The correct option is (c) 3.55 Times 10^7 Ohm^-1 m^-1. Conductivity is defined as the reciprocal of resistivity.
We can calculate the conductivity of a 5.5 m long aluminum wire that has a resistance of 0.40 ω and
ρ=2.82 x 10^-8 ωm and
α=4.29x10^-3 oc^-1 as follows:
Formula of resistance of the wire: R=ρL/A
Where, R is the resistance of the wire, L is the length of the wire, ρ is the resistivity of the wire material, and A is the cross-sectional area of the wire.
Rearrange the formula to solve for A:
A = (ρL)/R,
Substitute given values: L = 5.5 m,
ρ = 2.82 x 10^-8 ωm, and
R = 0.40 ω.
A = (2.82 x 10^-8 ωm × 5.5 m) / (0.40 ω)
A = 3.849 x 10^-7 m^2
Calculate the diameter of the wire:
Diameter = √[(4A)/π]
Diameter = √[(4 × 3.849 x 10^-7 m^2) / π]
Diameter = 2.212 x 10^-4 m.
Calculate the change in length of the wire:
ΔL = αLΔT
Where, α is the coefficient of linear expansion of aluminum, ΔT is the change in temperature.
Substituting values in the above formula,
ΔL = 4.29 x 10^-3
oc^-1 × 5.5 m × 60
oc = 1.9677 m.
Calculate the final length of the wire:
Final length = initial length + change in length,
Final length = 5.5 m + 1.9677 m
Final length = 7.4677 m.
The resistance of the wire is given by the formula:
R = (ρL) / A
Substituting the given values,
R = (2.82 × 10-8 ωm) (7.4677 m) / (π × (2.212 × 10-4 m)2)
R = 0.394 ω
Conductivity is defined as the reciprocal of resistivity i.e.,
σ = 1/ρ
Substitute the given value of resistivity in the above formula:
σ = 1 / 2.82 x 10^-8 ωm
σ = 3.55 x 10^7 ohm^-1 m^-1.
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calculate the mass of each of a solid with a volume of 1.68ft^3 and a density of 9.2g/ml
The mass of the solid with a volume of 1.68 ft and density of 9.2g/ml is 14.85 kilograms.
To calculate the mass of the solid, we need to use the formula: Mass = Density × Volume.
First, we need to convert the volume from cubic feet to milliliters, as the density is given in grams per milliliter.
1 cubic foot is equal to 28,316.8466 milliliters (ml). So, the volume of the solid is 1.68 ft^3 × 28,316.8466 ml/ft^3 = 47,594.768 ml.
Now, we can calculate the mass by multiplying the density (9.2 g/ml) by the volume (47,594.768 ml).
Mass = 9.2 g/ml × 47,594.768 ml = 437,186.38 grams.
Finally, we convert grams to kilograms by dividing by 1,000, resulting in a mass of approximately 437.19 kilograms or rounded to 14.85 kilograms.
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Birds sitting on a single power line don't get shocked. But if they were to place one foot on each of two lines, ___________ would flow between them and they would receive a terrible shock
When birds sit on a single power line, they are not grounded, which means they do not provide a path for current to flow from the high voltage power line through their body to the ground. But if they were to place one foot on each of two lines, they would complete a circuit, and current would flow through their body, and they would receive a terrible shock.
Electricity flows through a circuit when there is a path for current to flow from a power source to the ground. The power lines carry high voltage electricity, which can be dangerous to living organisms, including birds. However, birds sitting on a single power line don't get shocked because they are not providing a path for current to flow from the power line through their body to the ground.The reason birds are not grounded when they sit on a single power line is that they have only one point of contact with the power line.
Therefore, the current cannot flow through their body and reach the ground. In other words, they are not part of the circuit.In conclusion, birds sitting on a single power line do not get shocked because they are not grounded and do not provide a path for current to flow through their body to the ground. However, if they were to place one foot on each of two lines, they would complete a circuit, and current would flow through their body, resulting in a terrible shock.
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If the back of a person's eye is too close to the lens, this person is suffering from a) chromatic aberration b)nearsightedness c)astigmatism d)farsightedness e)spherical aberration
If the back of a person's eye is too close to the lens, this person is suffering from b) nearsightedness, also known as myopia.
Nearsightedness is a common refractive error that affects the ability to see distant objects clearly. In this condition, the eyeball is slightly elongated or the cornea is too curved, causing light rays to focus in front of the retina rather than directly on it.
When the back of the eye is too close to the lens, it means that the distance between the lens and the retina is too short. As a result, light entering the eye converges too much before reaching the retina, causing the image formed on the retina to be blurry. Nearsighted individuals typically have clear vision for objects that are up close, but struggle with distant objects.
To correct nearsightedness, concave lenses are used to diverge the incoming light rays before they reach the eye, effectively moving the focal point farther back and allowing the image to focus properly on the retina. These corrective lenses help to compensate for the longer-than-normal eyeball length or excessive corneal curvature, enabling the person to see distant objects more clearly.
In summary, if the back of a person's eye is too close to the lens, they are likely suffering from nearsightedness (myopia). This condition can be corrected with the use of concave lenses to adjust the focal point and improve distance vision.
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What is the relationship between the valence electrons of an atom and the chemical bonds the atom can form?
Answer:
Valence electrons are outer shell electrons with an atom and can participate in the formation of chemical bonds. In single covalent bonds, typically both atoms in the bond contribute one valence electron in order to form a shared pair. The ground state of an atom is the lowest energy state of the atom.
The Earth has a gravitational pull on a single nitrogen molecule (N2) in the air. In comparison, the gravitational pull of the nitrogen molecule on the Earth is:
1.) Weaker, but, no zero.
2.) Zero.
3.) The same size.
4.) Stronger.
The mean orbital radius of the earth around the sun 1.5 × 108 km. Calculate the
mass of the sun if G = 6.67 × 10-11 Nm2/kg -2?
Answer:
M = 1.994 × 10^(30) kg
Explanation:
We are given;
Orbital radius; r = 1.5 × 10^(8) km = 1.5 × 10^(11) m
Gravitational constant; G = 6.67 × 10^(-11) N.m²/kg²
If the orbit is circular, the it means the gravitational force is equal to the centripetal force.
Thus; F_g = F_c
GMm/r² = mv²/r
Simplifying gives;
GM/r = v²
M = v²r/G
Now, v is the speed of the earth around the sun and from online sources it has a value of around 29.78 km/s = 29780 m/s
Thus;
M = (29780^(2) × 1.5 × 10^(11))/6.67 × 10^(-11)
M = 1.994 × 10^(30) kg
A block of wood is floating in a pool of water. One third of the block is above the surface of the water. Discuss the buoyant force that is acting on the log. Is the buoyant force greater than, less than or equal to the weight of the block? Explain your answer. Is the volume of water displaces by the block greater than, less than or equal to the volume of the block? Explain your answer after watching the following video.
The required,
The buoyant force is equivalent to the weight of the block.The volume of water displaced by the block is equal to the volume of the submerged portion of the block, which is two-thirds of the total volume of the block.The buoyant force functioning on the block of wood is equal to the weight of the water displaced by the block. According to Archimedes' principle, when an object is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid it displaces.
In this case, one-third of the block is above the surface of the water, which signifies two-thirds of the block is submerged. The buoyant force is equal to the weight of the water displaced by the submerged portion of the block.
Since the block is floating, it is in equilibrium, which means the buoyant force is equal to the weight of the block. If the buoyant force were more significant than the weight of the block, the block would rise to the surface and float higher. If the buoyant force were less than the weight of the block, the block would sink.
Therefore, the buoyant force is equal to the weight of the block. Both forces have the same magnitude but act in opposite directions. The weight of the block acts downward, while the buoyant force acts upward.
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Three resistors R1= 3 Ω, R2= 5 Ω, and R3 = 2 Ω are connected with 150 V power supply. What is the voltage across R2 ?
a.75 V
b.15 V
c.10 V
d.32 V
If the resistors are in series, it's 75 volts.
If they're in parallel, it's 150 volts.
You never told us series or parallel.
Is Algae Biotic or Abiotic?
An electron and a proton are fixed at a separation distance of 911 nm. Find the magnitude and direction of the electric field at their midpoint Magnitude: Number 1.388 x 104 N/ C Direction: O Toward the electrorn O Toward the proton Perpendicular to the line of the particles O Cannot be determined
The direction of the electric field at the midpoint is toward the proton.
Given that the separation distance between the electron and the proton is 911 nm (9.11 x 10^-7 m) and the charges of an electron and a proton are equal in magnitude but opposite in sign, we can consider the electric field created by both charges separately.Using Coulomb's law, the magnitude of the electric field created by each charge at the midpoint is calculated as E = k * (|q| / r^2), where k is the electrostatic constant (8.99 x 10^9 N m^2/C^2), |q| is the magnitude of the charge, and r is the separation distance.For each charge, |q| = 1.6 x 10^-19 C, and the separation distance is half of the initial distance, i.e., 0.5 * 9.11 x 10^-7 m = 4.555 x 10^-7 m.Calculating the electric field magnitude for each charge and adding them together, we have E = k * (|q| / r^2) + k * (|q| / r^2) = 2 * k * (|q| / r^2) ≈ 1.388 x 10^4 N/C. Thus, the magnitude of the electric field at the midpoint is approximately 1.388 x 10^4 N/C. Now, to determine the direction of the electric field at the midpoint, we consider the forces experienced by a positive test charge placed at that point. Since opposite charges attract each other, the electric field points toward the positive charge. In this case, the proton is positively charged, so the electric field is directed toward the proton. Therefore, the direction of the electric field at the midpoint is toward the proton.
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A box weighing 18 newtons requires a force of 6 newtons to drag it. the coefficient of kinetic friction is
When a box weighs 18 newtons, a force of 6 newtons is required to drag it, the coefficient of kinetic friction is 0.333. Friction is the force that opposes motion when an object is pushed along a surface or in contact with another object.
It always acts in the opposite direction to the direction of movement. There are two types of friction, kinetic friction and static friction. The friction acting on an object that is already moving is kinetic friction. Friction acting on an object that is at rest is called static friction. The coefficient of kinetic friction is the ratio of the friction force between two objects and the force pressing them together. It's a dimensionless scalar quantity. To be precise, the formula for the coefficient of kinetic friction is given as: Coefficient of Kinetic Friction = Frictional Force / Normal Force. Where, Normal Force = The perpendicular force exerted by a surface on an object in contact with it. The force required to drag the box is 6N, so the kinetic frictional force on the box is 6N. The formula for coefficient of kinetic friction is :Coefficient of Kinetic Friction = Frictional Force / Normal Force. If the force required to drag the box is 6N, then the normal force acting on the box is 18N. So, the coefficient of kinetic friction will be: Coefficient of Kinetic Friction = 6N / 18N = 0.333
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compute the kinetic energy of a proton (mass 1.67×10−27kg ) using both the nonrelativistic and relativistic expressions for speed of 9.00×107 m/s . enter your answers in joules separated by a comma.
The kinetic energy of the proton is 7.515 × 10⁻¹¹ J (nonrelativistic) and 2.144 × 10⁻¹¹ J (relativistic).
To compute the kinetic energy of a proton using both the nonrelativistic and relativistic expressions, we can use the following formulas:
1. Nonrelativistic expression:
The kinetic energy (K) of a particle is given by the formula:
K = (1/2) * m * v²
where m is the mass of the proton and v is its velocity.
Substituting the values into the formula:
K = (1/2) * (1.67 × 10⁻²⁷ kg) * (9.00 × 10⁷ m/s)²
Calculating the kinetic energy using the above formula, we get:
K = 7.515 × 10⁻¹¹ J
2. Relativistic expression:
The relativistic expression for kinetic energy takes into account the effects of special relativity and is given by the formula:
K = [(γ - 1) * m * c²]
where γ is the Lorentz factor, m is the mass of the proton, and c is the speed of light.
The Lorentz factor (γ) is given by:
γ = 1 / √(1 - (v²/c²))
Substituting the values into the formulas:
γ = 1 / √(1 - [(9.00 × 10⁷ m/s)² / (3.00 × 10⁸ m/s)²])
γ = 2.029
K = [(2.029 - 1) * (1.67 × 10⁻²⁷ kg) * (3.00 × 10⁸ m/s)²]
Calculating the kinetic energy using the above formula, we get:
K = 2.144 × 10⁻¹¹ J
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Question:
(need answers now I have time)
A freely-falling object is accelerating.
A. True
B. False
Answer:
the answer is true.
Explanation:
hope it will help you
PLS ANWSER FAST WILL GIVE BRAINL!!!!
Explain to me in YOUR own words, how convection currents create a cycle? In other words, tell me how heat and cooling create a cycle.
Answer:
because it get the energy from the heat and the cold mixed together
Explanation:
a very long, thin wire has a uniform linear charge density of 91 µc/m. what is the electric field (in n/c) at a distance 8.0 cm from the wire? (enter the magnitude.)
Therefore, the electric field (magnitude only) at a distance of 8.0 cm from the wire is approximately 3.24 x 10^4 N/C.
The electric field of a long, thin wire can be determined by Coulomb's law. Coulomb's Law states that the electric force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
For a long, thin wire, the electric field is given by;
E = λ/2πε₀r
Where;
λ = linear charge density = 91 µC/m,
ε₀ = permittivity of free space = 8.85 x 10^-12 C^2/Nm^2
r = distance from the wire = 8.0 cm = 0.08 m.
Substitute the given values into the formula to find the electric field;
E = (91 x 10^-6)/(2 x π x 8.85 x 10^-12 x 0.08)
E≈ 32433.8 N/C
E≈ 3.24 x 10^4 N/C.
Electric field refers to the force per unit charge that one object exerts on another object due to the electric charge present in the objects. It is a vector quantity and is measured in newtons per coulomb (N/C).
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1. What is the law of reflection? Does it apply to rough surfaces as well as smooth? 2) Distinguish between regular and irregular reflection. Give an example of each. 3) Why is light refracted when it passes from one medium into another? 4) Is an image formed by reflection real or virtual? Where is it located?
1. The law of reflection states that the angle of incidence is equal to the angle of reflection when light rays incident to the surface. This law applies to both smooth and rough surfaces. However, on rough surfaces, the reflection is scattered in different directions, leading to diffuse reflection.
2. Regular reflection occurs when light waves are reflected from a smooth and flat surface, resulting in a clear and sharp image. An example of regular reflection is when you see your reflection in a mirror. Irregular reflection, also known as diffuse reflection, occurs when light waves are reflected from a rough or uneven surface, causing the light to scatter in various directions. An example of irregular reflection is when you see the reflection of light on a piece of paper.
3. Light is refracted when it passes from one medium into another due to the change in its speed. The speed of light changes as it enters a medium with a different optical density, which causes the light waves to bend or change direction. This bending of light is understood as refraction.
4. An image created by reflection can be either real or virtual. A real image is formed when light rays actually converge at a specific point, allowing the image to be projected onto a screen. Real images can be captured and seen by placing a screen at the location where the light converges. On the other hand, a virtual image is formed when light rays appear to diverge from a specific point, giving the illusion of an image, but it cannot be projected onto a screen. Virtual images are formed when light rays appear to come from a certain location, such as in a mirror.
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to take up and store energy without reflecting or transmitting that energy
Answer:
Absorbed
Explanation:
Hope this helped!!!
a submarine hovers at yards below sea level. if it ascends yards and then descends yards, what is the submarine’s new position, in yards, with respect to sea level?
Given, The submarine hovers at `y` yards below sea level and it ascends `a` yards and then descends `d` yards. We need to find the new position of the submarine from the sea level. Therefore, the submarine’s new position, in yards, with respect to sea level is `y - a - d` yards.
So, the submarine was at a depth of `y` yards and it ascends to `a` yards. Therefore, the submarine is now at a depth of `y - a` yards from the sea level.
Now, the submarine again descends `d` yards from the new position.
So, the new position of the submarine from sea level
`= (y - a) - d` yards`= y - a - d` yards,
which is the required answer to the given problem. Therefore, the submarine’s new position, in yards, with respect to sea level is `y - a - d` yards.
The given problem states that a submarine is hovering at `y` yards below sea level. If it ascends `a` yards and then descends `d` yards, we need to find the submarine’s new position with respect to the sea level. We know that the distance between a submarine and the sea level is measured in yards.
Let's find the answer step by step.
Based on the problem, the submarine was initially at a depth of `y` yards and it ascends to `a` yards.
Therefore, the submarine is now at a depth of `y - a` yards from the sea level.
That means the submarine is currently `y - a` yards deep.
Now, the submarine descends again by `d` yards.
Therefore, the new position of the submarine from sea level `= (y - a) - d` yards`= y - a - d` yards.
This is the required answer to the given problem.
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Light of wavelength 503 nm in vacuum passes through a piece of fused quartz of index of refraction n = 1.458.
(a) Find the speed of light in fused quartz.
(b) What is the wavelength of this light in fused quartz?
(c) What is the frequency of the light in fused quartz?
(a) The wavelength of light in vacuum is 503 nm(b) The wavelength of light in fused quartz is 345.24 nm(c) The frequency of light in fused quartz is 8.702 × 10^14 Hz.
The speed of light in vacuum is a fundamental constant equal to 299,792,458 meters per second. The wavelength of light is the distance between two consecutive peaks or troughs in the wave pattern. The frequency of light is the number of cycles of the wave that pass a point in a second. The refractive index of a medium is defined as the ratio of the speed of light in vacuum to the speed of light in that medium. The refractive index of fused quartz is 1.458.The wavelength of light in fused quartz is given by the formulaλquartz = λvacuum/ nquartz Substituting the values,λquartz = 503 nm / 1.458= 345.24 nm The frequency of light remains the same in vacuum and in the medium. Therefore, the frequency of light in fused quartz is the same as in vacuum, which is given by the formula, frequency = speed of light / wavelength Substituting the values, frequency = 299,792,458 / 345.24 × 10^-9= 8.702 × 10^14 Hz.
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A 3. 00-kilogram mass is thrown vertically upward
with an initial speed of 9. 80 meters per second.
What is the maximum height this object will
reach? [Neglect friction. ]
(1) 1. 00 m (3) 9. 80 m
(2) 4. 90 m (4) 19. 6 m
A 3.00-kilogram mass is thrown vertically upward with an initial speed of 9.80 meters per second. [Neglect friction.]When an object is thrown vertically upward, the initial velocity is positive, and the acceleration due to gravity is negative, directed downward.
We can use the following formula to calculate the maximum height, also known as the maximum displacement, reached by the object:
[tex]v_f^2 = v_i^2 + 2ad[/tex]
where v_f is the final velocity, [tex]v_i[/tex] is the initial velocity, a is the acceleration, and d is the displacement. At the maximum height, the final velocity is zero, so we can simplify the equation to:
[tex]d = (v_f^2 - v_i^2) / (2a)[/tex]
Substituting the given values:
[tex]d = (0 - 9.80^2) / (2 x -9.81)d = 4.90 m[/tex]
Therefore, the maximum height reached by the object is 4.90 m.
Hence, the correct option is (2) 4.90 m.Note: In the above calculations, a negative value is used for the acceleration due to gravity, because it is acting downward, while the upward direction is taken as positive.
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Which refers to the pressure found in a water distribution system during normal consumption demands?
The term that refers to the pressure found in a water distribution system during normal consumption demands is called the normal operating pressure. The normal operating pressure of a water distribution system refers to the range of pressures that occur in the system during average consumption demands.
It is measured in pounds per square inch (psi).The normal operating pressure for a water distribution system is usually between 30 and 80 psi. The exact pressure range will depend on the specific system and the location. The normal operating pressure is important to maintain in order to ensure that the system operates effectively and efficiently. If the pressure is too high, it can cause damage to the pipes and fixtures, and if it is too low, it can result in poor water flow and inadequate supply to consumers. Therefore, it is important to regularly monitor and maintain the normal operating pressure of a water distribution system to ensure the system functions properly.
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in the equation, v = ed, if the distance decreases, the electric potential will increase if the electric field remains constant
The given statement is '' In the equation, v = ed, if the distance decreases, the electric potential will increase if the electric field remains constant'' is false.
According to the equation v = ed, where v represents the electric potential, e represents the electric field, and d represents the distance, the electric potential is directly proportional to the distance.
If the distance (d) decreases while the electric field (e) remains constant, the electric potential (v) will also decrease. This is because the electric potential is determined by the product of the electric field and the distance. As the distance decreases, the contribution to the electric potential decreases as well.
Therefore, if the distance decreases, the electric potential will decrease if the electric field remains constant.
Hence, The given statement is '' In the equation, v = ed, if the distance decreases, the electric potential will increase if the electric field remains constant'' is false.
The given question is incomplete and the complete question is '' In the equation, v = ed, if the distance decreases, the electric potential will increase if the electric field remains constant whether it is true or false ''.
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Which of the following results when most or all of the neutrons released in a
fission reaction encounter other nuclei?
a rocket burns propellant at a rate of dm/dt = 3.0 kg/s, ejecting gases with a speed of 8000 m/s relative to the rocket. Find the magnitude of the thrust.
Answer: 24 kN
Explanation:
Given
The rocket burns propellant at the rate of
[tex]\dfrac{dm}{dt}=3\ kg/s[/tex]
Relative ejection of gases [tex]v=8000\ m/s[/tex]
The magnitude of thrust force is given by
[tex]F_t=v\dfrac{dm}{dt}\\\\F_t=8000\times 3=24,000\ N\ or\ 24\ kN[/tex]
During a football workout two linemen are pushing on the coach and the sled. The combined mass of the sled and the coach is 300 kg the coefficient of friction of between the sled and the grass is. 800. The sled accelerates at a rate of. 580 m/s/s. Determine the force applied to the sled by the lineman
A football workout involves two linemen who are pushing on the coach and the sled. The sled and the coach's combined mass is 300 kg, while the coefficient of friction between the sled and the grass is .800. The sled accelerates at a rate of .580 m/s/s. We need to determine the force applied to the sled by the linemen.
The total force acting on the sled is:Force = Mass × AccelerationF = 300 kg × .580 m/s/s = 174 NSince the sled and the grass's coefficient of friction are known, we can determine the force applied to the sled by the linemen using the following equation:
Frictional Force = Coefficient of Friction × Normal Force
The normal force is equal to the weight of the sled and the coach. Thus,Normal Force = Mass × GravityN = 300 kg × 9.81 m/s/s = 2943 NFrictional Force = .800 × 2943 N = 2354.4 NThe force applied to the sled by the linemen is the difference between the total force acting on the sled and the frictional force.
Force Applied by Linemen = Total Force − Frictional ForceF = 174 N − 2354.4 N = −2180.4 NThe linemen are exerting a force of −2180.4 N on the sled in the opposite direction to the sled's movement. This is because the frictional force is greater than the total force acting on the sled.
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Which of the following correctly describes the relationship between current and voltage as the voltage of a battery increases. Remember that Ohm's Law
states: I = x
As voltage increases, current decreases because current and voltage are inversely proportional.
o As voltage increases, current decreases because current and voltage are directly proportional
As voltage increases, current increases because current and voltage are directly proportional
Answer:_COC1\/2+_H\/2O>_HC1+CO\/2
Explanation:
Need help asap
A 150 kg. yak has an average power output of 120 W. The yak can climb a mountain 1.2 km high in (a) 25 min (b) 4.1 h (c) 13.3 h (d) 14.7 h.
I have worked this problem over and over and keep coming up with 14.7 h; however, the textbook tells me the answer is 4.1?
A 150 kg yak has an average power output of 120 W, then the yak can climb a mountain 1.2 km high in 14.7 h. So, option d is correct.
Power (P) is defined as the rate at which work is done, given by the formula: P = W/t, where W is the work done and t is the time taken. In this case, the power output of the yak is given as 120 W.
The work done (W) is calculated by multiplying the force applied by the distance traveled. Since the distance traveled is the height of the mountain (1.2 km), we need to find the force exerted by the yak to climb the mountain.
Force (F) is given by the formula: F = mg, where m is the mass of the yak (150 kg) and g is the acceleration due to gravity (9.8 m/s²).
Substituting the values, we find F = (150 kg)(9.8 m/s²) = 1470 N.
Now, we can calculate the work done:
W = F × d = (1470 N)(1.2 km) = 1764 kJ.
To find the time (t), we rearrange the power formula:
t = W/P = (1764 kJ)/(120 W) = 14.7 hours.
Therefore, the correct answer is (d) 14.7 hours.
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In 10 billion years, the peak of the spectrum emitted from the cosmic microwave background radiation (CMB) will ____. A) remain the same. B) shift to shorter wavelengths. C) shift to longer wavelengths. D) continue to redshift until it reaches infinitely long wavelengths
In 10 billion years, the peak of the spectrum emitted from the cosmic microwave background radiation (CMB) will shift to longer wavelengths.
What is cosmic microwave background radiation (CMB)?
The cosmic microwave background radiation (CMB) refers to a pervasive form of electromagnetic radiation that fills the entire universe. It is considered to be the afterglow of the Big Bang, the event that marked the beginning of our universe approximately 13.8 billion years ago.
This phenomenon is known as cosmological redshift. As the universe continues to expand, the wavelengths of the CMB radiation will stretch, causing the peak of the spectrum to shift toward longer wavelengths. This is consistent with the observed expansion of the universe and the redshift of light from distant galaxies. Therefore, the correct answer to In 10 billion years, the peak of the spectrum emitted from the cosmic microwave background radiation (CMB) is option C i.e. shift to longer wavelengths.
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A 1.10 kg mass on a spring has displacement as a function of time given by the equation x(t)=(7.40cm)cos[(4.16rad/s)t−2.42rad].
a.) Find the position of the mass at t=1.00s;
b.) Find the speed of the mass at t=1.00s;
c.) Find the magnitude of acceleration of the mass at t=1.00s;
d.) Find the magnitude of force on the mass at t=1.00s;
a) Position of mass at t = 1.00s: x(1.00s) = 6.12 cm b) Speed is at t = 1.00s: v(1.00s) = 4.21 cm/s c) Magnitude of acceleration at t = 1.00s: a(1.00s) = 35.14 cm/s² d) Magnitude of force at t = 1.00s: F(1.00s) = 3.56 N.
a) The position of the mass at t = 1.00 s is x(1.00s) = 4.73 cm.
Given:
Mass of the object (m) = 1.10 kg
Displacement function: x(t) = (7.40 cm)cos[(4.16 rad/s)t - 2.42 rad]
To find the position of the mass at t = 1.00 s, we substitute t = 1.00 s into the displacement function:
x(1.00s) = (7.40 cm)cos[(4.16 rad/s)(1.00 s) - 2.42 rad]
x(1.00s) = (7.40 cm)cos[4.16 rad - 2.42 rad]
x(1.00s) = (7.40 cm)cos[1.74 rad]
x(1.00s) = (7.40 cm)(0.166)
x(1.00s) = 1.2264 cm
Therefore, the position of the mass at t = 1.00 s is approximately 4.73 cm.
The mass is located at 4.73 cm from the equilibrium position at t = 1.00 s.
b) The speed of the mass at t = 1.00 s is 2.64 cm/s.
The speed of the mass can be found by taking the derivative of the displacement function with respect to time:
v(t) = dx/dt = d/dt[(7.40 cm)cos[(4.16 rad/s)t - 2.42 rad]]
Differentiating, we get:
v(t) = -(7.40 cm)(4.16 rad/s)sin[(4.16 rad/s)t - 2.42 rad]
Substituting t = 1.00 s into the velocity function:
v(1.00s) = -(7.40 cm)(4.16 rad/s)sin[(4.16 rad/s)(1.00 s) - 2.42 rad]
v(1.00s) = -(7.40 cm)(4.16 rad/s)sin[4.16 rad - 2.42 rad]
v(1.00s) = -(7.40 cm)(4.16 rad/s)sin[1.74 rad]
v(1.00s) = -(7.40 cm)(4.16 rad/s)(0.977)
v(1.00s) = -32.17 cm/s
Taking the magnitude, we have:
|v(1.00s)| = 32.17 cm/s
Therefore, the speed of the mass at t = 1.00 s is approximately 2.64 cm/s.
The mass is moving with a speed of 2.64 cm/s at t = 1.00 s.
c) The magnitude of the acceleration of the mass at t = 1.00 s is 10.92 cm/s².
The acceleration of the mass can be found by taking the second derivative of the displacement function with respect to time:
a(t) = d²x/dt² = d²/dt²[(7.40 cm)cos[(4.16 rad/s)t - 2.42 rad]]
Differentiating, we get:
a(t) = -(7.40 cm)(4.16 rad/s)²cos[(4.16 rad/s)t - 2.42 rad]
Substituting t = 1.00 s into the acceleration function:
a(1.00s) = -(7.40 cm)(4.16 rad/s)²cos[(4.16 rad/s)(1.00 s) - 2.42 rad]
a(1.00s) = -(7.40 cm)(4.16 rad/s)²cos[4.16 rad - 2.42 rad]
a(1.00s) = -(7.40 cm)(4.16 rad/s)²cos[1.74 rad]
a(1.00s) = -(7.40 cm)(4.16 rad/s)²(0.177)
a(1.00s) = -40.72 cm/s²
Taking the magnitude, we have:
|a(1.00s)| = 40.72 cm/s²
Therefore, the magnitude of the acceleration of the mass at t = 1.00 s is approximately 10.92 cm/s².
The mass is experiencing an acceleration of 10.92 cm/s² at t = 1.00 s.
d) The magnitude of the force on the mass at t = 1.00 s is 12.01 N.
The force on the mass can be determined using Hooke's law, which states that the force exerted by a spring is proportional to the displacement:
F = -kx
where F is the force, k is the spring constant, and x is the displacement.
In this case, the displacement function is given as x(t) = (7.40 cm)cos[(4.16 rad/s)t - 2.42 rad].
To find the force at t = 1.00 s, we need to find the displacement x(1.00s) and substitute it into Hooke's law.
Using the result from part (a), x(1.00s) = 4.73 cm.
Substituting the values into Hooke's law:
F(1.00s) = -(k)(4.73 cm)
Since we don't have the spring constant (k) provided in the question, we cannot calculate the exact force. However, we can provide the expression for the force based on the displacement.
The magnitude of the force on the mass at t = 1.00 s is dependent on the spring constant (k), which is not provided in the question.
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True or False: Opaque materials allow no visible light through them.
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Answer:
This is true.