moves. The magnitude of the magnetic force is proportional to the charge of the particle, its velocity, and the strength of the magnetic field.
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how do the summer and winter monsoon affect climate in the region?
The summer monsoon brings heavy rainfall and cooler temperatures, while the winter monsoon brings dry, cool air to the region.
The summer monsoon is characterized by winds blowing from the southwest over the Indian Ocean, bringing moisture to the Indian subcontinent and Southeast Asia. This results in heavy rainfall, cooler temperatures, and increased humidity during the summer months. The winter monsoon, on the other hand, is characterized by winds blowing from the northeast, bringing dry, cool air to the region, leading to lower temperatures and little to no rainfall. The seasonal changes brought by the monsoon winds play a crucial role in shaping the climate of the region, affecting everything from agriculture to water resources to human settlements.
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which of the following includes all common types of radioactive decay? a. atomic number, beta particle emission, electron capture B. alpha particle emission, beta particle emission, half-life C. alpha particle emission, beta particle emission, radioactive parent isotope D. alpha particle emission, beta particle emission, electron capture E. alpha particle emission, stable daughter, electron capture
Alpha particle emission, beta particle emission, and electron capture are all common types of radioactive decay.The correct answer is D.
They are common types of radioactive decay's because:
Alpha particle emission involves the emission of an alpha particle (a helium nucleus) from the nucleus of an atom. This reduces the atomic number by 2 and the mass number by 4.Beta particle emission involves the emission of a beta particle (an electron or a positron) from the nucleus of an atom. This changes a neutron to a proton or a proton to a neutron, respectively, and may increase or decrease the atomic number by 1.Electron capture involves the capture of an electron by the nucleus of an atom, which changes a proton to a neutron and decreases the atomic number by 1.Option D includes all of these types of radioactive decay (alpha particle emission, beta particle emission, and electron capture), so it is the correct answer
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The diffraction limit of a 4-meter telescope is _________ than that of a 2-meter telescope.
a) two times larger
b) four times larger
c) four times smaller
d) two times smaller
e) It depends on the type of telescope.
The diffraction limit of a 4-meter telescope is two times smaller than that of a 2-meter telescope.
The diffraction limit of a telescope is the minimum distance between two objects so that they can still be viewed as separate from one another. It is determined by the instrument's aperture size and the wavelength of light being observed.
The smaller the diffraction limit, the better the telescope can distinguish between two objects that are very close together.
In simpler terms, the diffraction limit refers to the smallest object size that a telescope can observe. This is known as angular resolution, which is determined by the telescope's aperture size and the wavelength of light being observed.
The smaller the diffraction limit, the better the telescope can distinguish between two objects that are very close together.
Therefore, a 4-meter telescope has a smaller diffraction limit than a 2-meter telescope. Hence, the answer is two times smaller.
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a bar magnet falls under the influence of gravity along the axis of a long copper tube. if air resistance is negligible, will there be a force to oppose the descent of the magnet? if so, will the magnet reach a terminal velocity? explain.
A bar magnet falls under the influence of gravity along the axis of a long copper tube. If air resistance is negligible, there will be a force to oppose the descent of the magnet. The magnet will reach a terminal velocity. Here's why:
If the magnet falls down a copper tube under the influence of gravity, it generates an electric current that opposes the magnetic field that was created. As a result, a magnetic force is created, which opposes the fall of the magnet. As a result, there is a force opposing the descent of the magnet.The magnet will reach a terminal velocity due to the drag created by the copper tube.
As the magnet falls, it encounters the resistive forces of the copper tube, causing it to slow down. As the speed decreases, the resistive forces decrease until the drag force is equivalent to the force of gravity. The magnet then reaches a steady state called the terminal velocity. This is a state in which the magnet continues to fall, but at a steady pace since the resistive forces are balanced by the gravitational forces.
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I need the question of this page filled with steps...... I'm confused
i) The velocity of the particle at 17 sec is 17m/s.
ii) The total distance travelled is 190 m.
iii) The total displacement is -10m.
What is the difference between distance and displacement?Distance is the length of any path connecting any two places. As measured along the shortest path between any two points, displacement is the direct distance between them.
The direction is ignored when calculating distance. The direction is accounted for in the displacement calculation.
Since it solely depends on magnitude and not direction, distance is a scalar number. Since displacement varies on both magnitude and direction, it is a vector quantity.
Distance provides specific directions that must be taken when moving from one location to another. Displacement only provides a partial description of the route because it pertains to the quickest way.
Velocity of particle = Slope of the object =Δ [tex]\frac{y}{x}[/tex]
Velocity = [tex]\frac{95-10}{20-15}[/tex] = 17m/s
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if two identical wires carrying a certain current in the same direction are placed parallel to each other, they will experience a force of repulsion. select one: a. true b. false
The given statement "If two identical wires carrying a certain current in the same direction are placed parallel to each other, then they will experience a force of repulsion" is true. This can be explained through Lenz's law.
What is Lenz's law?Two parallel wires which are carrying the same magnitude of current in the same direction experience a force of repulsion due to the electric currents in each of the wire which are creating a magnetic field in the same direction. This force of repulsion is known as the Lenz's Law.
When two identical wires are carrying a certain magnitude of electric current in the same direction and these are placed in parallel to each other, then they will experience a force of repulsion. This is due to the principle of the electromagnetic force and Lenz's law. When the two current-carrying wires are kept near each other, then they exert force on each other, and that force is called as the force of repulsion or the force of attraction depending on the direction of the current flowing through the wire. The direction of the force is given by the Fleming's left-hand rule, which is the most common way to determine the direction of the force in such cases.
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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
Running on a treadmill is slightly easier than running outside because there is no drag force to work against. Suppose a 60 kg runner completes a 5.0 km race in 22 minutes. Determine the drag force on the runner during the race. Suppose that the cross section area of the runner is 0.72 m2 and the density of air is 1.2 kg/m3.I know how to get the drag force, but have no idea how to get the drag coefficient, in order to plug into the equation! I found the velocity in m/s, then went to find the force using F=1/2(density of air)(velocity^2)(drag coefficient)(cross section area) but don't know what to use for the drag coefficient.
Running on a treadmill is slightly easier than running outside because there is no drag force to work against. Suppose a 60 kg runner completes a 5.0 km race in 22 minutes. The drag force on the runner during the race is 13.4 N.
Running on a treadmill is slightly easier than running outside because there is no drag force to work against. Drag force is a form of air resistance that acts on objects moving through air. When a runner is running on a treadmill, there is no drag force to work against.
In order to calculate the drag force on the runner during the race, we need to determine the drag coefficient. The drag coefficient is a dimensionless number that represents the ratio of drag force to dynamic pressure. It is affected by the shape and size of the object as well as the fluid (air) it is moving through. Generally, a higher drag coefficient means that more force is required to move the object.
To calculate the drag coefficient, we can use the following formula: Cd = Fd / (1/2 * ρ * v2 * A), where Fd is the drag force, ρ is the density of the air, v is the velocity of the object, and A is the cross-sectional area of the object.
For our example, we are given a runner that is 60 kg and completed a 5 km race in 22 minutes. The velocity of the runner can be calculated by v = d/t, where d is the distance traveled and t is the time taken. This gives us a velocity of 8.3 m/s. The density of the air is given to be 1.2 kg/m3 and the cross-sectional area is 0.72 m2.
Plugging these values into the formula gives us a drag coefficient of 0.385. This means that for every 1 unit of dynamic pressure, the drag force is 0.385. We can now calculate the drag force on the runner by multiplying the drag coefficient by 1/2 * ρ * v2 * A. In this case, the drag force is 13.4 N.
In conclusion, the drag force on the runner during the race is 13.4 N. This was calculated by determining the drag coefficient using the formula Cd = Fd / (1/2 * ρ * v2 * A) and then multiplying it by 1/2 * ρ * v2 * A.
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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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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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what is the difference between constant speed and acceleration? Explain mathematically
Answer:
A constant velocity of an object ensures that the rate of change of velocity with time is null, and hence, the acceleration of the object is zero. A constant acceleration of an object ensures that the velocity of the object is changing continuously with time, and the velocity will not be constant.
Explanation:
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1) The formation of freezing rain involves:
A) snow passing through a fairly thick layer of above freezing air before passing through a thin layer of subfreezing temperatures near the surface.
B) air temperatures decreasing uniformly with height, producing the cold conditions necessary for freezing rain formation.
C) air temperatures increasing uniformly with height, producing the cold conditions necessary for freezing rain formation.
D) snow passing through a fairly thin layer of above freezing air before passing through a thick layer of subfreezing
temperatures near the surface.
Complete the following sentence.
A diameter is also a...
Answer:
A diameter is also a double of radius
In SEC, in what volume would you expect molecules that are much smaller than the fractionation range of the Sephadex SP to elute? A. Vi B. Vm C. Vav D. Vr E. Vo
The void volume (Vo), which is represented by option E, is where molecules in SEC that are significantly smaller than the fractionation range of the Sephadex SP are anticipated to elute.
Using a stationary phase, such as Sephadex SP, that contains various-sized holes packed inside a column, size exclusion chromatography (SEC) divides molecules into groups according to their sizes as they travel through the column. Smaller molecules can enter deeper into the matrix before eluting out, but bigger molecules must elute out first because they cannot fit through smaller holes. Although certain molecules may be far smaller than the fractionation range of the stationary phase and pass through the matrix unaltered, this is not always the case. These molecules are anticipated to elute in the void volume (Vo), which is the portion of the column's volume that the buffer or solvent occupies instead of the stationary phase. As a result, Vo, option E, is the right response.
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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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if the variable capacitor in an fm receiver ranges from 10.9 pf to 16.4 pf , what inductor should be used to make an lc circuit whose resonant frequency spans the fm band?
To create an LC circuit spanning the FM band with a variable capacitor of 10.9-16.4 pF, use the formula L = 1/(4π²f²C).
The inductor needed to make an LC circuit whose resonant frequency spans the FM band depends on the variable capacitor in the FM receiver. In your case, the variable capacitor ranges from 10.9 pF to 16.4 pF. To determine the inductor needed for the LC circuit, you can use the following formula:
L = (1/ (4π² * f² * C))
Where:
"L" is the inductor. "f" is the frequency of the LC circuit. "C" is the capacitor.For example, if you set the variable capacitor to 10.9 pF, the inductor needed to make an LC circuit whose resonant frequency spans the FM band would be:
L = (1/ (4π² * f² * 10.9 pF))
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A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are useful for communication and weather observation because the satellite remains above the same point on Earth (provided it orbits in the equatorial plane in the same direction as Earth’s rotation). The ratio r3T2 for the moon is 1.01×1018km3y2. Calculate the radius of the orbit of such a satellite. All work must be shown for full credit. The choices are: 2.75x10E3 km; 1.96x10E4km; 1.40x10E5km; 1.00x10E6km.
The radius of the orbit of such a satellite will be about 1.40 × 10⁵ kilometers.
What is the radius of orbit?To calculate the radius of the orbit of a geosynchronous Earth satellite, we must use the equation:
r³T² = 1.01 × 10¹⁸ km³y²
where, r is the radius of the orbit and T is the orbital period of the satellite, which is 1 day. We can rearrange the equation to calculate r, giving us:
r = (1.01 × 10¹⁸km³y²)1/3/(1 day)2/3
To calculate the radius of the orbit, we need to convert the units of 1 day to seconds: 1 day = 86400 seconds. We can substitute this into the equation:
r = (1.01 × 10¹⁸km³y²)1/3/(86400 seconds)2/3
Finally, we can calculate the radius of the orbit: r = 1.40 × 10⁵ km
Therefore, the radius of the orbit will be about 1.40 × 10⁵ km.
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(a) Find the current in an 8.00 {eq}\Omega {/eq} resistor connected to a battery that has an internal resistance of 0.15 {eq}\Omega {/eq} if the voltage across the battery (the terminal voltage) is 9.00 V.
(b) What is the emf of the battery?
(a) The current in the 8.00 Ω resistor connected to a battery that has an internal resistance of 0.15 Ω and a terminal voltage of 9.00 V is 1.0 A.
To calculate this, use Ohm's Law, which states that voltage = current x resistance.
Rearrange this equation to solve for current: current = voltage / resistance. Plug in the values for voltage and resistance to get:
current = 9.00 V / 8.00 Ω + 0.15 Ω = 1.0 A.
(b) The EMF (electromotive force) of the battery is 9.00 V. This is the same as the terminal voltage since the internal resistance of the battery is very small.
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Alice holds a small battery operated device used for tuning instruments that emits the frequency of middle C (262 Hz) while walking with a constant speed of 4.68 m/s toward a building which presents a hard smooth surface and hence reflects sound well. (Use343 m/s as the speed of sound in air.)
(a) Determine the beat frequency Alice observes between the device and its echo. (Enter your answer to at least 1 decimal place.)
(b) Determine how fast Alice must walk away from the building in order to observe a beat frequency of 6.19 Hz.
(A) Alice observes a beat frequency of approximately 3.9 Hz between the device and its echo. (B) Alice must walk away from the building at a speed of approximately 7.05 m/s to observe a beat frequency of 6.19 Hz.
(A) The given values are:
Speed of Alice, vA = 4.68 m/s.
The frequency emitted by the device, f1 = 262 Hz
Speed of sound in air, v = 343 m/s(a)
The beat frequency, f beat is given by the formula: fbeat = |f1 - f2| where f2 is the frequency of the reflected sound.
Since the speed of sound is reflected, the distance traveled by the sound to the building and back is 2d.
Therefore, the time taken is given by t = 2d/v.
The frequency f2 is given by f2 = v/(2d).
The distance d = vt/2 = (vA t)/2
The time t is given by: t = d/vA
The frequency f2 is given by f2 = v/(2d) = vA/(2v t)
Therefore, the beat frequency is: fbeat = |f1 - f2| = |262 - vA/(2v t)|
Thus, substituting the given values, we get: fbeat = |262 - 343/(2 × 4.68 × t)|
To solve this, we can use trial and error method.
We can check if fbeat is approximately equal to 2, 3, 4, 5, or 6 Hz.
Using t = 0.01 s, we get: fbeat = |262 - 343/(2 × 4.68 × 0.01)|≈ 4.4 Hz
Using t = 0.011 s, we get: fbeat = |262 - 343/(2 × 4.68 × 0.011)|≈ 3.9 Hz
Therefore, Alice observes a beat frequency of approximately 3.9 Hz between the device and its echo.
(b) Let's suppose that Alice walks with a velocity of vA' away from the building. Therefore, the distance traveled by the sound in the same time interval t = d/vA' is d' = vA' t/2.The time taken is given by t = d/vA = d'/vA'
Now, the frequency f2 is given by f2 = v/(2d') = vA'/(2v t)
The beat frequency is:fbeat = |f1 - f2| = |262 - vA'/(2v t)|
Thus, substituting the given values, we get: fbeat = |262 - 343/(2 × vA' × t)|
Let's suppose that fbeat = 6.19 Hz.
Using trial and error, we get that t ≈ 0.018 s.
Substituting this value, we get:6.19 = |262 - 343/(2 × vA' × 0.018)|
Therefore, vA' ≈ 7.05 m/s
Thus, Alice must walk away from the building at a speed of approximately 7.05 m/s to observe a beat frequency of 6.19 Hz.
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Which of the following is an example of potential energy?A .A vibrating pendulum at its maximum displacement from its mean positionB. A body at rest from some height from the ground.C. A wound clock spring.D. A vibrating pendulum when it is just passing through its mean position
The best example that shows the potential energy is a body at rest from some height from the ground, thus the correct answer is option b.
Potential energy is defined as the energy stored by an object or system in a position that can contribute to doing work when released. It is the stored energy of an object or system.
In this case, the body at rest has potential energy because of its height above the ground. As it falls, the potential energy is converted to kinetic energy.
Option A describes kinetic energy as the vibrating pendulum at its maximum displacement, and option D describes a momentary state of rest in a pendulum's motion, which does not involve potential energy. Option C describes the potential energy stored in a wound clock spring, but it possesses elastic potential energy.
Thus, the body at rest has potential energy because of its height above the ground. Thus, option b is correct.
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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 scientist is studying an organism that is similar to early life on Earth. The scientist observes structures form in the organism that appear as oily spheres with an inner fluid. Of which type of macromolecule is the sphere made? carbohydrate lipid nucleic acid protein
The structure described by the scientist, which is an oily sphere with an inner fluid, is most likely a lipid vesicle.
Lipids are a class of macromolecule that are hydrophobic and non-polar, which means that they do not cling to water. To reduce their exposure to the polar water molecules when lipids are in water, they often group together. This may result in the development of lipid vesicles, which have an interior space that is sealed off from the outside world by a lipid bilayer. Since they can self-assemble in water and provide a safe space for molecules to interact, lipid vesicles have been suggested as a potential precursor to cells. This is comparable to how basic organic molecules may have produced lipid vesicles during the first stages of life on Earth, which later gave rise to the first cells.
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two objects, one of mass 4 m and the other of mass 2m, are dropped from the top of a building. assuming friction is negligible, when the two objects hit the ground
a. Both of them will have the same kineic energy
b. The heavier one will have twice the kineic energy of the lighter one
c. The heavier one will have four imes the kineic energy of the lighter one
d. The heavier one will have √2 imes the kineic energy of the lighter one
The kinetic energy of the heavier object (4m) is twice that of the lighter object (2m) when they hit the ground assuming the friction is negligible. Option B is correct.
The potential energy of an object of mass m at a height h above the ground is given by PE = mgh,
where g is the acceleration due to gravity.
When the two objects are dropped from the top of the building, they both have the same potential energy due to their same height.
At the point of impact with the ground, all of the potential energy is converted to kinetic energy,
which is given by KE = 1/2*mv²,
where v is the velocity of the object just before hitting the ground.
Since both objects are dropped from the same height, they will have the same velocity just before hitting the ground. Therefore, the kinetic energy of the objects will be proportional to their masses, as given by:
KE_{4m} = 1/2 (4m) v² = 2mv²
KE_{2m} = 1/2 (2m) v² = mv²
Comparing both of them we know the kinetic energy of the heavier object (4m) is twice that of the lighter object (2m) when they hit the ground.
Therefore, the correct answer is (b) The heavier one will have twice the kinetic energy of the lighter one.
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Determine the relationship which governs the velocities of the three cylinders, and state the number of degrees of freedom. Express all velocities as positive down.
If vA = 2. 47 m/s and vC = 1. 08 m/s, what is the velocity of B?
If v_A = 2. 47 m/s and v_C = 1. 08 m/s, So the velocity of B is -1.1575 m/s.
Write the equation for the length of the cable between the pulleys E and F.
[tex]L_1[/tex] = a+2y+π[tex]r_2[/tex]+ π[tex]r_1[/tex] + x
Differentiate the equation with respect to time.
0=2y+x
Write the equation for the length of the cable between the pulleys H and F.
[tex]L_2[/tex] = p +π[tex]r_4[/tex]+z+π[tex]r_3[/tex] +(z - y)
= p +π[tex]r_4[/tex] +2z+π[tex]r_3[/tex] - y
Differentiate the equation with respect to time.
0 = p + 2ż - y
y=p+2ż
x+2y=0
x+2(p+2ż)=0
x+2p+4z=0
[tex]v_A[/tex]+2[tex]v_c[/tex]+4[tex]v_B[/tex]=0
(2.47)+2(1.08)+4[tex]v_B[/tex] = 0
[tex]v_B = - \frac{ ((2.47)+2(1.08))}{4}[/tex]
[tex]v_B[/tex] = -1.1575 m/s
As two variables are required to specify the positions of all parts of
the system, y=p+2ż
DOF = 2
Velocity is a physical quantity that describes the rate at which an object changes its position in a given period of time. The magnitude of velocity is the speed at which the object is moving, while the direction of velocity is the direction in which the object is moving. It can also be expressed in other units such as miles per hour (mph), kilometers per hour (km/h), or feet per second (ft/s).
Velocity is a fundamental concept in classical mechanics and is used extensively in physics, engineering, and other fields of science. It is often used to calculate the displacement of an object, the distance traveled by the object over a given time, and the acceleration of the object.
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