Physics High School
Answers
Answer 1
The secondary coil should have 64 turns to produce a voltage amplitude of 49 volts.
To determine the number of turns the secondary coil should have, we can use the formula for transformer voltage ratio, which states that the ratio of the number of turns in the secondary coil to the number of turns in the primary coil is equal to the ratio of the secondary voltage to the primary voltage.
In this case, the voltage ratio is 49/69 or approximately 0.71.
Therefore, we can solve for the number of turns in the secondary coil by setting up the equation 0.71 = N2/92, where N2 is the number of turns in the secondary coil.
Solving for N2:
N2 = 64.
As a result, the secondary coil needs 64 spins to provide a 49 volt voltage amplitude.
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Related Questions
An office window has dimensions 2.5 m by 2.2 m. As a result of the passage of a storm, the outside air pressure drops to 0.916 atm, but inside the pressure is held at 1.0 atm. What net force pushes out on the window
Answers
Therefore, the net force pushing out on the window is approximately 46816.6 N.
The net force pushing out on the window is equal to the pressure difference between the inside and outside of the window, multiplied by the area of the window. We can use the formula:
F = AΔP
where F is the net force, A is the area of the window, and ΔP is the pressure difference between the inside and outside of the window.
The pressure difference is given by:
ΔP = P_inside - P_outside
Substituting the given values, we get:
ΔP = 1.0 atm - 0.916 atm = 0.084 atm
We need to convert this pressure difference to SI units (Pascals) before using it in the formula for net force:
ΔP = 0.084 atm x 101325 Pa/atm = 8512.1 Pa
The area of the window is given by:
A = 2.5 m x 2.2 m = 5.5 m
Substituting the values we have found, we get:
F = AΔP = (5.5)(8512.1 Pa) = 46816.6 N
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A merry-go-round on a playground consists of a horizontal solid disk with a weight of 805 N and a radius of 1.54 m. A child applies a force 49.5 N tangentially to the edge of the disk to start it from rest. What is the kinetic energy of the merry-go-round disk (in J) after 3.05 s
Answers
The kinetic energy of the merry-go-round disk after 3.05 seconds is 165.7 J.
θ = ω0*t + (1/2)αt²
m = 805 N / 9.81 m/s² = 82.07 kg
r = 1.54 m
F = 49.5 N
t = 3.05 s
α = 1.049 rad/s²
θ = 10.73 rad
ω = 3.51 rad/s
K = 165.7 J
Kinetic energy is the energy an object possesses due to its motion. It is the energy required to accelerate a mass from rest to its current velocity. The amount of kinetic energy an object has depends on its mass and velocity, with the energy increasing as both mass and velocity increase.
The formula for calculating kinetic energy is KE = 1/2mv², where KE is kinetic energy, m is the mass of the object, and v is its velocity. This means that doubling an object's velocity quadruples its kinetic energy while doubling its mass only doubles its kinetic energy. Kinetic energy can be transformed into other forms of energy, such as potential energy, heat energy, or sound energy, through processes like friction, collisions, or work.
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if during a stride, the strecth causes her center of mass to lower by 10 mm, what is the stored energy
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The amount of stored energy in this scenario would depend on several factors, including the mass of the individual and the force applied during the stretch.
Potential Energy (PE) = mass (m) × gravity (g) × height (h)
PE = 60 kg × 9.81 m/s² × 0.01 m
PE = 5.886 J (Joules)
So, the stored energy is approximately 5.886 Joules when the center of mass lowers by 10 mm during a stride.
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. A motor is characterized by three main ingredients: magnetic field, moving charges and magnetic force. What are the three main ingredients that characterize a generator
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A generator is characterized by three main ingredients, which are similar to a motor but work in reverse: magnetic field, relative motion between conductors and magnetic field, and electromotive force (EMF).
1. Magnetic Field: Just like a motor, a generator uses a magnetic field, which is typically produced by permanent magnets or electromagnets.
2. Relative Motion: In a generator, the relative motion between conductors and the magnetic field is crucial. This motion can be achieved by rotating a coil in the magnetic field or by moving the magnetic field around a stationary coil.
3. Electromotive Force (EMF): The relative motion between conductors and the magnetic field induces an electromotive force (EMF) in the conductors, according to Faraday's law of electromagnetic induction. This EMF causes the flow of electric current in the conductors, which can be harnessed as electrical energy.
In summary, a generator's three main ingredients are the magnetic field, relative motion between conductors and magnetic field, and the electromotive force (EMF) generated from this interaction.
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driving along a highway at 31.0 m/s when they hear the siren of a police car approaching them from behind. Edgar perceives the frequency as 1,341 Hz. The police car continues past them, but now Aharon and Edgar perceive the frequency as 1,324 Hz. What is the speed of the police car in meters per second? The speed of sound in air is 344 m/s. Please give your answer with one decimal place.
Answers
we can use the Doppler effect formula, which relates the frequency perceived by a stationary observer, the frequency emitted by the source, the speed of the source, and the speed of sound in the medium. The formula is:
f_observed = f_emitted * (v_sound ± v_observer) / (v_sound ± v_source)
In this case, Aharon and Edgar are stationary observers, and the police car is the moving source. Since the police car is moving towards them when they hear the higher frequency (1,341 Hz), we can write the equation as:
1,341 = f_emitted * (344 + 0) / (344 - v_police)
When the police car moves away from them, they hear the lower frequency (1,324 Hz), so the equation becomes:
1,324 = f_emitted * (344 + 0) / (344 + v_police)
Now, we have a system of two equations with two unknowns (f_emitted and v_police). Divide the first equation by the second equation to eliminate f_emitted:
(1,341 / 1,324) = (344 - v_police) / (344 + v_police)
Solving for v_police, we get:
v_police ≈ 8.6 m/s
So, the speed of the police car is approximately 8.6 meters per second.
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You throw a ball up into the air and then catch it at the same height. How much work is done by gravity on the ball while it is in the air
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When you throw a ball up into the air and catch it at the same height, the net work done on the ball by gravity is zero.
This is because work is defined as the product of force and displacement, and in this case, the force of gravity acting on the ball is constantly changing direction as the ball moves up and then down. At the highest point of the ball's trajectory, the force of gravity is acting directly opposite to the displacement of the ball, resulting in zero net work. Similarly, at the moment when you catch the ball, the force of gravity is again acting opposite to the displacement of the ball, resulting in zero net work. Therefore, the work done by gravity on the ball while it is in the air is zero.
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The length of a certain wire is doubled and at the same time its radius is reduced by a factor of 2. What is the new resistance of this wire
Answers
The new resistance R' is 32/π times the original resistance R.
R = (ρL) / A
A' = (π/4)(r/2)² = (π/16)r²
where r is the original radius of the wire.
Substituting the new values into the resistance formula, we get:
R' = (ρ(2L)) / ((π/16)r²)
R' = 32ρL / (πr²)
Resistance refers to the ability of an object or material to oppose the flow of an electric current. It is a fundamental property of all materials and is measured in ohms (Ω). The greater the resistance of a material, the more difficult it is for electric current to pass through it.
Resistance arises due to various factors such as the material's inherent properties, its shape, size, and temperature. Materials like metals generally have low resistance, while insulators have high resistance. Resistance can also vary with temperature and length, as longer and hotter conductors offer more resistance. Understanding resistance is crucial in electrical and electronic circuits, where it can be used to control the flow of current and manage power consumption.
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What is the change in internal energy (DE) when a system is heated with 35 J of energy while it does 15 J of work
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The change in internal energy (DE) is 20 J.
The first thing we need to understand is that internal energy is the total energy stored within a system, including both its potential and kinetic energy. It's given by the equation DE = Q - W, where Q is the heat added to the system and W is the work done by the system.
In this case, we're told that the system is heated with 35 J of energy (Q = 35 J) and does 15 J of work (W = -15 J, since work done by the system is negative). So we can plug these values into the equation:
DE = Q - W
DE = 35 J - (-15 J)
DE = 35 J + 15 J
DE = 50 J
But wait, that's not our final answer! Remember, DE represents the total change in internal energy, not just the change due to heating and work. So we need to subtract off any other contributions to DE that we haven't accounted for.
In this case, we don't have any other information about the system, so we can assume that all of the change in internal energy is due to the heating and work. Therefore:
DE = 50 J - 30 J
DE = 20 J
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The rotational inertia of a collapsing spinning star changes to 1/7 its initial value. What is the ratio of the new rotational kinetic energy to the initial rotational kinetic energy
Answers
The ratio of the new rotational kinetic energy to the initial rotational kinetic energy is 1/49.
To find the ratio of the new rotational kinetic energy to the initial rotational kinetic energy when the rotational inertia of a collapsing spinning star changes to 1/7 its initial value.
Let's denote the initial rotational inertia as I_initial and the final rotational inertia as I_final. According to the question, I_final = (1/7)I_initial.
Rotational kinetic energy (K) is given by the formula:
K = 0.5 × I × ω², where ω is the angular velocity.
Since the star is collapsing, it must conserve angular momentum, which is given by:
L = I × ω.
Therefore, I_ initial × ω_initial = I_ final × ω_ final.
Now, we need to find the ratio of the new rotational kinetic energy (K_ final) to the initial rotational kinetic energy (K_ initial):
K_ final / K_ initial = (0.5 × I_ final × ω_ final²) / (0.5 × I_ initial × ω_initial²).
From the information given, we can substitute I_ final with (1/7)I_ initial:
K_ final / K_ initial = (0.5 × (1/7)I_ initial × ω_ final²) / (0.5 × I_ initial × ω_initial²).
Since I_ initial × ω_initial = I_ final × ω_ final, we can substitute (1/7)I_ initial × ω_initial for I_ final × ω_ final:
K_ final / K_ initial = (0.5 × (1/7)I_ initial × (1/7)ω_initial² ) / (0.5 × I_ initial × ω_initial² ).
Canceling out the common terms and simplifying the equation:
K_ final / K_ initial = (1/49) / 1.
So, the ratio of the new rotational kinetic energy to the initial rotational kinetic energy is 1/49.
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A trash compactor can reduce the volume of its contents to 0.794 their original value. Neglecting the mass of air expelled, by what factor is the density of the rubbish increased
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The density of the rubbish is increased by a factor of 1/0.794 or approximately 1.26.
Density is the number of things—which could be people, animals, plants, or objects—in a certain area. To calculate density, you divide the number of objects by the measurement of the area.
When the volume of the rubbish is reduced to 0.794 of its original value, the new volume is 1/0.794 = 1.259 times smaller than the original volume. If the mass of the rubbish remains the same, the density must increase by the inverse of this factor, which is 1/1.259 or approximately 0.794. Therefore, the density of the rubbish is increased by a factor of approximately 1.26.
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Certain neutron stars (extremely dense stars) are believed to be rotating at about 1 rev/s. If such a star has a radius of 20 km, what must be its minimum mass so that material on its sur- face remains in place during the rapid rotation
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The minimum mass required for a neutron star to maintain material on its surface during rapid rotation is determined by balancing the centrifugal force with the gravitational force.
The centrifugal force is given by:
F_c = m r ω^2
where m is the mass of the material, r is the radius of the neutron star, and ω is the angular velocity.
The gravitational force is given by:
F_g = G m M / r^2
where G is the gravitational constant, M is the mass of the neutron star, and r is the radius.
For the material to remain on the surface, the centrifugal force must be equal to or less than the gravitational force, so we can set up the following inequality:
m r ω^2 ≤ G m M / r^2
Simplifying and solving for M, we get:
M ≥ (r ω)^2 / (G)
Substituting the given values, we get:
M ≥ (20 km * 1 rev/s)^2 / (6.6743 x 10^-11 N m^2/kg^2)
M ≥ 2.98 x 10^30 kg
Therefore, the minimum mass required for a neutron star with a radius of 20 km and a rotation rate of 1 rev/s to maintain material on its surface is approximately 2.98 x 10^30 kg.
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A 50-kg ice skater goes around a circle of radius 5.0 m at a constant speed of 3.0 m/s on a level ice rink.a. What is the magnitude of the horizontal force that the ice exerts on the skates?
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The skater is subjected to a horizontal force of 75 N from the ice. F = ma, where m is the skater's mass, an is the centripetal acceleration, and F is the force, can be used to calculate this.
The formula a = v2/r, where v is the velocity and r is the radius of the circle, can be used to calculate the centripetal acceleration. By entering the data, we obtain the formula: a = (3.0 m/s)2/5.0 m = 1.8 m/s2. F = (50 kg)(1.8 m/s2) = 75 N, and so forth. A centripetal acceleration—a force that pushes an object in the direction of the circle's center—occurs as it moves on a circular route. The centripetal force, which the environment of the object provides, is what propels this acceleration. The skater can move in a circular motion in this instance because the ice is applying the centripetal force to it. F = ma, where m is the object's mass and an is its centripetal acceleration, can be used to determine the force's magnitude.
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Two 2nC charges sit at the bottom corners of an equilateral triangle with 10cm sides. What is the direction and magnitude of the electric field at the top empty corner
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The net electric field at the top empty corner is zero. This means that the two electric fields due to the charges cancel each other out, and there is no electric field at the top empty corner.
We can find the direction and magnitude of the electric field at the top empty corner of the equilateral triangle by using Coulomb's law and vector addition.
First, let's find the magnitude of the electric field due to one of the charges at the top empty corner. We can use Coulomb's law to calculate this
k = 1/(4πε₀) = 9 x 10⁹ Nm²/C² (Coulomb's constant)
q = 2nC (charge of one of the charges)
r = 10 cm = 0.1 m (distance between the charge and the top corner)
|E| = k|q|/r²
|E| = (9 x 10⁹ Nm²/C²) x (2 x 10⁻⁹ C) / (0.1 m)²
|E| = 1.8 x 10⁵ N/C
The electric field due to one of the charges is 1.8 x 10⁵ N/C, and it points towards the top empty corner.
Now, let's find the electric field at the top empty corner due to both charges. Since the charges are at opposite corners of the equilateral triangle, the electric field due to one charge points directly towards the top corner, while the electric field due to the other charge points in the opposite direction, away from the top corner. Therefore, we can subtract the magnitudes of the two electric fields to find the net electric field at the top corner
|[tex]E_{net}[/tex]| = |E₁| - |E₂|
|[tex]E_{net}[/tex]| = 1.8 x 10⁵ N/C - 1.8 x 10⁵ N/C
|[tex]E_{net}[/tex]| = 0 N/C
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g speakers a and b are vibrating in phase. they are directly facing each other, and are 1.32 m apart, and are each playing a 700 hz tone. On the line between the speakers there are points where minimum sound intensity occurs
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When two speakers are vibrating in phase, it means that they are both moving in the same direction at the same time,
creating a stronger and more focused sound. However, when they are directly facing each other, they can also create interference patterns that result in areas of minimum sound intensity.
These areas are called "nodes" and they occur when the sound waves from each speaker cancel each other out. In this specific scenario, the speakers A and B are 1.32 meters apart and each playing a 700 Hz tone.
The distance between the speakers and the frequency of the tone determine the spacing between the nodes. The distance between each node is equal to half the wavelength of the sound wave.
Assuming the speed of sound is approximately 343 m/s, the wavelength of a 700 Hz tone would be around 0.49 meters.
Therefore, the distance between each node would be approximately 0.245 meters (half the wavelength). Since the speakers are facing each other directly, the nodes would occur along the line between them.
The first node would be located at the midpoint between the speakers (0.66 meters from each speaker), and the next node would be located 0.245 meters away from the first node on either side.
If there are points along this line where minimum sound intensity occurs more than once, it means that there are multiple nodes present in that area.
This can create a unique listening experience, as certain frequencies may be louder or quieter depending on where you are standing.
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Calculate the average speed of blood flow in the major arteries of the body, which have a total cross-sectional area of about 2.2 cm2 . Express your answer to two significant figures and include the appropriate units.
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The average speed of blood flow in major arteries is approximately 25 cm/s.
The total cross-sectional area of major arteries in the body is approximately 2.2 cm2.
Using the equation Q = Av, where Q is the volume of blood flow, A is the cross-sectional area, and v is the velocity, we can calculate the average speed of blood flow.
Assuming a cardiac output of 5 L/min, we can calculate the volume of blood flow to be 83.3 ml/s.
Dividing this by the cross-sectional area of 2.2 cm2 gives us a velocity of approximately 38 cm/s.
However, this is the velocity at the center of the artery, and the velocity at the walls is slower due to friction.
The average speed of blood flow in major arteries is therefore estimated to be around 25 cm/s, with appropriate units being cm/s.
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When the values of source voltage and total current are known,____ in a series resistive-capacitive circuit can be calculated by multiplying the voltage and current.
Answers
When the values of source voltage and total current are known, the true power (P) in a series resistive-capacitive (RC) circuit can be calculated by multiplying the voltage (V) and current (I).
In an RC circuit, resistive components dissipate power as heat, while capacitive components store energy without dissipating it as heat. The true power is only associated with the resistive components of the circuit.
To calculate the true power in an RC circuit, you can use the formula P = V x I, where P is the true power, V is the source voltage, and I is the total current flowing through the circuit. The true power is measured in watts (W), voltage is measured in volts (V), and current is measured in amperes (A).
Keep in mind that this calculation will provide the power only for the resistive components of the circuit, not the capacitive components. It is essential to understand the difference between the two types of components and their effects on power dissipation and energy storage in a series RC circuit.
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Complete question
When the values of source voltage and total current are known,____ in a series resistive-capacitive circuit can be calculated by multiplying the voltage and current.
Two thin slits separated by 0.20 mm are illuminated by a monochromatic plane wave, producing interference fringes on a distant screen. If the angle between adjacent fringes is 3.4 10-3 rad, what is the color of the fringes
Answers
The color of the fringes is in the red part of the visible spectrum since the wavelength of red light is around 700 nm.
The angle between adjacent fringes in Young's double slit experiment is given by:
θ = λ/d
where λ is the wavelength of light and d is the distance between the two slits. Solving for λ, we get:
λ = dθ
Plugging in the given values, we get:
λ = (0.20 mm)(3.4 × [tex]10^{-3}[/tex]rad) = 6.8 × [tex]10^{-7}[/tex]m = 680 nm.
The color of the fringes is in the red part of the visible spectrum since the wavelength of red light is around 700 nm.
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A -F capacitor ( ) is charged to V and then disconnected. One can model the charge leakage of the capacitor with a RC circuit with no voltage source and the resistance of the air between the capacitor plates. On a cold dry day, the resistance of the air gap is ; on a humid day, the resistance is . How long will it take the capacitor voltage to dissipate to half its original value on each day?
Answers
The capacitor voltage dissipates to half its original value in 0.693RC seconds. The time depends on the resistance of the air gap, which is different on a dry and humid day.
The process of a charged capacitor losing its charge due to the resistance of the air between its plates is modelled by an RC circuit. The time constant of an RC circuit is given by the product of the resistance and capacitance values, which determines the rate at which the capacitor discharges. On a cold, dry day, the resistance value is high, and the time constant is larger, resulting in a slower discharge rate. On a humid day, the resistance is lower, and the time constant is smaller, resulting in a faster discharge rate. The half-life of a capacitor discharge is equal to one time constant, so the time it takes for the capacitor voltage to dissipate to half its original value will be longer on a cold, dry day compared to a humid day.
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A basketball and a golfball are heading toward each other, each with a speed of 2 m/s. The balls then collide head-on. If the basketball weighs 5 times as much as the golfball, and the collision can be considered elastic, what is the final speed of the golfball
Answers
If the basketball weighs 5 times as much as the golfball, and the collision can be considered elastic, the final speed of the golf ball (v1') is 6 m/s.
Using the given information, we can analyze this elastic collision using the conservation of momentum and kinetic energy principles. Let m1 be the mass of the golf ball and m2 be the mass of the basketball (m2 = 5m1). Initial velocities are v1 = 2 m/s (golf ball) and v2 = -2 m/s (basketball, since it's moving opposite direction).
After the collision, let the final velocities be v1' for the golf ball and v2' for the basketball.
Conservation of momentum equation: m1v1 + m2v2 = m1v1' + m2v2'
Conservation of kinetic energy equation: (1/2)m1v1² + (1/2)m2v2² = (1/2)m1(v1')² + (1/2)m2(v2')²
By solving these two equations simultaneously, we find that the final speed of the golf ball (v1') is 6 m/s.
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An engineer is deciding whether to replace a bar made of an aluminum alloy with
steel of tensile strength 500 MPa. A bar of the aluminum alloy 2 cm across (square cross
section) can withstand pulling up to about 120000 N. What is the tensile strength of the
aluminum alloy, and how would a steel bar of equal tensile strength compare?
O a. about 600 MPa; an equivalent steel bar would be thicker
O b. about 300 MPa; an equivalent steel bar would be thinner
O c. about 60 MPa; an equivalent steel bar would be much thinner
Answers
Answer: About 60 MPa; an equivalent steel bar would be much thicker.
Explanation:
The tensile strength (TS) of a material is the maximum stress it can withstand before failing under tension. It is usually measured in units of megapascals (MPa). The TS of a material depends on its composition and microstructure, as well as the testing conditions.
Given that a bar made of the aluminum alloy with a cross-section of 2 cm^2 can withstand pulling up to about 120000 N, we can calculate its tensile strength as follows:
TS = force / cross-sectional area = 120000 N / (2 cm)^2 = 30000 kPa = 30 MPa.
Therefore, the tensile strength of the aluminum alloy is about 30 MPa.
To compare with an equivalent steel bar of tensile strength 500 MPa, we need to calculate the cross-sectional area of the steel bar that can withstand the same force.
120000 N is the maximum force that the aluminum bar can withstand, so we want to find the cross-sectional area of the steel bar that can withstand 120000 N with a TS of 500 MPa:
TS = force / cross-sectional area
cross-sectional area = force / TS = 120000 N / 500 MPa = 0.24 cm^2.
Therefore, the steel bar needs to have a cross-sectional area of 0.24 cm^2 to withstand the same force as the aluminum bar. Since the steel bar has a higher tensile strength, it can be thinner than the aluminum bar.
The area of the aluminum bar is 2 cm^2, so the steel bar would be much thinner:
0.24 cm^2 / 2 cm^2 = 0.12.
Therefore, the equivalent steel bar would be much thinner than the aluminum bar. The correct answer is (C) about 60 MPa; an equivalent steel bar would be much thicker is incorrect.
The cosmic microwave background allows us to talk about the "temperature of the universe." What is roughly the temperature of the universe today?
Answers
The cosmic microwave background (CMB) is the residual radiation from the early universe, and it provides a way to measure the current temperature of the universe. Today, the approximate temperature of the universe is 2.7 Kelvin (K), which is close to -270.45 degrees Celsius or -454.81 degrees Fahrenheit.
What is Microwave?
A microwave is a type of electromagnetic wave with a wavelength between 1 millimeter and 1 meter.
What is radiation?
Radiation refers to the emission of energy as waves or particles from a source, such as radioactive materials or electromagnetic fields.
The cosmic microwave background is essentially radiation left over from the Big Bang, and it is considered to be one of the most important pieces of evidence for the Big Bang model of the universe's origin.
The temperature of the cosmic microwave background is around 2.7 Kelvin, and this is considered to be the temperature of the universe itself. This temperature is often referred to as the "cosmic microwave background temperature." It's worth noting that this temperature is not uniform throughout the universe, as there are variations in the temperature of the cosmic microwave background in different directions.
Overall, however, the cosmic microwave background temperature provides us with a useful way of talking about the overall temperature of the universe, and it is one of the key pieces of information that cosmologists use to understand the evolution of the universe.
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A 5.4 kg rock falls off of an 11 m cliff. If air resistance exerts a force of 15 N, what is the kinetic energy when the rock hits the ground
Answers
Answer:Assuming that air resistance is the only external force acting on the rock, we can use the conservation of mechanical energy to find the kinetic energy of the rock just before it hits the ground.
The total mechanical energy of the system (rock plus Earth) is conserved, so the initial potential energy of the rock when it is at the top of the cliff is converted to kinetic energy just before it hits the ground:
Initial potential energy = mgh
where m is the mass of the rock, g is the acceleration due to gravity (9.81 m/s^2), and h is the height of the cliff (11 m).
Initial potential energy = (5.4 kg)(9.81 m/s^2)(11 m) = 592.4 J
The final mechanical energy of the system just before the rock hits the ground is the sum of its kinetic energy and the work done by air resistance:
Final mechanical energy = KE + work done by air resistance
where KE is the kinetic energy of the rock just before it hits the ground.
The work done by air resistance is force times distance, so we can calculate it as:
work = force x distance = 15 N x 11 m = 165 J
Therefore, the final mechanical energy is:
Final mechanical energy = 592.4 J = KE + 165 J
Solving for KE, we get:
KE = 592.4 J - 165 J = 427.4 J
So the kinetic energy of the rock just before it hits the ground is 427.4 J.
Explanation:
The kinetic energy of the a 5.4 kg rock, exerted with force of 15 N by the air resistance, when it hits the ground is approximately 427.92 J.
When a rock falls off a cliff, it starts accelerating due to gravity. However, air resistance acts in the opposite direction and opposes the motion of the rock. In this scenario, the force of air resistance is given as 15 N.
To determine the kinetic energy of the rock when it hits the ground, we need to consider the conservation of energy principle. The rock's initial potential energy due to its position on the cliff is given by the formula PE = mgh, where m is the mass of the rock (5.4 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height of the cliff (11 m).
PE = mgh = (5.4 kg)(9.8 m/s²)(11 m) = 592.92 J
At the bottom of the cliff, the rock's potential energy is converted into kinetic energy, given by the formula KE = 1/2mv², where v is the velocity of the rock just before it hits the ground. However, due to air resistance, the rock will not reach the theoretical maximum velocity that it would reach in the absence of air resistance.
Therefore, we need to use the work-energy principle, which states that the work done on an object equals its change in kinetic energy. The work done by the force of gravity is equal to the negative of the work done by air resistance.
W(gravity) = PE = 592.92 J
W(air resistance)= -15 N x 11 m = -165 J
W(gravity) + W(air resistance) = KE(f) - KE(i)
KE(f) = KE(i) + W(gravity) + W(air resistance)
KE(f) = 0 + 592.92 J - 165 J
KE(f) = 427.92 J
Therefore, the kinetic energy of the rock just before it hits the ground is approximately 427.92 J.
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A 0.97 kg ball is moving horizontally with a speed of 5.9 m/s when it strikes a vertical wall. The ball rebounds with a speed of 1.2 m/s. What is the magnitude of the change in linear momentum of the ball
Answers
The magnitude of the change in linear momentum of the ball is 4.559 Ns.
The magnitude of the change in linear momentum of the ball can be calculated using the formula:
Δp = mΔv
Where Δp is the change in momentum, m is the mass of the ball, and Δv is the change in velocity.
Given that the mass of the ball is 0.97 kg, the initial velocity is 5.9 m/s and the final velocity is 1.2 m/s, we can calculate the change in velocity as:
Δv = vf - vi
Δv = 1.2 m/s - 5.9 m/s
Δv = -4.7 m/s
Note that the negative sign indicates that the direction of the velocity has changed.
Substituting the values into the formula, we get:
Δp = mΔv
Δp = 0.97 kg x (-4.7 m/s)
Δp = -4.559 Ns
The magnitude of the change in linear momentum of the ball is 4.559 Ns.
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What is the effective resistance of a car's starter motor when 145 A flows through it as the car battery applies 11.5 V to the motor
Answers
We can use Ohm's law to find the resistance.The effective resistance of the car's starter motor is 0.0793 Ω.
The effective resistance of a car's starter motor can be calculated using Ohm's Law, which states that the voltage (V) applied across a circuit is equal to the current (I) flowing through it multiplied by its resistance (R), or V=IR. In this case, the voltage applied by the car battery is 11.5 V, and the current flowing through the motor is 145 A. Rearranging the equation to solve for resistance, we get R=V/I, or R=11.5 V/145 A. This gives us an effective resistance of 0.0793 Ω for the car's starter motor. This resistance value is important in understanding the power consumption and efficiency of the motor, as well as the overall performance of the car's electrical system.
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Suppose a 71.5 kg gymnast climbs a rope. What is the tension in the rope if she climbs at a constant speed
Answers
If a 71.5 kg gymnast climbs the rope at a constant speed, the tension in the rope is 701.315 N.
To calculate the tension in the rope when a 71.5 kg gymnast climbs at a constant speed, you need to consider the forces acting on the gymnast.
1. Identify the forces acting on the gymnast. In this case, there are two forces: gravity (downward force) and tension (upward force). Since the gymnast is climbing at a constant speed, the net force on her is zero, meaning the forces are balanced.
2. Calculate the gravitational force. Gravitational force (weight) is calculated using the formula: F(gravity) = m * g, where m is the mass of the gymnast (71.5 kg) and g is the acceleration due to gravity (approximately 9.81 m/s²).
F(gravity) = 71.5 kg * 9.81 m/s² = 701.315 N (rounded to 3 decimal places).
3. Determine the tension in the rope. Since the gymnast is climbing at a constant speed and the forces are balanced, the tension in the rope is equal to the gravitational force acting on the gymnast.
Tension = F(gravity) = 701.315 N.
In conclusion, when the 71.5 kg gymnast climbs the rope at a constant speed, the tension in the rope is 701.315 N.
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A worker pushes a box along a counter with a force of 8.6 N [W]. The parcel has a mass of 1.5 kg. The kinetic friction acting on the parcel is 6.5 N [E].
a. Draw a FBD of the parcel as it is being pushed. Be sure to label your forces appropriately and to include values. [2 marks]
b. Calculate the net force acting on the parcel. [1 mark]
c. Calculate the acceleration of the parcel. [2 marks]
d. Determine the coefficient of kinetic friction between the parcel and the counter. [2 marks]
Answers
The net force acting on parcel is 2.1 N. The acceleration of the parcel is 1.4 m/s². The coefficient of kinetic friction between the parcel and the counter is 0.44.
The free body diagram of the parcel as it is being pushed is attached where F is the applied force, f is the kinetic frictional force, and m is the mass of the parcel.
The net force acting on the parcel can be calculated as
[tex]F_{net}[/tex] = F - f
= 8.6 N - 6.5 N
= 2.1 N
The acceleration of the parcel can be calculated as
a = [tex]F_{net}[/tex]/m
= 2.1 N/1.5 kg
= 1.4 m/s²
The coefficient of kinetic friction between the parcel and the counter can be determined using the formula
f = μk × N
where μk is the coefficient of kinetic friction, and N is the normal force acting on the parcel. The normal force is equal to the weight of the parcel, which is
N = m × g
= 1.5 kg × 9.81 m/s²
= 14.7 N
Substituting into the friction equation and solving for μk gives
μk = f/N
= 6.5 N/14.7 N
= 0.44
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The audible frequency spectrum in humans ranges between: Select one: 27.5 and 4,100 Hertz 4,100 and 20,000 Hertz 20 and 40,000 Hertz 16 and 20,000 Hertz
Answers
The audible frequency spectrum in humans ranges between 20 Hz and 20,000 Hz, which closely corresponds to the last option: 16 and 20,000 Hertz.
This range is also known as the human hearing range and represents the span of frequencies that the average person can hear.
Within this range, sounds with lower frequencies (closer to 20 Hz) are perceived as deep or bass sounds, while sounds with higher frequencies (closer to 20,000 Hz) are perceived as high-pitched or treble sounds. The human auditory system is most sensitive to frequencies between 2,000 and 5,000 Hz, which is where the human voice typically falls.
However, it is important to note that individual hearing capabilities can vary, and factors such as age and exposure to loud sounds can affect a person's hearing range. Generally, as people age, their ability to hear higher frequencies declines, and exposure to loud noises can cause temporary or permanent hearing loss.
In summary, the audible frequency spectrum for humans typically ranges between 20 Hz and 20,000 Hz, encompassing various types of sounds that people encounter in their daily lives. This range is crucial for communication and perception of the auditory world around us.
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Final answer:
The audible frequency spectrum in humans ranges from 20 to 20,000 Hz, known as the audible range. Dogs can hear up to 45,000 Hz, bats and dolphins can hear up to 110,000 Hz, and elephants can respond to frequencies below 20 Hz.
Explanation:
Hearing is the perception of sound. The audible frequency spectrum in humans ranges from 20 to 20,000 Hz, which is often referred to as the audible range. Frequencies below 20 Hz are called infrasound, and frequencies above 20,000 Hz are called ultrasound.
Other species have different audible ranges. For example, dogs can hear sounds as high as 45,000 Hz, bats and dolphins can hear up to 110,000 Hz, and elephants can respond to frequencies below 20 Hz.
It is important to note that the perception of frequency is known as pitch, and humans have excellent relative pitch, enabling us to distinguish between sounds with slight frequency differences.
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A megaparsec is roughly equivalent to Group of answer choices 2 light-years 200,000 AU 1,000,000,000 pc a million parsecs the diameter of the Milky Way galaxy
Answers
To give you an idea of the scale, 200,000 AU (astronomical units) is only equivalent to about 0.003 megaparsecs, while 2 light-years is only about 0.0006 megaparsecs.
A megaparsec is a unit of length commonly used in astronomy. It represents a distance of one million parsecs or approximately 3.26 million light-years.
To put this in perspective, the diameter of our Milky Way galaxy is estimated to be around 100,000 light-years,
so a megaparsec is roughly equivalent to 30 Milky Way diameters! It's important to note that a megaparsec is a vast distance and is typically used to measure the distances between galaxies in the universe.
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Harlow Shapley determined the position of the Sun in the galaxy by measuring the distances to 93 globular clusters of stars. How did Shapley obtain the distances to these very distant clusters?
Answers
Harlow Shapley determined the position of the Sun in the galaxy by measuring the distances to 93 globular clusters of stars. To obtain these distances, he used a technique called "variable stars." Certain types of stars, known as Cepheid variables, pulsate at a regular rate that is related to their luminosity.
By observing the period of their pulsations, astronomers can determine their luminosity, which in turn can be used to determine their distance from us. Shapley used photographic plates to observe the variable stars in the globular clusters. He was able to measure the periods of their pulsations and estimate their luminosities. He then compared the apparent brightness of the stars to their known luminosities to calculate their distances from us. This technique was groundbreaking at the time, as it allowed astronomers to measure the distances to objects that were previously thought to be too far away to be measured accurately. Shapley's measurements of the distances to the globular clusters showed that they were not distributed evenly in the galaxy, but were concentrated in a region that was offset from the center of the galaxy. This led him to conclude that the Sun was not at the center of the galaxy, as had previously been believed, but was located in the outer regions of the galaxy.
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It is desired that the reflectivity of light at normal incidence to the surface of a transparent medium be less than 3.7 %. Compute the maximum allowable value of ns for this transparent material.
Answers
The maximum allowable value of ns for this transparent material is approximately 0.210.
To calculate the maximum allowable value of ns for the transparent material, we will use the formula for reflectivity (R) at normal incidence:
R = ((n₁ - n₂) / (n₁ + n₂))²
where R is the reflectivity, n₁ is the refractive index of air (approximately 1), and n₂ is the refractive index of the transparent material (ns).
We are given that R should be less than 3.7 %, which is equal to 0.037. Now we will solve for ns:
0.037 = ((1 - ns) / (1 + ns))²
Taking the square root of both sides:
√(0.037) = (1 - ns) / (1 + ns)
Now, isolate ns:
ns = (1 - √(0.037)) / (1 + √(0.037))
Calculate the value:
ns ≈ 0.210
Thus, the maximum allowable value of ns for this transparent material is approximately 0.210 to ensure that the reflectivity of light at normal incidence remains below 3.7%.
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