The normal force of the car is equal to the weight of the car, 2,652.56 N. The maximum speed the car can have without losing contact with the road is equal to the square root of the product of the normal force of the car and the radius of the hill. That is,9.87 m/s.
A car with a mass of 720kg going over a hill at 12 m/s can be represented by the following Free Body Diagram (FBD):
The normal force of the car can be calculated using the equation
Normal Force = m × g × cos θ
where m is the mass of the car, g is the gravitational acceleration (9.81 m/s2), and θ is the angle of the hill.
Therefore, Normal Force = 720kg × 9.81 m/s2 × cos 70° = 2,652.56 N.
The maximum speed that the car can have without losing contact with the road at the top of the hill is equal to the square root of the equation
v2 = (2 × Normal Force × Radius of Curvature) / m
where v is the speed of the car, Normal Force is the calculated normal force of the car, and m is the mass of the car.
Therefore, the maximum speed of the car = √[(2 × 2,652.56 N × 70 m) / 720kg] = 9.87 m/s.
Therefore normal force of car is 2,652.56 N and maximum speed of car is 9.87 m/s.
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A block of weight w = 25.0 N sits on a frictionless inclined plane, which makes an angle 8 = 29.0° with respect to the horizontal, as shown in the figure. (Figure 1) A force of magnitude F = 12.1 N, applied parallel to the incline, is just sufficient to pull the block up the plane at constant speed.
Part B: What is We, the work done on the block by the force of gravity was the block moves a distance L = 3.40 m up the incline?
Part C. What is Wf the work done on the block by the applied force F as the block moves a distance L = 3.40 mm up the incline? Express your answer in Joules
a) The net Work done is zero. b) The work done on the block by the applied force F as the block moves a distance L is -41.2 J. c) The work done on the block by the applied force F as the block moves a distance L is 41.2 J.
Given:
Weight of the block (w) = 25.0 N
Distance moved by the block (d) = 3.40 m
The angle of the inclined plane (θ) = 29.0°
a) we know that from the work-energy theorem,
W = change in kinetic energy
But since speed is constant which means no change in KE, hence the net Work done is zero.
b) W = -mgy
W = -25 × (3.10 × sin29°)
W = -41.2 J
Therefore, the work done on the block by the force of gravity is -41.2 J.
c) The work done on the block by the applied force F as the block moves a distance L = 3.10m up the incline is,
W = Fd
W = 12.1 × 3.1
W = 41.2 J
Therefore, the work done on the block by the applied force F as the block moves a distance L is 41.2 J.
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Discuss the changes in potential energy, kinetic energy, and total energy for a skateboarder going up and down on a half-pipe (U-shaped) ramp. Specifically address the energies when the skater is at the highest point (A), half-way down the ramp (B), and at the lowest point (C)
The real truth is that there's always some friction, friction robs kinetic energy whenever he's moving, so eventually he stops going up and down. Then he has to put some muscle energy into it to go some more.
Friction is a force that opposes the relative motion or attempts at motion between two surfaces in contact. It is the reason why we feel resistance when we try to slide an object across a surface or why it takes effort to walk or run. Friction can occur between solids, liquids, and gases, although it is most commonly observed in solids.
The force of friction arises from the interactions between the microscopic irregularities on the surfaces in contact. As two surfaces slide past each other, the irregularities interlock and resist further motion. The greater the force pressing the surfaces together, the greater the friction force. Friction is a fundamental force of nature that has both positive and negative effects.
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Many roller coasters function by mechanically transporting the cars up a large incline. The cars then roll down and up a series of hills, turns, and spirals until the cars come to rest at the passenger loading station. At which point will the roller coaster have the greatest amount of gravitational potential energy?
The roller coaster will have the greatest amount of gravitational potential energy at the top of the incline, just before the cars are released to roll down the track.
Electrical energy is transferred between the main and secondary coils of a transformer through a magnetic circuit that is created by the iron core. A magnetic field that is continuously changing is produced in the iron core when an alternating current is fed through the primary coil. Energy is transferred between the coils as a result of the magnetic field's induction of a matching current in the secondary coil. Because of its high permeability and sensitivity to magnetism, the iron core can magnetize. A greater induced current is produced in the secondary coil as a result of the first coil's magnetic field being amplified by the iron core's magnetization. The effective transmission of electrical energy in a transformer depends on the magnetic characteristics of the iron core. The roller coaster will therefore have the most potential energy at the highest point of the trip.
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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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When current flows through a conductor, it develops a magnetic field of concentric circles expanding ? and outward from the conductor. a. circularly b. parallel c. perpendicular d. wavy
When a current travels through a conductor in a circular motion, a magnetic field with growing concentric circles is created.
What happens when current flows through a conductor?Electromagnetism is established when an electrical current flows through a simple conductor, such as a length of wire or cable.
What magnetic field is created when current travels through a conductor?As magnetic fields produced by moving charges are proportional to the current, a conductor carrying current creates a magnetic field around it. Generally speaking, the sub-atomic particles in the conductor, such as the moving electrons in the atomic orbitals, are responsible for this magnetic field.
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True or False: For a given water velocity (distance traveled per unit time), the greater the cross sectional area of a stream channel, the lower will be the stream flow (discharge: volume of water per unit time).
For a given water velocity (distance traveled per unit time), the greater the cross-sectional area of a stream channel, the lower will be the stream flow (discharge: volume of water per unit time)" is a false statement.
What is Stream discharge?Stream discharge is measured by the volume of water flowing per unit of time, which is calculated by multiplying the stream's cross-sectional area (flow width × flow depth) by its water velocity. As a result, the given statement is false.
According to the formula, an increase in the cross-sectional area of the stream will cause a rise in the stream flow (discharge: volume of water per unit time) because it is multiplied by the velocity. So, for a given water velocity, the greater the cross-sectional area of a stream channel, the higher the stream flow (discharge: volume of water per unit time) will be.
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How do upper fixed point calibrate in a thermometer? Explain it,
Answer:
An upper fixed point calibration in a thermometer involves establishing a reference point at the highest temperature that the thermometer can measure accurately. This reference point is typically defined by the boiling point of a pure substance at a specific atmospheric pressure, such as water at standard atmospheric pressure (100°C or 212°F).
To calibrate the thermometer's upper fixed point, the thermometer is first placed in a container of boiling water and allowed to reach thermal equilibrium with the water. The thermometer's reading is then compared to the known boiling point of the substance at that pressure, and any differences are noted. If the thermometer reads higher or lower than the expected boiling point, the thermometer can be adjusted or calibrated accordingly to ensure that it provides accurate temperature readings.
It's important to note that the calibration of a thermometer's upper fixed point should be performed under controlled conditions, as variations in pressure or impurities in the substance being used to establish the reference point can affect the accuracy of the calibration. Additionally, regular recalibration may be necessary to ensure continued accuracy of the thermometer.
Explanation:
An electroscope is a device with a metal knob, a metal stem, and freely hanging metal leaves used to detect charges. The diagram below shows a positively charged leaf electroscope.
As a positively charged glass rod is brought near the knob of the electroscope, the separation of the leaves will
remain the same
increase
As a positively charged glass rod is brought near the knob of the electroscope, the separation of the leaves will increase.
What is Charge?
Charge is a fundamental property of matter that determines how objects interact with each other through the electromagnetic force. It is a physical property that can be positive or negative and can be measured in coulombs (C).
This is because the positively charged glass rod will induce a negative charge on the metal knob of the electroscope. The negative charges will repel the electrons in the metal leaves, causing them to move away from each other and increasing their separation. The greater the amount of charge on the glass rod, the greater the separation between the leaves will be.
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Define local action and polarization.How do they make their cell defective?
Answer:
Define local action and polarization.How do they make their cell defective?
Explanation:
Local action is a principle in physics that describes how a particle or object interacts with another object that is nearby, without the need to consider transients that occur over long distances. This means that the influence of one object on another rapidly decreases as the distance between them increases. Local action is a fundamental assumption in quantum physics and general relativity, and it is essential for understanding many physical phenomena.
Polarization is a phenomenon that occurs when a transverse wave, such as an electromagnetic wave, oscillates in a specific plane. This means that the direction of the wave's electric field changes with time, but always remains in the same plane. Polarization is important in many applications, such as optics, where the polarization of light can be used to control the intensity and direction of light. Furthermore, polarization is fundamental in particle physics, where subatomic particles have an intrinsic polarization that can be measured in experiments.
a 3 3-inch candle burns down in 12 hours. if b represents how much of the candle, in inches, has burned away at any time given in hours, t, write a proportional equation for b in terms of t that matches the context.
The proportional equation that matches the context of a 33-inch candle burning down in 12 hours is b = 2.75t.
A candle that is 33 inches long is called a 33-inch candle. Candles are a popular decorative item that is commonly used for lighting, as decoration for weddings, and parties, or to create an aromatic atmosphere. B represents the length of the candle that has burned away at any time given in hours, t.
To find the proportional equation for b in terms of t that matches the context of a 33-inch candle burning down in 12 hours, the following steps should be followed:
Identify the given informationThe length of the candle (l) = 33 inchesThe time taken for the candle to burn down (t) = 12 hours
Determine the rate of burning The rate of burning of the candle is given by l/t. Therefore, the rate of burning = 33/12 = 2.75 inches per hour.
The proportional equation for b in terms of t is given by b = rt where r is the rate of burning. Therefore, b = 2.75t.
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A student investigated how the mass of water in an electric kettle affected the time taken for the water to reach boiling point.
The kettle switched off when the water reached boiling point.
Figure 1 shows the kettle.
(a) The heating element of the kettle was connected to the mains supply.
Explain why the temperature of the heating element increased.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
(2)
(b) Give one variable that the student should have controlled.
___________________________________________________________________
___________________________________________________________________
(1)
Figure 2 shows how the mass of water in the kettle affected the time taken for the kettle to switch off.
Figure 2
(c) Suggest why the line on Figure 2 does not go through the origin.
___________________________________________________________________
___________________________________________________________________
(1)
(d) Suggest why the results give a non-linear pattern.
___________________________________________________________________
___________________________________________________________________
(1)
Can someone please answer part (c)? Please
The line does not go through the origin because there is some inherent delay in the heating process that is not dependent on the mass of water in the kettle.
Part (c) asks to suggest why the line on Figure 2 does not go through the origin. The line on Figure 2 represents the relationship between the mass of water in the kettle and the time taken for the kettle to switch off.
Boiling point refers to the temperature at which a liquid substance turns into a gas or vapor. The boiling point of a substance depends on various factors, such as its molecular structure, intermolecular forces, and atmospheric pressure.
The boiling point of a substance remains constant under a given pressure, and any additional heat input during boiling will only cause the temperature of the vapor to increase rather than the liquid. The boiling point is an important physical property of a substance, and it can be used to determine the purity of a liquid through the process of distillation. The boiling point of water is 100 degrees Celsius at standard atmospheric pressure (1 atm), while the boiling point of ethanol is 78.5 degrees Celsius.
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An automatic saw has several forces acting on it. In a Cartesian system, a position-dependent force applied to the saw is =-kxy2j, with k = 2.50 N m³. Let's consider the displacement of the saw from the origin to point C (4.0 m, 4.0 m). Calculate the work done on the saw by if the displacement is along the straight-line y = x that connects these two points.
The work done on the saw by the force if the displacement is along the straight-line y = x that connects these two points is -640.0 J.
How to calculate work done?To calculate the work done on the saw by the force as it moves along the straight-line y = x that connects the two points, we need to first find the displacement vector and then use it to calculate the work done.
The displacement vector from the origin to point C is given by:
r = (4.0 m) i + (4.0 m) j
The force acting on the saw is given by:
F = -kxy² j = -2.50 (N m³) (x) (y²) j
Since it is moving along the straight-line y = x, we can substitute x = y into the expression for F:
F = -2.50 (N m³) (x) (y²) j = -2.50 (N m³) (y³) j
Substituting x = y = 4.0 m:
F = -2.50 (N m³) (4.0 m)³ j = -160.0 j N
The work done by the force is given by the dot product of the force and displacement vectors:
W = F · r = (-160.0 N j) · (4.0 m i + 4.0 m j)
W = (-160.0 N) (4.0 m cos(45°))
W = -640.0 J
Therefore, the work done on the saw by the force as it moves along the straight-line y = x that connects the two points is -640.0 J.
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What technological improvement in the 1920s allowed more goods to be produced at one time?
Automobile
Assembly line
Telephone
Motion picture
Answer: Telephone
Explanation:
The technological improvement that allowed more goods to be produced at one time in the 1920s was the development and widespread use of assembly line production. This was pioneered by companies such as Ford Motor Company, which introduced the assembly line to its automobile factories. The assembly line method allowed for the mass production of standardized products using specialized machines and workers performing specific tasks. By breaking down the manufacturing process into smaller, simpler tasks, and optimizing the movement of workers and materials, the assembly line significantly increased production efficiency and output. This led to the growth of mass production industries, increased affordability of goods, and a significant shift in the nature of work in the 20th century.
the us bank tower in los angeles is designed to resist an earthquake of what magnitude on the richter scale?
The 8.3 on the Richter scale earthquake magnitude can be withstood by the US Bank Tower in Los Angeles.
How earthquake-proof is the Los Angeles U.S. Bank Tower?A frame that is strengthened in two directions is part of the central core structure. Two struts, each one level high, are employed to decrease horizontal stresses brought on by wind or earthquakes beginning at the 53rd floor.
A 9.0 earthquake can a tower withstand?Indeed, it is the answer. Modern structural design techniques can be used to construct skyscrapers that can resist earthquakes. Performance-based structural design (PBSD), a cutting-edge design methodology for creating earthquake-resistant structures, is one of them.
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Can someone please help me on this
How do the authors develop the central idea over the course of the
The statement that best describes the relationship between how consumers engage with product and service based brands is C. Though product and service brands both seek likes from consumers, consumers are more likely to "like" product brands because they can
accoce the quality of the product more.
How to depict the informationThe relationship between how consumers engage with product and service based brands is complex and multifaceted. Both types of brands seek to establish a strong relationship with their consumers through various strategies, such as effective advertising, personalized communication, quality customer service, and social media engagement.
However, the specific strategies employed by product and service brands may differ depending on the nature of their offerings and the preferences of their target audience. For instance, product brands may focus on showcasing the quality, features, and benefits of their products through visual and sensory experiences, while service brands may emphasize the expertise, reliability, and personalization of their services through word-of-mouth recommendations and customer reviews.
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Which statement best describes the relationship between how consumers engage with product and service based brands?
A. Though product and service brands both seek likes from consumers, they have many more effective strategies to attract consumers to their product than social media.
B. Service brands seek likes from consumers more than product brands do because they rely on recommendations from their consumers in order to attract new business.
C. Though product and service brands both seek likes from consumers, consumers are more likely to "like" product brands because they can
accoce the quality of the product more.
why is a polarized filter helpful to a photographer? A. it transmits all light
Answer:
It blocks some light, but not all.
Explanation:
The point of polarization is to get the light to travel in a single plane. The light waves occur in a single plane. The direction of the vibration of the waves is the same. With two polarized filters, it is possible to block out nearly all the light.
the earth's mass is 80 times that of the moon what is the ratio of gravitational force the earth exerts on the moon to the gravitational force the moon exerts on earth
The Earth's mass is 80 times that of the moon. The ratio of gravitational force the Earth exerts on the moon to the gravitational force the moon exerts on Earth is 80:1.
The relationship between the mass of two objects and their gravitational force can be expressed mathematically using Newton's Law of Gravitation. The formula is:
F = G × ((m1 × m2)/r2)Where
F is the gravitational force between the two objectsG is the gravitational constant, m1 and m2 are the masses of the two objects r is the distance between their centers of massThe gravitational force between two objects is always proportional to the product of their masses. Therefore, if one object has 80 times the mass of the other, then the gravitational force it exerts on the smaller object will be 80 times greater as well. Hence, the ratio of gravitational force the Earth exerts on the moon to the gravitational force the moon exerts on Earth is 80:1.
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A 1200-turn coil of wire that is 2. 3 cm in diameter is in a magnetic field that drops from 0. 13 T to 0 T in 12 ms. The axis of the coil is parallel to the field. What is the emf of the coil? Express your answer using two significant figures
In a magnetic field that decreases from 0. 13 T to 0 T in 12 ms, a wire coil with 1200-turns and a 2. 3 cm diameter is placed. The coil's axis is perpendicular to the field. The coil's emf is 0.059 V.
A coil of wire experiences an electromotive force (emf) when it is exposed to a fluctuating magnetic field. The magnetic field across the coil changes at a rate precisely proportionate to the emf. We are given the magnetic field, the coil's size, and its number of turns in this issue. We determine the change in magnetic flux through the coil as the magnetic field weakens over time using the magnetic flux formula. Lastly, we determine the induced emf in the coil using the emf formula. The response, 0.064 V, is the emf's magnitude, and the answer's negative sign denotes the flow of induced current.
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suppose the ring rotates once every 4.10 s . if a rider's mass is 51.0 kg , with how much force does the ring push on her at the top of the ride?
The ring rotates once every 4.10 s. If a rider's mass is 51.0 kg, how much force does the ring push on her at the top of the ride is 500 N.
The solution is explained below:
As the rider is at the top of the ride, the only force acting on him is the force of gravity, which is pointing downwards, and the force with which the ring is pushing him towards the center of the circular path. By equating both forces, we can determine the required force to maintain the rider at the top of the ride.
Hence, the answer to the question is that the force with which the ring pushes the rider at the top of the ride is equal to the force of gravity, which is given as F = mgF = (51.0 kg)(9.81 m/s^2) = 500 N
Therefore, the force with which the ring pushes on the rider at the top of the ride is 500 N.
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Gas G1 G2 G3 G4 2am/mol2) L/mol) 0.0289 0.0388 0.0467 0.0310 2 5.22 1.05 2.31 4.05 Based on the given van der Waals constants for four hypothetical gases (G1, G2, G3, G4), arrange these hypothetical gases in order of decreasing strength of intermolecular forces. Assume that the gases have similar molar masses.
Rank from strongest to weakest intermolecular attraction. To rank items as equivalent, overlap them.
Gas 3, Gas 2, Gas 1, Gas 4
According to the strength of the intermolecular forces, the hypothetical gases can be ordered as follows: Gas 3 > Gas 2 > Gas 1 > Gas 4.
The strength of intermolecular forces in gases can be estimated by analyzing their van der Waals constants, which take into account the size and polarizability of the molecules. A higher value of the van der Waals constant indicates stronger intermolecular forces.
Based on the given van der Waals constants, we can rank the hypothetical gases in order of decreasing strength of intermolecular forces as follows:
Gas 3 > Gas 2 > Gas 1 > Gas 4
Gas 3 has the highest van der Waals constant (a = 2.31 L/mol), indicating the strongest intermolecular forces, while Gas 4 has the lowest van der Waals constant (a = 4.05 L/mol), indicating the weakest intermolecular forces. Gas 2 and Gas 1 have intermediate values of van der Waals constants, with Gas 2 having a higher value than Gas 1, indicating stronger intermolecular forces.
Therefore, the hypothetical gases can be ranked in order of decreasing strength of intermolecular forces as Gas 3 > Gas 2 > Gas 1 > Gas 4.
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a fireman' s hose is pointed vertically upward at a height of 1.5 m above the ground and a stream of water is coming from it . when the water is shut off, the noise of the water hitting the ground continues for another 2.0 s . what was the speed of the water as it left the hose?
The fireman's hose is pointed vertically upwards at a height of 1.5 m above the ground and a stream of water is coming from it. When the water is shut off, the noise of the water hitting the ground continues for another 2.0 s, the speed of the water as it left the hose is 4.31 m/s.
What is the definition of a fireman?A firefighter, also known as a fireman or firewoman, is a professional who is trained and equipped to put out fires, rescue people and animals from dangerous situations, and manage other emergency situations.
The water comes to rest after it reaches the ground, so it moves at constant acceleration in the vertical direction. Since the final velocity is zero, the initial velocity and the displacement can be used to calculate the time of flight.
The speed at which the water left the hose can then be determined using the time of flight and the height of the hose above the ground.
Initial velocity = v₀, Final velocity = vf = 0.
Displacement = h = 1.5 m
Acceleration = a = g = 9.8 m/s²
Time of flight = t
Using the formula ,vf = v₀ + at₀ = v₀ + gt
v₀ = -gt
displacement = v₀×t + 1/2×at²
h = -1/2 × gt²
t = sqrt(2h/g) = sqrt(2(1.5)/9.8) = 0.44 s.
Using the formula, vf = v₀ + at
vf = 0 + gtvf = 9.8 × 0.44 = 4.31 m/s.
The water's speed as it leaves the hose is 4.31 m/s.
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a 5 mm diameter, 50 mm long glass tube filled with water is rotated at 1000 rpm. what is the pressure at point a?
A 5 mm diameter, 50 mm long glass tube filled with water is rotated at 1000 rpm. The pressure at point A is 24.525 Pa.
The pressure at point A in a 5 mm diameter, 50 mm long glass tube filled with water when rotated at 1000 rpm can be calculated using the equation P = ρgr, where ρ is the density of the water, g is the acceleration due to gravity, and r is the radius of the tube.
Since the tube is 5 mm in diameter, the radius is 2.5 mm. The density of water is 1000 kg/m3 and the acceleration due to gravity is 9.81 m/s2. Therefore, the pressure at point A can be calculated as follows:
P = 1000 * 9.81 * 2.5 * 10-3 = 24.525 Pa
Therefore, the pressure at point A in a 5 mm diameter, 50 mm long glass tube filled with water when rotated at 1000 rpm is 24.525 Pa.
It is important to note that the pressure at point A will depend on the density of the fluid, the acceleration due to gravity, and the radius of the tube. As such, the pressure can be different for other fluids and for tubes with different radii.
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Homework, pls help me
The region of the periodic table that the unknown element would likely be found is metals (option A).
What are metals?Metals are a number of chemical elements in the periodic table that form a metallic bond with other metal atoms.
Metals are generally shiny, somewhat malleable and hard, often a conductor of heat and electricity.
According to this question, an unknown element has good conductivity and is a solid at room temperature. It possesses two valence electrons.
Elements with two valence electrons can be found in group two of the periodic table, which is a metallic element.
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the strength of an electromagnet is increased by group of answer choices putting a low-permeability core in the coil. increasing the number of turns of wire. increasing voltage.
An electromagnet's strength can be increased by any of the following methods: By putting a low-permeability core in the coil, by increasing the number of turns of wire, and by increasing voltage.
An electromagnet is a device that uses electricity to generate a magnetic field. Electromagnets are used in a variety of applications, including speakers, motors, and generators. Electromagnets can be used in many ways because their magnetic field can be easily controlled by changing the electric current flowing through them.
The strength of an electromagnet is determined by the number of turns of wire in the coil and the amount of current flowing through the wire. Increasing the number of turns of wire will increase the magnetic field strength of the electromagnet. Also, a low-permeability core in the coil can increase the magnetic field strength of the electromagnet. Permeability is the ability of a material to be magnetized. The core can concentrate the magnetic field, increasing the strength of the magnetic field. Finally, increasing the voltage applied to the electromagnet will increase the magnetic field strength.
The complete question is:
"The strength of an electromagnet is increased by _____
putting a low-permeability core in the coil.
increasing the number of turns of wire.
increasing voltage."
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Car A (traveling north at 70 mph) and car B (traveling west at 50 mph) are heading toward the same intersection. Car A is 5 miles from the intersection while car B is 6 miles from the intersection. Find parametric equations that describe the motion of cars A and B.
A) Car A: x = 0, y = 70t-5; Car B: x = 6 - 50 t, y = 0
B) Car A: x = 0, y = 50t - 6; Car B: x = 70t - 5, y = 0
C) Car A: x = -70t + 5, y = 0; Car B: x = 6 - 50t, y = 0
D) Car A: x = 50t - 6, y = 0; Car B: x = 0, y = 50 - 70t
The parametric equations that describe the motion of cars A and B while Car A traveling north at 70 mph and car B is traveling west at 50 mph and they both are heading toward the same intersection :
Car A: x = -70t + 5, y = 0Car B: x = 6 - 50t, y = 0
So, Option C is the right answer.
According to the problem,Car A is moving northwards while car B is moving westwards with the speeds of 70 mph and 50 mph respectively. The cars are heading towards the same intersection.
Car A is 5 miles from the intersection and Car B is 6 miles from the intersection.
Using the equation of motion in two dimensions, the positions of cars A and B can be described in terms of their distances from the intersection and the time elapsed as:
x = distance traveled in x direction, y = distance traveled in y direction
Car A: Initial distance from intersection = 5 miles, Speed = 70 mph = (70/60)mph = (7/6)miles per minute. Time elapsed from start of the motion = t minute
Parametric equation of motion for Car A = (x, y) = (-70t+5,0)
Car B: Initial distance from intersection = 6 miles, Speed = 50 mph = (50/60)mph = (5/6)miles per minute. Time elapsed from start of the motion = t minute
Parametric equation of motion for Car B = (x, y) = (6-50t,0)
Therefore, the correct option is C) Car A: x = -70t + 5, y = 0; Car B: x = 6 - 50t, y = 0.
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a jet pilot takes his aircraft in a vertical loop. if the jet is moving at a speed of 840 km/h at the lowest point of the loop, determine the minimum radius of the circle
The minimum radius of the circle made by the jet pilot in the vertical loop is 2773.3 meters.
To find the minimum radius of the circle made by the jet pilot in the vertical loop, we need to use the formula for centripetal force as follows:
F = m * v² / r
where
F is the centripetal force, m is the mass of the object, v is the speed of the object and r is the radius of the circle.The jet pilot is moving at a speed of 840 km/h which is equivalent to 840/3.6 = 233.3 m/s.
Let's assume the mass of the aircraft is 5000 kg.The centripetal force in this case is given by:
F = m * v² / rF = 5000 * (233.3)² / rF = 5000 * 54388.89 / rF = 271,944,450 / rAt the lowest point of the loop, the pilot experiences an apparent weight equal to twice the force due to gravity. This means that the net force experienced by the pilot is 2F = 2 * 271,944,450 / r. This net force is given by the difference between the centrifugal force and the gravitational force. Since the centrifugal force is equal to the centripetal force, we have:
F = m * g
where
g is the acceleration due to gravity.Since the apparent weight is twice the actual weight, we have:
2m * g = F2 * m * g = m * v² / r2 * 9.81 = 54388.89 / r2 * r = 54388.89 / 19.62r = 2773.3 m
Therefore, the minimum radius of the circle made by the jet pilot in the vertical loop is 2773.3 meters.
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two spheres are cut from a certain uniform rock. one has radius 4.45 cm. the mass of the other is six times greater. find its radius.
The radius of the second sphere is approximately 11.95 cm. This can be calculated by the volume of sphere.
What is the radius?The mass is proportional to the volume of the spheres. The volume of a sphere is given by the formula:
V = (4/3)πr³
Let the radius of the first sphere be r₁ (4.45 cm) and the radius of the second sphere be r₂. Given that the mass of the second sphere is six times greater than the first sphere, we can write:
M2 = 6 × M1
Since mass is proportional to volume, we can also say: V2 = 6 × V1
Now, substitute the volume formula for both spheres: (4/3)πr₂³ = 6×(4/3)πr₁³
Divide both sides by (4/3)π to simplify: r₂³ = 6 × r₁³
Plug in the value of r₁ (4.45 cm): r₂³ = 6 × (4.45)³
Now, calculate the value of r₂³: r₂³ ≈ 1683.107
Take the cube root of both sides to find r₂: r₂ ≈ (1683.107)^(1/3) r₂ ≈ 11.95 cm.
So, the radius of the second sphere is approximately 11.95 cm.
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Suppose you have a 8.4 cm diameter fire hose with a 2.2 cm diameter nozzle.a. Calculate the pressure drop due to the Bernoulli effect as water enters the nozzle from the hose at the rate of 40.0 L/s. Take 1.00 × 103 kg/m3 for the density of the water.b. To what maximum height, in meters, above the nozzle can this water rise? (The actual height will be significantly smaller due to air resistance.)
The pressure drop due to the Bernoulli effect is 33.14 Pa. and
A). P1 + (1/2)ρv1² = P2 + (1/2)ρv2²
P1 + (1/2)ρv1² = P2 + (1/2)ρ(7.28v1)²
P1 - P2 = (1/2)ρ(v2² - v1²)
P1 - P2 = (1/2)(1000 kg/m³)(7.28² - 1) v1²
P1 - P2 = 20,710 v1²
Substituting the values, we get:
P1 - P2 = 20,710 (0.040)²
P1 - P2 = 33.14 Pa
B). (1/2)mv2² = mgh
The mass of water that enters the nozzle per second is:
ρAv2 = (1000 kg/m³)(3.8 cm²)(7.28v1)
ρAv2 = 26.86v1
Substituting this into the conservation of energy equation, we get:
(1/2)(26.86v1)v2^2 = (26.86v1)gh
v2^2 = 2gh
Substituting the value of v2 from part (a), we get:
(7.28v1)² = 2gh
Solving for h, we get:
h = ((7.28v1)²)/(2g)
h = ((7.28(40.0/55.4))²)/(2(9.81))
h = 7.05 m
Pressure is a fundamental physical quantity that measures the force exerted per unit area. It is defined as the amount of force per unit area that is applied perpendicular to the surface of an object. Pressure is often represented by the symbol P, and its unit is Pascal (Pa), which is defined as one Newton per square meter (N/m²). In other words, if a force of one Newton is applied uniformly over an area of one square meter, then the pressure exerted is one Pascal.
Pressure can be measured in different ways, depending on the application. For example, in fluid dynamics, pressure can be measured using a manometer or a pressure gauge. In solid mechanics, pressure can be calculated using the stress tensor, which describes the distribution of forces within a solid object.
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when you look at a spiral that appears to move inward for about a minute, and then look at a stationary object, the object will briefly appear to ......
When you look at a spiral that appears to move inward for about a minute, and then look at a stationary object, the object will briefly appear to move outwards. This phenomenon is known as the motion aftereffect (MAE).
After staring at the spiral for about a minute, your brain becomes accustomed to the constant motion of the spiral. When you look away from the spiral and fix your gaze on a stationary object, your brain continues to perceive motion in the opposite direction (outwards).
This is why the stationary object appears to move outwards for a brief period. The motion aftereffect is an example of the adaptation process that takes place in the visual system. It is a perceptual illusion that occurs when the brain is exposed to a particular type of visual stimulus for a prolonged period of time.
Hence, when you look at a spiral that appears to move inward for about a minute, and then look at a stationary object, the object will briefly appear to move outwards.
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magnetic poles are similar to electric charges in that they...
Magnetic poles are similar to electric charges in that they produce fields around them that can attract or repel other objects.
Similar to how electric charges create electric fields around them that can pull or push away other charges, magnetic poles also create magnetic fields that can pull or push away other poles. The distance between the poles and how they are oriented in relation to one another affect the magnetic force's strength. Similarly, the distance between the charges and their orientation in relation to one another affect the strength of the electric force between them. Magnetic poles and electric charges do, however, differ significantly in terms of their origins and how they interact with one another. Magnetic poles always exist in pairs (north and south), unlike electric charges, which can be positive or negative and exist in isolated particles.
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