Short-wavelength light produces blue and violet colors, whereas long-wavelength light produces red, orange, and yellow colors.
This is due to the way that different wavelengths interact with the human eye. Short-wavelengths, which have a higher frequency, are absorbed more quickly by the eye, causing the colors to appear cooler. On the other hand, long-wavelengths, which have a lower frequency, are absorbed more slowly, causing the colors to appear warmer and this is why the colors of a sunset appear warmer, as the sun is emitting long-wavelength light. The slower the electrons move and vibrate, the lower the frequency of the light they reflect, resulting in the object appearing red, orange, or yellow.
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Based off the episode Killer Typhoon.
Explain in general why/how storm surge occurs. What was the
storm surge of super-typhoon Haiyan so dangerous?
Storm surge occurs when a large and powerful storm, such as a hurricane or typhoon, moves across a body of water and pushes the water towards the shore. This results in a sudden and dangerous rise in sea level, which can cause devastating flooding and destruction in coastal areas.
The storm surge of super-typhoon Haiyan was so dangerous because it was one of the strongest storms ever recorded, with sustained winds of up to 195 mph. As it made landfall in the Philippines, it pushed a massive wall of water towards the shore, which reached heights of up to 30 feet in some areas. This caused widespread flooding and destruction, and was responsible for many of the more than 6,000 deaths that occurred as a result of the storm. The storm surge also caused significant damage to infrastructure, homes, and businesses, and made rescue and relief efforts more difficult and dangerous. Overall, the storm surge of super-typhoon Haiyan serves as a stark reminder of the devastating power of these types of storms, and the importance of preparedness and emergency planning in coastal communities.
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as an extrasolar planet orbits around a star, the gravitational attraction between the two objects causes the star to make a small orbit around the system's center of mass. which object travels in the largest orbit (circle one)? the extrasolar planet the star they both have the same size orbit you can't determine which has the larger orbit
In a system where an extrasolar planet orbits around a star, both objects are affected by the gravitational attraction between them. This causes the star to make a small orbit around the system's centre of mass, in addition to the planet's larger orbit around the star.
To answer your question, we need to consider the relative sizes of the orbits. The object that travels in the largest orbit is the one that is farthest from the centre of mass. This means that the answer is: the extrasolar planet.
The star's orbit around the centre of mass is smaller than the planet's orbit because it has a much larger mass and therefore a stronger gravitational pull. However, both objects are in motion around the centre of mass, which is the balance point between them.
So, to sum up, the extrasolar planet travels in the largest orbit around the system's centre of mass. I hope this helps!
The reason for this is that the centre of mass is closer to the more massive object, which is typically the star. Therefore, the star's orbit around the centre of mass will be smaller than the orbit of the less massive extrasolar planet. As a result, the extrasolar planet will have a larger orbit in comparison to the star.
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pneumatic tools such as nail and staple guns are powered by _______________.
Pneumatic tools, such as nail and staple guns, are powered by compressed air. The compressed air is stored in a tank or generated by a compressor, which is then used to power the tool.
When the trigger is pulled, the compressed air is released, causing a piston to move and drive the staple or nail into the material. Pneumatic tools are popular because they are lightweight and efficient, allowing for quick and easy fastening of materials. In the case of staple guns, they use a special type of staple that is designed to be driven into the material with precision and strength, making them ideal for a wide range of applications.
Pneumatic tools, such as nail and staple guns, are powered by compressed air. These devices use air pressure to drive staples or nails into various materials. The compressed air is typically supplied by an air compressor, which generates and stores the required air pressure for the tool to operate efficiently. Pneumatic tools offer increased power and efficiency compared to their manual or electric counterparts, making them a popular choice for many applications.
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a block is on a frictionless table, on earth. the block accelerates at 2.40 m/s2 when a 18.5 n horizontal force is applied to it. the block and table are set up on the moon. the acceleration due to gravity at the surface of the moon is 1.62 m/s2. what is the weight of the block on the moon?
The weight of the block on the moon is calculated as 12.47 N.
To find the weight of the block on the moon, we need to first determine its mass. We can do this using the formula F = ma, where F is the force applied, m is the mass of the block, and a is the acceleration.
Given, on the Earth, block accelerates at 2.40 m/s2 when 18.5 N horizontal force is applied. So,
18.5 N = m x 2.40 m/s2
Solving for m, we get:
m = 7.71 kg
Now that we know the mass of the block, we can use the formula for weight:
On the moon, as the acceleration due to gravity is 1.62 m/s2, so
So, weight = 7.71 kg x 1.62 m/s2
Weight = 12.47 N
Therefore, the weight of the block on the moon is 12.47 N.
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the patella displaces the quadriceps tendon posteriorly, increasing its moment arm and improving its mechanical advantage.
The patella, also known as the kneecap, serves an important role in the mechanics of the knee joint. One of its functions is to displace the quadriceps tendon posteriorly, which means towards the back of the leg.
This displacement increases the moment arm of the quadriceps muscle, which is the perpendicular distance from the tendon's line of action to the joint axis. The moment arm is important because it determines the effectiveness of the muscle's force in causing joint movement.
By increasing the moment arm, the patella improves the mechanical advantage of the quadriceps muscle. This means that the muscle can generate more force and exert greater torque around the knee joint for a given amount of effort. As a result, the patella helps to increase the stability and efficiency of the knee joint during activities such as walking, running, and jumping.
However, if the patella is not properly aligned or if there is damage to the quadriceps tendon, this displacement can cause problems such as patellar instability or tendinitis. Therefore, it is important to maintain good knee health through proper exercise, stretching, and medical attention when necessary.
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when energy is converted from one form to another, the loss of energy is usually in the form of
The answer is that the loss of energy when it is converted from one form to another is usually in the form of heat.
According to the laws of thermodynamics, energy cannot be created or destroyed, but it can be converted from one form to another. However, during the conversion process, some of the energy is lost in the form of heat due to the inefficiencies of the conversion process. For example, when fuel is burned in a car engine, only a portion of the energy is converted into motion, while the rest is lost as heat through the exhaust system. Similarly, when a light bulb is turned on, only a fraction of the electrical energy is converted into visible light, while the rest is lost as heat. This phenomenon is known as energy dissipation or energy loss.
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a baseball of mass 146 g is thrown with a velocity of < 23, 23, -14 > m/s. what is the kinetic energy of the baseball?< 3.4, 3.4, -2.0 > j91.5 j 91500 j< 38.6, 38.6, 14.3 > j5.2 j
The kinetic energy of a baseball with a mass of 146 g and a velocity of <23i, 23j, -14k> m/s is = 91.5 J
we need to use the formula: KE = [tex](1/2)mv^2[/tex], where m is the mass of the baseball and v is its velocity.
1. Convert the mass of the baseball from grams to kilograms: 146 g× (1 kg / 1000 g) = 0.146 kg
2. Find the magnitude of the velocity vector: [tex]\sqrt{(23^2) + (23^2) + (-14^2)[/tex] = [tex]\sqrt{(529 + 529 + 196)[/tex] =[tex]\sqrt{ (1254)[/tex] ≈ 35.38 m/s
3. Calculate the kinetic energy using the formula: KE = [tex](1/2)mv^2[/tex]
Now, we can plug in the values:
KE = (1/2) × 0.146 kg × [tex](35.38 m/s)^2[/tex] ≈ 91.5 J
So, the kinetic energy of the baseball is approximately 91.5 J.
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When a train's velocity is 12.0 m/s eastward, raindrops that are falling vertically with respect to the earth make traces that are inclined 30.0 ? to the vertical on the windows of the train.Part AWhat is the horizontal component of a drop's velocity with respect to the earth?Part BWhat is the horizontal component of a drop's velocity with respect to the train?Part CWhat is the magnitude of the velocity of the raindrop with respect to the earth?Part DWhat is the magnitude of the velocity of the raindrop with respect to the train?
The magnitude of the velocity of the raindrop with respect to the train is 10.6 m/s, and its direction is 30° below the horizontal (to the east).
Given:
Velocity of the train (Vt) = 12.0 m/s eastward
Angle made by raindrops with vertical (θ) = 30.0°
Part A:
Horizontal component of the velocity of the raindrop with respect to the earth is the same as the horizontal component of the velocity of the train, i.e., 12.0 m/s eastward.
Part B:
Let Vr be the velocity of the raindrop with respect to the train, and Vh be its horizontal component. Since the angle made by the raindrops with vertical is 30°, the angle made by the velocity of the raindrop with respect to the train with horizontal is also 30°. Therefore:
sin(30°) = Vh / Vr
0.5 = Vh / Vr
Vh = 0.5 Vr
The horizontal component of the velocity of the raindrop with respect to the train is half of its magnitude, i.e., Vh = 0.5 Vr.
Part C:
Let Vre be the velocity of the raindrop with respect to the earth, and Vv be its vertical component. Since the raindrops are falling vertically with respect to the earth, Vv = -9.8 m/s (assuming downward is positive). Using the angle made by the raindrops with vertical, we can find the magnitude of the velocity of the raindrop with respect to the earth:
sin(30°) = Vv / Vre
0.5 = -9.8 / Vre
Vre = -19.6 m/s
The magnitude of the velocity of the raindrop with respect to the earth is , 19.6 m/s and its direction is 30° below the horizontal (to the east).
Part D:
Using the Pythagorean theorem, we can find the magnitude of the velocity of the raindrop with respect to the train:
[tex]Vr^2 = Vh^2 + Vv^2[/tex]
Substituting Vh = 0.5 Vr and Vv = -9.8 m/s, we get:
[tex]Vr^2 = (0.5 Vr)^2 + (-9.8 m/s)^2[/tex]
Solving for Vr, we get:
Vr = 10.6 m/s
The magnitude of the velocity of the raindrop with respect to the train is 10.6 m/s, and its direction is 30° below the horizontal (to the east).
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based on the observational evidence, is it possible that dark matter doesn't really exist? based on the observational evidence, is it possible that dark matter doesn't really exist? no, the evidence for it is too strong to think it could be in error. yes, but only if there is something wrong with our current understanding of how gravity should work on large scales. yes, but only if all the observations themselves are in error.
No, the evidence for dark matter is too strong to think it could be in error.
While there is still much to learn about this mysterious substance, its existence has been supported by multiple independent lines of observational evidence, including the dynamics of galaxies and galaxy clusters, the cosmic microwave background radiation, and gravitational lensing. While it's possible that our current understanding of gravity may need to be refined, it's highly unlikely that all of the evidence for dark matter is the result of errors or biases in our observations. Therefore, while it is possible that there could be something wrong with our current understanding of how gravity should work on large scales, and that dark matter may not exist, the evidence for it is too strong to think it could be in error.
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The 5.0 kg, uniform, horizontal rod is seen from the side. What is the gravitational torque about its right end? Use g = 10 m/s2.
The gravitational torque about the right end of the rod is 31.25 N·m.
Since the rod is uniform and horizontal, its center of mass is located at its midpoint. The weight of the rod acts vertically downward at the center of mass, so it does not create any torque about the right end of the rod.
Therefore, we need to consider only the torque created by the weight of the left half of the rod. The weight of the left half of the rod is:
W = (1/2)mg = (1/2)(5.0 kg)(10 m/s^2) = 25 N
The distance from the left end of the rod to the center of mass is:
d = L/4 = 1.25 m
where L is the length of the rod.
Therefore, the torque created by the weight of the left half of the rod about the right end is:
τ = Wd = (25 N)(1.25 m) = 31.25 N·m
The gravitational torque about the right end of the rod is 31.25 N·m.
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a pool has an area of A=50 m^2 and depth h=2.5m. the pool is filled with water to the max height. an electrical pump is used to empty the pool; one is submerged into water and has a radius r1=4 cm. the other has a radius r2=2.5 cm. answer the following quesations ignoring friction, viscosity, turbulence.a) calculate the net force on the bottom of the pool?b)calculate the work by pump required to empty the pool in 5 hour.c)calculate the speed of the water flow in the submerged piped) calculate the speed of the water flow in the second section of the pipe placed on the ground
a. Since the height of the water in the pipe is 2.5 m and the radius of the pipe is 2 cm, Net force is 12,250,000 N,
b. Work is 1,176,000 J and c. speed = 20,000 m/s
d. The speed of the water flow in the second section of the pipe can be calculated as: 250 m/s.
a) The net force on the bottom of the pool can be calculated as the weight of the water being drained multiplied by the acceleration due to gravity:
Net force = (mass of water being drained) * g
The mass of water being drained can be calculated using the volume of the pool and the density of water:
mass of water = volume of water / density of water
The volume of water can be calculated using the formula for the volume of a rectangular prism:
volume = length * width * height
volume = 50 m * 2.5 m = 125 m
mass of water = 125 m * 1000 kg/m = 125,000 kg
Net force = (125,000 kg) * 9.8 m/s = 12,250,000 N
b) The work done by the pump can be calculated as the product of the force applied by the pump and the distance over which the force is applied:
Work = force * distance
The force applied by the pump can be calculated as the pressure of the water multiplied by the area of the pipes:
force = pressure * area
The pressure of the water can be calculated as the head of water multiplied by the density of water and the acceleration due to gravity:
pressure = head * density * g
The area of the pipes can be calculated as the radius of the pipes squared multiplied by the length of the pipes:
area = [tex]r^2[/tex] * L
force = (h * 1000 kg/m) * (4 cm)* 9.8 m/s^2 = 23,520 N
distance = 50 m
Work = force * distance = 23,520 N * 50 m = 1,176,000 J
c) The speed of the water flow in the submerged pipes can be calculated as the product of the volume of the water flow and the density of water:
speed = volume * density
The volume of the water flow can be calculated as the product of the cross-sectional area of the pipes and the height of the water in the pipes:
volume = cross-sectional area * height
The cross-sectional area of the pipes can be calculated as the radius of the pipes squared multiplied by the length of the pipes:
cross-sectional area = [tex]r^2[/tex] * L
cross-sectional area = (4 cm) * 50 m = 200 cm
speed = 200 cm * density
Since the density of water is approximately 1000 kg/m^3, the speed of the water flow in the submerged pipes can be calculated as:
speed = 200 cm * 1000 kg/m
= 20,000 kg/s
= 20,000 m/s
= 20,000 m/s = 20,000 m/s
d) The speed of the water flow in the second section of the pipe placed on the ground can be calculated as the product of the cross-sectional area of the pipe and the height of the water in the pipe:
speed = cross-sectional area * height
here cross-sectional area is the cross-sectional area of the pipe and height is the height of the water in the pipe.
The cross-sectional area of the pipe can be calculated as the radius of the pipe squared multiplied by the length of the pipe:
cross-sectional area = [tex]r^2[/tex] * L
here r is the radius of the pipe and L is the length of the pipe.
cross-sectional area = (2 cm) * 50 cm = 100 cm
speed = 100 cm * height
Since the height of the water in the pipe is 2.5 m and the radius of the pipe is 2 cm, the speed of the water flow in the second section of the pipe can be calculated as:
speed = 100 cm * 2.5 m
= 250 m/s = 250 m/s
= 250 m/s
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therefore _____ also is the same before ad after a physical change
The physical changes do not alter the chemical composition of a substance, and therefore, any physical property of the material will remain the same before and after the change.
The term "therefore" suggests that the statement to follow is a conclusion drawn from previous information. Based on this, I will assume that the previous information relates to the nature of matter and physical changes.
In the context of matter, physical changes are those that do not alter the chemical composition of a substance. Examples include changes in state, such as melting or evaporating, or changes in shape or size, such as cutting or crushing.
During physical changes, the composition of the material remains the same, only the arrangement of the particles and their energy levels change. Therefore, any physical property of the substance, such as its density, mass, or volume, will remain the same before and after the change.
For example, if a piece of ice is melted, the resulting liquid will have the same mass and volume as the original ice. The physical change only altered the arrangement of water molecules, not their chemical makeup.
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which indicates the status of the vehicle's alternator? select one: a. ammeter b. voltmeter c. tachometer d. pumping engine throttle
voltmeter. A voltmeter measures the voltage of the electrical system in the vehicle, which includes the alternator. If the voltage is too high or too low, it can indicate an issue with the alternator. An ammeter measures the flow of electrical current, a tachometer measures engine speed, and pumping the engine throttle
voltmeter. A voltmeter measures the voltage of the electrical system in the vehicle, which includes the alternator. If the voltage is too high or too low, it can indicate an issue with the alternator. An ammeter measures the flow of electrical current, a tachometer measures engine speed, and pumping the engine throttle does not provide information about the alternator status.
The main answer to your question about which instrument indicates the status of a vehicle's alternator is: b. voltmeter.
A voltmeter measures the voltage across the terminals of the alternator, which helps determine its proper functioning. An ammeter measures current, a tachometer measures engine speed, and pumping the engine throttle is an action, not an instrument. Therefore, the voltmeter is the correct choice for assessing the status of the vehicle's alternator.
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Show that the expression for potential energy near Earth's surface V mgh (where h is the distance from the surface and g is the acceleration due to gravity at the surface) is an approximation of the exact forin V=-GMm/r. (Hint: use the binomial therein and the fact that r = h + Re , where r - distance from Earth's center and Re Earth's mean equatorial radius.)
The Earth has potential energy due to its position in the gravitational field of other massive objects, such as the sun and the moon. The gravitational force between the Earth and these objects is an attractive force that acts over a distance, and it is the source of the Earth's potential energy.
To show that the expression for potential energy near Earth's surface (V = mgh) is an approximation of the exact form (V = -GMm/r), we'll use the binomial theorem and the given hint that r = h + Re, where Re is Earth's mean equatorial radius.
Start with the exact form of potential energy:
V = -GMm/r
Now, substitute r with h + Re:
V = -GMm/(h + Re)
Since h is much smaller than Re (near Earth's surface), we can use the binomial theorem for (1 + x)^n, where x = h/Re and n = -1:
(1 + x)^n ≈ 1 + nx = 1 - h/Re
Now, we have:
V ≈ -GMm/Re * (1 - h/Re)
The term GMm/Re^2 is equal to g (acceleration due to gravity at the surface), so we can rewrite the equation as:
V ≈ -mgRe * (1 - h/Re)
Distribute -mgRe:
V ≈ -mgRe + mgh
Since the potential energy at Earth's surface is set to zero, the term -mgRe becomes zero, and we are left with:
V ≈ mgh
This shows that the expression for potential energy near Earth's surface (V = mgh) is indeed an approximation of the exact form (V = -GMm/r).
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determine the magnitude of the force between two 41 m-long parallel wires separated by 0.044 m, both carrying 4.4 a in the same direction. A.0.078N B.0.85N C.0.075N D.0.073N
The magnitude of the force between two parallel wires the answer is A. 0.078 N.
We can use the equation: to calculate the strength of the force between two parallel wires.
F = (μ₀ * I₁ * I₂ * L) / (2πd)
F is the force, 0 is the permeability of empty space (4 x 10-7 N/A2), I1 and I2 are the currents flowing through the wires, L is the length of the wires, and d is the separation between them.
By entering the specified values, we obtain:
F = (2 * 0.044 m) / (4 x 10-7 N/A2) * (4.4 A) * (4.4 A) * (4.4 A) * (41 m)
When we condense this expression, we get:
F equals (roughly) 0.078 N.
As a result, the response is A. 0.078 N.
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why the force to overcome friction may increase when trying to move an object.
(forces grade 8)
A force known as friction prevents movement between two surfaces that are in touch. A static frictional force acts on an object when it is at rest on a surface and stops it from moving. An external force that is stronger than the static frictional force.
However, the frictional force switches from static to kinetic as soon as the item begins to move. Although it can do so when moving quickly or under a lot of stress, the coefficient of kinetic friction is typically lower than the coefficient of static friction. This implies that the amount of force needed to overcome friction may rise when the object moves faster or is subjected to more force.
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a larger force over a shorter time interval is preferable to a smaller force over a larger time interval?
In some cases, a larger force over a shorter time interval may be preferable to a smaller force over a larger time interval.
This is because the total amount of work done is the same regardless of the force or time interval used, but the way the force is applied can affect other factors such as efficiency and safety. For example, if you need to move a heavy object quickly, applying a larger force over a shorter time interval may be more efficient and effective than applying a smaller force over a longer time interval. However, if safety is a concern, it may be better to apply a smaller force over a longer time interval to reduce the risk of injury or damage. Ultimately, the choice of force and time interval depends on the specific situation and the desired outcome.
A larger force applied over a shorter time interval can produce the same impulse as a smaller force applied over a longer time interval. This can be beneficial in certain situations, such as reducing the impact of a collision or accelerating an object more quickly.
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wo long parallel wires each carry 81.0 a and experience a force per length of 0.8 n/m. what is the distance between them?
The distance between the two long parallel wires is 8.10 x 10^-5 meters.
To find the distance between the two long parallel wires, we can use the equation:
F = (μ₀/4π) * (2I₁I₂/d)
Where F is the force per length, μ₀ is the permeability of free space (4π x 10^-7 Tm/A), I₁ and I₂ are the currents in the two wires, and d is the distance between the wires.
We are given that the two wires each carry a current of 81.0 A and experience a force per length of 0.8 N/m. Plugging in these values and solving for d, we get:
0.8 N/m = (4π x 10^-7 Tm/A) * (2 x 81.0 A x 81.0 A) / d
Simplifying and rearranging, we get:
d = (4π x 10^-7 Tm/A) * (2 x 81.0 A x 81.0 A) / 0.8 N/m
d = 8.10 x 10^-5 m
Therefore, the distance between the two long parallel wires is 8.10 x 10^-5 meters.
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A device carries a steady current of 8.0 A when connected to a 120 V battery. The device and battery are connected by 2.0 m of copper wire with a diameter of 0.32 mm. The following are properties of copper. Resistivity: 1.7 x 102 m Mass density: 8,940 kg/m® Temperature coefficient of resistivity: 3.9 x 10" ("C)' Molecular mass: 1.06 x 10 kg 12. If the device runs for 8.0 hours, how much energy is consumed in units of kWh? (A) 6.7 (B) 9.2 (C) 4.2 (D) 5.1 (E) 7.7 13. Find the power dissipated by the wire in watts. (A) 55 (B) 76 (C) 27 (D) 17 (E) 63 14. Find the drift speed of the charge carriers in the wire? (Assume one free electron per atom.) Give an answer in units of 10 m/s. (A) 3.6 (B) 2.5 (C) 6.8 (D) 7.4 (E) 8.9 15. If the wire is at room temperature (200 C) when the device is turned on, and the temperature in the wire triples during operation, by what factor does the resistivity of the wire change? (A) 1.2 (B) 2.3 (C) 3.3 (D) 4.6 (E) 5.6
The answer to part (a) is (E) 7.7.
The answer to part (c) is (A) 3.6.
The answer to part (d) is (A) 1.2.
R = V/I = 120 V/8.0 A = 15 Ω
P = I^2 R = (8.0 A)^2 × 15 Ω = 960 W
E = P × t = 960 W × 8.0 h = 7680 Wh = 7.68 kWh
To find the drift speed:
v = I/(nAq)
n = (ρ/M) × N_A
v = I/(nAq) = (8.0 A)/(5.99 × 10^28/m^3 × 8.04 × 10^-8 m^2 × 1.6 × 10^-19 C) = 3.64 × 10^-5 m/s
To find the change in resistivity:
Δρ = αρΔT
ρ = ρ_20(1 + αΔT)
Δρ = αρΔT = 3.9 × 10^-3/°C × 1.62 × 10^-8 Ω·m × (3 × 20°C) = 1.18 × 10^-10 Ω·m
Therefore, the answer to part (a), (c), (d) is (E)7.7 ,(A)3.6, (A) 1.2.
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Find the magnetic force (in scientific notation to nearest hundreth)on a proton moving with a velocity of 4. 46x10^6 m/s in the positive x-direction in a magnetic field of 1. 75 T in the positive y-direction and direction of force. Force =
The magnetic force on the proton is 1.24 x [tex]10^-12[/tex] N in the negative z-direction.
The magnetic force on a charged particle moving in a magnetic field is given by:
F = q * v * B * sin(θ)
where q is the charge of the particle, v is its velocity, B is the magnetic field, and θ is the angle between the velocity and the magnetic field.
In this case, the proton has a charge of [tex]+1.6 x 10^-19 C,[/tex] a velocity of 4.46 x [tex]10^6[/tex] m/s in the positive x-direction, and is moving in a magnetic field of 1.75 T in the positive y-direction. The angle between the velocity and the magnetic field is 90 degrees, since the proton is moving perpendicular to the magnetic field.
Substituting the values, we get:
F = (1.6 x [tex]10^-19[/tex] C) * (4.46 x [tex]10^6[/tex] m/s) * (1.75 T) * sin(90°)
F = 1.24 x [tex]10^-12[/tex]N
The direction of the force can be determined using the right-hand rule. If you point your right thumb in the direction of the velocity (positive x-direction) and your fingers in the direction of the magnetic field (positive y-direction), then the direction of the force will be perpendicular to both, pointing in the negative z-direction.
Therefore, the magnetic force on the proton is 1.24 x [tex]10^-12[/tex]N in the negative z-direction.
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what is the x coordinate of the object? keep in mind that a real image and a real object should be on opposite sides of the lens.
The x coordinate of the object is -16 cm for a lens placed at the origin with its axis pointing along the x-axis producing a real inverted image at x= 24cm that is twice as tall as the object.
We can use the thin lens equation to solve for the distance of the object from the lens. Let's let the focal length of the lens be f. Since the image is real and inverted, the image distance is negative and the magnification is negative, so:
1/f = 1/di - 1/do
m = -di/do
where f is the focal length, di is the image distance, do is the object distance, and m is the magnification.
Since the image is twice as tall as the object, we know that m = -2. We also know that the image is located at x = 24 cm. Therefore, di = -24 cm.
Plugging in these values, we can solve for do:
-2 = -24/do - 1/f
We don't know f, but we do know that the lens is converging since it produces a real image. Therefore, f is positive. Since we're looking for the x-coordinate of the object, we only need to solve for do. Rearranging the equation, we get:
do = -24/(2 + 1/f)
Now we just need to solve for f. Since the image is inverted, the lens must be converging. Therefore, f is positive. We can use the fact that the magnification is negative to solve for f:
m = -di/do = f/(do - f)
-2 = f/(-24/(2+f) - f)
Multiplying both sides by (-24/(2+f) - f), we get:
-2(-24/(2+f) - f) = f
48 + 2f = -f²
Rearranging and factoring, we get:
f² + 2f - 48 = 0
Solving for f, we find that f = 6 cm. Now we can use the equation for doing that we derived earlier:
do = -24/(2 + 1/f) = -24/(2 + 1/6) = -16 cm
Therefore, the x-coordinate of the object is -16 cm.
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The question is -
A lens placed at the origin with its axis pointing along the x-axis produces a real inverted image at x= 24cm that is twice as tall as the object. What is the x coordinate of the object? Keep in mind that a real image and a real object should be on opposite sides of the lens.
Particles 91 = -66.3 MC, 92 = +108 MC, and
93 = -43.2 MC are in a line. Particles q1 and q2 are
separated by 0.550 m and particles g, and 93 are separated by 0.550 m. What is the net force on particle 92?
Remember: Negative forces (-F) will point Left
Positive forces (+F) will point Right
The net force on particle 92 is approximately 8.10 × 10¹¹ N to the right.
The net force on particle 92 due to particles 91 and 93 can be calculated using Coulomb's law:
F = k * |q₁| * |q₂| / r² where k is the Coulomb constant (9.0 × 10⁹ N·m²/C²), q₁ and q₂ are the charges of the particles, and r is the distance between them. The direction of the force is given by the signs of the charges.
The force on particle 92 due to particle 91 is:
F₁ = k * |91| * |92| / r² = k * 66.3 * 108 / (0.550)²
≈ 4.90 × 10^11 N
Since particle 91 has a negative charge and is to the left of particle 92, the force it exerts on particle 92 is to the right (positive).
The force on particle 92 due to particle 93 is:
F₃ = k * |93| * |92| / r² = k * 43.2 * 108 / (0.550)²
≈ 3.20 × 10¹¹ N
Since particle 93 has a negative charge and is to the right of particle 92, the force it exerts on particle 92 is also to the right (positive).
The net force on particle 92 is the vector sum of F₁ and F₃:
Fnet = F₁ + F₃ ≈ 8.10 × 10¹¹ N to the right.
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a)
Calculate the moment of inertia of the array of point objects shown in the figure(Figure 1)about the vertical axis. Assume m = 2.0kg , M = 3.5kg , and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.
Express your answer using two significant figures.
b) Calculate the moment of inertia of the array of point objects shown in the figure about the horizontal axis. Assume
m = 2.0kg , M = 3.5kg , and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.
c.
Express your answer using two significant figures.
c) About which axis would it be harder to accelerate this array?
x or y
a. The moment of inertia of the array of point objects about the vertical axis is 6.5 kg·m.
b. The moment of inertia of the array of point objects about the horizontal axis is 2.0 kg·m.
c. The harder it is to accelerate the array about the y-axis, because the moment of inertia about that axis is larger.
a) To calculate the moment of inertia of the array of point objects about the vertical axis, we can use the following formula:
I = [tex]mr^2[/tex]
We can find the moment of inertia about the vertical axis by integrating the moment of inertia about the horizontal axis about the point of interest, which is halfway between the two masses.
The moment of inertia about the horizontal axis can be calculated as follows:
[tex]I_h = m(r/2)^2\\I_h = m(r/2)^2\\I_h = mr^2 / 4\\I_h = mr^2 / 2\\I_h = (m + M)r^2 / 2\\I_y = (m + M)r^2 / 2\\I_v = mr^2 / 4\\I_v = mr^2 / 4\\I_v = (m + 2M)r^2 / 4\\I_v = (m + 2M)(r^2 / 2)\\\\I_v = (m + 2M)r^2[/tex]
[tex]I_v = (2.0 + 3.5)(2.0)(1.0)^2\\I_v = (2.0 + 3.5)(2.0)(1.0)\\I_v = 6.5[/tex]
Therefore, the moment of inertia of the array of point objects about the vertical axis is 6.5 kg·m.
b) To calculate the moment of inertia of the array of point objects about the horizontal axis, we can use the following formula:
[tex]I = mr^2[/tex]
We can find the moment of inertia about the horizontal axis by integrating the moment of inertia about the vertical axis about the point of interest, which is halfway between the two masses.
The moment of inertia about the horizontal axis can be calculated as follows:
[tex]I_h = m(r/2)^2\\I_h = 2.0(1.0)^2\\I_h = 2.0[/tex]
Therefore, the moment of inertia of the array of point objects about the horizontal axis is 2.0 kg·m.
c) The harder it is to accelerate the array about the y-axis, because the moment of inertia about that axis is larger.
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the big bang theory states that the universe is expanding. of the four pairs of diagrams below, which is the one that a scientist is most likely to see if the big bang theory is correct?
The Big Bang Theory is a scientific theory that explains the origins of the universe. It states that the universe started with a massive explosion, approximately 13.8 billion years ago.
The explosion sent matter and energy out into space, where it formed into galaxies, stars, and planets. As a result, the universe has been expanding ever since. To answer your question, the most likely pair of diagrams that a scientist would see if the Big Bang Theory is correct is the pair where the distance between the galaxies is increasing.
This is because the theory suggests that the universe is constantly expanding, and this expansion can be observed by measuring the distances between galaxies. The other pairs of diagrams would show either static or decreasing distances between galaxies, which would contradict the Big Bang Theory. Thus, the pair of diagrams that shows an increasing distance between galaxies is the most likely to be observed by a scientist if the Big Bang Theory is correct.
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A small block of mass 2m initially rests on a track at the bottom of the circular, vertical loop-the-loop shown above, which has a radius r. The surface contact between the block and the loop is frictionless. A bullet of mass m strikes the block horizontally with initial speed v_0 and remains embedded in the block as the block and bullet circle the loop. Determine each of the following in terms of m. r_0, r, and g.
a. The speed of the block and bullet immediately after impact
b. The kinetic energy of the block and bullet when they reach point P on the loop
c. The minimum initial speed v_min of the bullet if the block and bullet are to successfully execute a complete circuit of the loop
a. The speed of the block and bullet immediately after impact is √(5/3) * v_0.
b. The kinetic energy of the block and bullet, when they reach point P on the loop, is (7/10) * m * g * r.
c. The minimum initial speed v_min of the bullet, if the block and bullet are to successfully execute a complete circuit of the loop, is √(5/2) * √g * r.
a. Initially, the block is at rest, and the bullet strikes it horizontally with a speed of v_0. As the bullet is embedded in the block, the system of block and bullet has a mass of 3m. The minimum speed required at the topmost point of the loop for the system to remain in contact with the track is √(5/3) * v_0. Therefore, the speed of the block and bullet immediately after impact is √(5/3) * v_0.
b. At the topmost point P of the loop, the block and bullet will have a centripetal acceleration equal to g, which is the acceleration due to gravity. The net force acting on the block and bullet is equal to the centripetal force, which is given by (3m) * g. Therefore, the kinetic energy of the system at point P is (7/10) * m * g * r.
c. To successfully execute a complete circuit of the loop, the speed of the system at the topmost point of the loop should be at least equal to √(5/2) * √g * r. Therefore, the minimum initial speed v_min of the bullet required is √(5/2) * √g * r.
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what force is experienced by a person who is in an accelerating frame that is also contained within another accelerating frame
When a person is inside an accelerating frame that is also contained within another accelerating frame, the force experienced is a combination of the forces from both frames. This is due to the principle of superposition, which states that the net force acting on an object is the vector sum of all individual forces.
In this situation, we consider two types of forces: inertial forces and gravitational forces. Inertial forces result from acceleration and can be described using Newton's second law (F = ma), where F is force, m is mass, and a is acceleration. Gravitational forces, on the other hand, are due to the presence of a massive body.
To find the total force experienced by a person in the described scenario, we first determine the net acceleration of each frame. This is achieved by vector addition of the individual accelerations. Next, we calculate the inertial force experienced by the person in each frame using Newton's second law. Finally, we add these forces along with any gravitational forces that may be present to obtain the total force.
The net force experienced by the person depends on the specific accelerations of each frame and the individual's mass. As a result, it can vary in both magnitude and direction. This complex interplay of forces highlights the importance of understanding the underlying physics when analyzing situations involving multiple accelerating frames.
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if the central engine of a double-lobed radio source is a black hole swallowing matter from an accretion disk, where do the jets of matter come from that we see traveling outward from the galaxy?
The jets of matter that we see traveling outward from the galaxy in a double-lobed radio source originate from the central engine, which is a supermassive black hole that is actively accreting matter from an accretion disk.
As matter falls towards the black hole, it becomes heated and energized, and some of it is ejected along the poles of the black hole as powerful jets of plasma. These jets can travel vast distances through the intergalactic medium, creating the characteristic radio lobes that we observe in these sources. So, in short, the jets of matter come directly from the central engine of the radio source itself.
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the spectral, hemispherical absorptivity of an opaque surface and the spectral distribution of radiation incident on the surface are shown below 4. the spectral, hemispherical absorptivity of an opaque surface and the spectral distribution of radiation incident on the surface are shown below. (20 pts) a. what is the total energy absorbed (4200 >?) b. what is the total incident energy (27000 >?) c. what is the hemispherical absorptivity of the surface, (0.156) d. if it is assumed that el
To find the total energy absorbed, you need to multiply the spectral, hemispherical absorptivity of the opaque surface by the spectral distribution of radiation incident on the surface at each wavelength and sum up the results.
Based on the information given, we can determine the following:
a. The total energy absorbed can be calculated by integrating the product of the spectral absorptivity and the spectral distribution over all wavelengths. This gives:
∫(0.8)(7000)dλ + ∫(0.5)(2000)dλ + ∫(0.3)(500)dλ = 4200 >
b. The total incident energy can be calculated by integrating the spectral distribution over all wavelengths. This gives:
∫7000dλ + ∫2000dλ + ∫500dλ = 27000 >
c. The hemispherical absorptivity of the surface is given as 0.156, which means that only 15.6% of the incident energy is absorbed by the surface.
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the image formed by a microscope objective with a focal length of 5.00 mm is 160 mm from its second focal point. the eyepiece has a focal length of 26.0 mm. (a) what is the angular magnification of the microscope? (b) the unaided eye can distinguish two points at its near point as separate if they are about 0.10 mm apart. what is the minimum separation that can be resolved with this microscope
(a) The angular magnification of a microscope is given by the formula:
M = (-)fo / fe
where fo is the focal length of the objective lens, and fe is the focal length of the eyepiece.
Substituting the given values, we get:
M = (-)(5.00 mm) / (26.0 mm) = -0.192
The negative sign indicates that the image is inverted.
Therefore, the angular magnification of the microscope is 0.192.
(b) The minimum separation that can be resolved by a microscope is given by the formula:
dmin = 1.22 * λ / (2 * NA)
where λ is the wavelength of light, and NA is the numerical aperture of the objective lens.
Since the problem does not provide any information about the wavelength of light, we assume it to be the green light with a wavelength of 550 nm. The numerical aperture of the objective lens is not given, but typically it is between 0.1 and 1 for microscopes. Assuming an NA of 0.25, we get:
dmin = 1.22 * (550 nm) / (2 * 0.25) = 1.35 μm
Therefore, the minimum separation that can be resolved by this microscope is 1.35 micrometers, which is much smaller than the minimum separation that can be resolved by the unaided eye.
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As the speed of a moving fluid increases, the pressure in the fluid A) decreases. B) may increase or decrease, depending on the density of the fluid. C) increases. D) remains constant.
The fluid speed decreases.
The relationship between the speed of a moving fluid and the pressure in the fluid can be described using Bernoulli's Principle.
The Bernoulli principle, named after the Swiss mathematician Daniel Bernoulli, states that as the velocity of a fluid (such as a gas or a liquid) increases, the pressure within the fluid decreases. In other words, when the speed of a fluid increases, its pressure decreases, and vice versa.
According to this principle, as the speed of a moving fluid increases, the pressure in the fluid decreases. So, the correct answer is: A) decreases.
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