We can use Coulomb's Law to solve this problem:
F = k * (q1 * q2) / r^2
where:
F = -5.5 N
k = Coulomb's constant (9.0 x 10^9 N·m^2/C^2)
q1 = charge of the balloon (-1.0 x 10^-6 C)
q2 = charge of the steel tube= ?
r = distance between the balloon and the steel tube (0.97 m)
Plugging in the given values and solving for q2:
-5.5 N = (9.0 x 10^9 N·m^2/C^2) * (-1.0 x 10^-6 C) * q2 / (0.97 m)^2
Solving for q2, we get:
q2 = (-5.5 N) * (0.97 m)^2 / [(9.0 x 10^9 N·m^2/C^2) * (-1.0 x 10^-6 C)]
q2 ≈ -6.4 x 10^-6 C
Therefore, the charge of the steel tube is approximately -6.4 x 10^-6 C.
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What is the tension on a stone of mass 50 g, tied to a string of length 50 cm and rotated at a speed of 1 m/s?
0.1
100
10
Answer: 0.1
Explanation:
To find the tension on the stone, we can use the centripetal force formula, which is given by F = (mv^2)/r, where m is the mass of the object, v is its velocity, and r is the radius of the circular path.
In this case, the stone is tied to a string and is moving in a circle of radius 50 cm (or 0.5 m), so we have:
F = (0.05 kg) x (1 m/s)^2 / 0.5 m
F = 0.1 N
Therefore, the tension on the string is 0.1 N.
So, the correct answer is 0.1.
What is the vector sum of a vector T~ given by 40 m, 30 degrees and a vector U~ given by 12
m, 225 degrees?
Hence, R = 28.97 m, 24.5 degrees is the vector sum of T and U.
Is a vector at 30 degrees?A vector's direction is frequently stated as a rotation of the vector's "tail" anticlockwise with respect to due East. In accordance with this practise, a vector having a direction of 30 degrees is a vector that has been anticlockwise rotated 30 degrees with respect to due east.
Let's begin by separating the components of the vector T:
T~ = 40 m, 30 degrees
T_x = 40 cos(30) = 34.64 m
T_y = 40 sin(30) = 20 m
Let's now decompose the vector U into its constituent parts:
U~ = 12 m, 225 degrees
U_x = 12 cos(225) = -8.49 m
U_y = 12 sin(225) = -8.49 m
It is possible to combine elements of the same type (x and y):
R_x = T_x + U_x = 34.64 m - 8.49 m = 26.15 m
R_y = T_y + U_y = 20 m - 8.49 m = 11.51 m
The Pythagorean theorem can be used to determine the size of the resulting vector R:
|R~| = sqrt(R_x² + R_y²) = sqrt((26.15 m)² + (11.51 m)²) = 28.97 m
The inverse tangent function can be used to determine the direction of the resulting vector R:
theta = tan⁻¹(R_y/R_x) = tan⁻¹(11.51 m/26.15 m) = 24.5 degree.
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Some help me with this pls
37. Segment B of the graph corresponds to the only solid state. ,38. Segment E of the graph corresponds to the melting point. and all answer given below:
What is Segment?Segment is a customer data platform (CDP) that enables businesses to collect, store, and analyze customer data from multiple sources. It allows companies to unify their customer data into one place, which can then be used to create more personalized customer experiences. With Segment, businesses can create custom segments of their customers and create targeted campaigns to meet their specific needs.
39. The melting point (temperature) is 300°C.
40. Segment F of the graph corresponds to the only liquid state.
41. Segment A of the graph corresponds to the only gas state.
42. Segment D of the graph corresponds to the boiling point.
43. No, the temperature decreases during freezing.
44. Segment C of the graph corresponds to the freezing point.
45. The boiling point (temperature) is 450°C.
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Now write the magnitude of the normal force again, this time in terms of the gravitational force Fg, g, θ, the radius of the track r, and the velocity that the car is traveling v. Please use proper number of parentheses in your denominator (Expert TA)
The magnitude of the normal force of the car is given by Fn = Fg cotθ.
What is the normal force of the car?The normal force is the force exerted by the racetrack perpendicular to the car's motion. Let's now derive the expression for the magnitude of the normal force of the car:
The perpendicular component of the normal force is given by:
Fn⊥ = Fg cosθ
The parallel component of the normal force provides the centripetal force required for circular motion.
The centripetal force (Fc) is given by:
Fc = mv²/r
where;
m is the mass of the car, v is the velocity of the car, and r is the radius of the circular path.The centripetal force can also be expressed in terms of the parallel component of the normal force:
Fc = Fn∥ = Fn sinθ
Equating the two expressions for Fc, we get:
Fn sinθ = mv²/r
Solving for Fn, we get:
Fn = mv²/(r sinθ)
Substituting the expression for Fg cosθ, we get:
Fn = Fg cosθ / sinθ
or
Fn = Fg cotθ
where;
Fg is the gravitational force, g is the acceleration due to gravity, θ is the angle of banking of the track, and r and v are the radius and velocity of the car respectively.Learn more about normal force here: https://brainly.com/question/14486416
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The complete question is below:
Circular turns of radius r in a racetrack are often banked at an angle θ to allow the cars to achieve higher speeds around the turns. Assume friction is not present.
Now write the magnitude of the normal force of the car, in terms of the gravitational force Fg, g, θ, the radius of the track r, and the velocity that the car is traveling v.
Maria is taking an emotional intelligence as that involves looking at abstract image and describing it she describes a couple relaxing on the beach at sunset which personality test is Maria taken
Maria is taking the Rorschach inkblot test.
What personality test involves looking at abstract image and describing it ?The test is designed to assess an individual's personality traits and psychological functioning based on their responses to the images.
The Rorschach inkblot test, which uses a set of inkblot images and asks participants to describe what they see. The Rorschach test is a projective test that is often used to assess an individual's personality, emotional functioning, and thought processes.
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Write a 16 line poem that describes centripal force utilizing all key concepts and terms.
A typical 16-line poem that described centripetal force can be found below.
Centripetal forceIn circular motion, a force we call,
Centripetal, it keeps things in thrall.
Directed towards the center of the path,
Without it, objects would face a wrath.
Angular velocity is key,
The rate of change of the angle we see.
And the radius of the circle too,
Both play a role in what we must do.
The mass of the object cannot be ignored,
It factors in with gravity's cord.
As the force pulls towards the center,
Centripetal force is what we enter.
It is the sum of all the forces in play,
Equal to mass times velocity squared, we say.
And if the force is too weak or too strong,
Off the circular path, the object goes wrong.
Thus, centripetal force is what we need,
To keep objects moving at the speed,
In a circular path, they're meant to be,
A force that keeps them in harmony.
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You are in charge of designing a study that determines how far the average fire ant travels from its colony to collect resources.
Plan an investigation to provide evidence of the distance traveled by fire ants.
Also describe the process you will use to accurately measure the distance traveled including the tools you will use and the data you will collect.
To accurately measure the distance traveled by the fire ants, we could use a measuring tape or a GPS device. For short distances, a measuring tape would suffice, while for longer distances, a GPS device would provide more accurate measurements.
How to investigate the distance traveled by fire ants to collect resources?
To investigate the distance traveled by fire ants to collect resources, we could follow the following plan:
Select a suitable study site: We need to select a study site where fire ants are present and are actively collecting resources. It should also be a site where we can easily track and observe the movement of the ants.Mark the location of the colony: Once we have identified a study site, we should locate the fire ant colony and mark its location.Place resources at varying distances: We should then place resources, such as food or sugar water, at varying distances from the colony, starting from the immediate vicinity of the colony and extending outwards in increasing increments.Observe and track ants: We should observe and track the ants as they leave the colony to collect resources. We can mark the ants with a non-toxic paint to identify and track their movement.Measure the distance traveled: We can use a measuring tape or a GPS device to accurately measure the distance traveled by the marked ants from the colony to the resource site.Record the data: We should record the distance traveled by each marked ant in a spreadsheet or database.Analyze the data: Once we have collected the data, we can use statistical analysis to determine the average distance traveled by fire ants to collect resources.To learn more about GPS device, visit: https://brainly.com/question/14996387
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How much energy is produced in J when the sun converts 2 kg of mass into energy?
Answer:
The energy produced by the sun when it converts 2 kg of mass into energy is given by Einstein's famous equation E = mc², where E is the energy produced, m is the mass converted, and c is the speed of light.
Substituting the values, we have:
E = (2 kg) x (299,792,458 m/s)²
E = 2 x 89,875,517,873,681,764 J
E ≈ 1.7975 x 10²⁰ J
Therefore, the sun produces approximately 1.7975 x 10²⁰ joules of energy when it converts 2 kg of mass into energy.
On the radio, the station KROQ (106.7) broadcasts radio waves at a frequency of 106,700,000 Hertz. If the velocity of a radio wave is approximately 300,000,000 m/s, what is the wavelength of KROQ’s radio waves?
Hence, the radio waves from KROQ have a wavelength of roughly 2.81 metres.
How can you determine a radio wave's frequency?A radio wave's frequency is determined by dividing its velocity (c = 299 792 458 m/s, or the speed of light) by its wavelength. Wavelength is the length in metres of a single complete wave. In maths, frequency is defined as f = c/.
The frequency of radio waves is 106,700,000 Hz, while the speed of light is roughly 300,000,000 m/s. The formula is as follows: c = fλ
where the wavelength is used.
When we rearrange this formula to account for, we obtain: λ = c / f
Inputting the values provided yields:
λ = 300,000,000 m/s / 106,700,000 Hz
λ ≈ 2.81 meters
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what two changes need to be made so that the plug is wired correctly ?
It is important to note that wiring a plug can be dangerous, and if you are not confident in your ability to do so, you should seek the help of a qualified electrician. Incorrectly wiring a plug can result in electrical shock.
What are the step for plug wired ?
The first change that may need to be made is to ensure that the correct wires are connected to the corresponding terminals on the plug. Typically, the green and yellow wire is connected to the earth terminal, the blue wire to the neutral terminal, and the brown wire to the live terminal.
How can you determine whether a plug is wired properly?Voltage can be measured with a multimeter. A probe should be inserted into each slot to measure the line voltage. A fully functioning outlet registers between 110 and 120 volts. Check the outlet and the wiring if there is no reading.
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4. A 25,000kg asteroid is flying towards the Earth at a speed of 1500.0m/s. How much Silly Putty would it take to stop the asteroid if we launched it at a velocity of -100.0m/s? Assume the Silly Putty sticks to the asteroid.
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of a system remains constant if there are no external forces acting on it. We can set the momentum of the asteroid before the collision equal to the momentum of the asteroid-Silly Putty system after the collision.
The momentum of the asteroid before the collision is:
P_before = m_ast * v_ast
where m_ast is the mass of the asteroid and v_ast is its velocity.
The momentum of the asteroid-Silly Putty system after the collision is:
P_after = (m_ast + m_sp) * v_final
where m_sp is the mass of the Silly Putty, v_final is the velocity of the asteroid-Silly Putty system after the collision, which we assume to be zero.
We can equate these two expressions for momentum and solve for the mass of the Silly Putty:
m_sp = (m_ast * v_ast) / (-v_final)
Substituting the given values:
m_ast = 25,000 kg
v_ast = 1500.0 m/s
v_final = -100.0 m/s
m_sp = (25,000 kg * 1500.0 m/s) / (-(-100.0 m/s))
m_sp = 375,000 kg m/s / 100.0 m/s
m_sp = 3750 kg
Therefore, we would need 3750 kg of Silly Putty to stop the asteroid if we launched it at a velocity of -100.0 m/s.
Which statement correctly identifies and interprets the figurative
language in this excerpt from the passage?
Other times, he seemed to saw himself in two, his legs driving him one way
while his head and torso faked another, his body rejoining at the rim to lay the
ball in with a knowing smirk.
The metaphor "sawing himself in two" highlights the basketball player's agility as his legs and upper body move in opposing directions before coming together at the rim to hit a shot.
Which one best defines figurative language?Essentially, employing figurative language involves distorting the meaning of words to convey a point, sound clever, or create a joke. Figurative language is a common technique used in narrative writing when the author wants to make the reader feel strongly about something.
What circumstance might figurative language be used in?Literature forms like poetry, drama, prose, and even speeches use figurative language. Figurative language is a literary element that is employed throughout
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Tamara is playing a game of billiards. The white cue ball has a mass of 0.17 kg and all the other balls have a mass of 0.16 kg. The cue ball is moving at a velocity of 6 m/s when it collides with the number seven ball. If the cue ball comes to a complete stop after the collision, then what will the resulting velocity be on the number seven ball?
Answer: (0.17 * 6) + ( 0.16 * 0 ) = (0.17 * 0) + ( 0.16 * v2)
v2 = 6.375 m/s
Explanation:
The answer is v2 = 6.375 m/s
(I did the equation and everything but just in case, check with someone else so you don't get the wrong answer)
What are the 3 major categories that the elements are grouped into?
A. Non-metals, metals, metalloids
B. Earth metals, Halogens, Noble gases
C. Alkali metals, acidic metals, neutral metals
D. Metals, metalloids, transition metals
Answer:
Metals, nonmetals, and metalloids are three different categories for the elements. Metals may be hammered into sheets and are malleable, ductile, and excellent conductors of heat and electricity (they can be drawn into wire).
Explanation:
Brainliest pls
Answer:
A. Non-metals, metals, metalloids
Explanation:
metals are Group I, II and III and IV
Non metals are Group VII, VI and VIII
a 2.5 Mass ball thrown vertically upward with 10 m/s calculate a the potential energy after the 0.2second
Answer:
35J
Explanation:
The mass of the ball=2.5kg
The initial speed=10m/s
we have to calculate the height= h
s=ut+1/2at^2
h=10*0.2 -1/2*10*0.04
h=2-0.2
h= 1.8m
the potential energy= mgh
= 2.5kg*10*1.8
= 25*1.8
= 35J
Two long parallel wires X and Y carry currents 3A and 5A respectively. if the force experienced per unit length by X is 5 *10^-5 N, the force per unit length of Y is _
The force per unit length of Y would be 1.25 * [tex]10^{-3[/tex] N/m.
Force per unit lengthThe force per unit length between two parallel wires carrying currents can be calculated using the equation:
F = μ0 * I1 * I2 * L / (2 * π * d)
where:
F = force per unit lengthμ0 = permeability of free space = 4π * 10^-7 T·m/AI1 and I2 = currents in wires X and Y, respectivelyL = length of wires X and Yd = distance between the wiresSubstituting the given values, we get:
F_X = μ0 * 3A * 5A * L / (2 * π * d) = 5 * 10^-5 N
Solving for F_Y, we get:
F_Y = 2 * F_X * π * d / (μ0 * 5A * L)
= 2 * (5 * 10^-5 N) * π * d / (4π * 10^-7 T·m/A * 5A * L)
= 1.25 * [tex]10^{-3[/tex] N/m
Therefore, the force per unit length experienced by wire Y is 1.25 * 10^-3 N/m.
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The fastest recorded pitch in Nippon Professional Baseball, thrown by Shohei Otani in 2016, was clocked at 102.5 mi/h. If a pitch were thrown horizontally at this speed, how far would the ball fall vertically (in ft) by the time it reached home plate, 60.5 ft away?
Incorrect: Your answer is incorrect.
ft
To solve this problem, we can use the kinematic equation for vertical motion under constant acceleration, which is given by:
[tex]y = vi*t + (1/2)at^2[/tex]
What is displacement?
Displacement is a vector quantity that refers to the overall change in position of an object from its initial position to its final position.
It is a straight line distance between the initial and final position, in a specific direction.
where y is the displacement (in this case, the vertical distance the ball falls), vi is the initial velοcity (0 in this case since the ball is thrοwn hοrizοntally), a is the acceleratiοn due tο gravity[tex](-32.2 ft/s^2)[/tex], and t is the time it takes fοr the ball tο reach hοme plate. We can find t by dividing the distance tο hοme plate by the hοrizοntal velοcity:
[tex]t = 60.5 ft / (102.5 mi/h * 5280 ft/mi * 1 h/3600 s) = 0.400 s[/tex]
Now we can use the kinematic equation to find y:
[tex]y = 0 + (1/2)(-32.2 ft/s^2)(0.400 s)^2 = -2.57 ft[/tex]
Note that the negative sign indicates that the displacement is downward. Therefore, the ball falls about 2.57 feet vertically by the time it reaches home plate.
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A Camot engine works between the se and the sink with efficiency 40% How much perature of the sink be lowered keeping the source parature constant so that its efficiency increases by 10%?
Answer:
if the temperature of the sink is lowered by 6.7%, the efficiency of the Carnot engine will increase by 10%.
Explanation:
The efficiency of a Carnot engine is given by the equation:
η = 1 - T_sink / T_source
where η is the efficiency, T_sink is the temperature of the sink, and T_source is the temperature of the source.
In this case, we are given that the efficiency of the engine is 40%. Therefore, we can write:
0.4 = 1 - T_sink / T_source
Rearranging this equation, we get:
T_sink / T_source = 1 - 0.4
T_sink / T_source = 0.6
Next, we are asked to find the temperature of the sink needed to increase the efficiency of the engine by 10%. Let's call this new efficiency η_new. Since the efficiency of a Carnot engine is given by the same equation as before, we can write:
η_new = 1 - T_sink_new / T_source
where η_new is the new efficiency, and T_sink_new is the new temperature of the sink.
We know that the new efficiency is 10% higher than the original efficiency, so we can write:
η_new = η + 0.1η = 0.4 + 0.1(0.4) = 0.44
Substituting this into the equation above, we get:
0.44 = 1 - T_sink_new / T_source
Rearranging this equation, we get:
T_sink_new / T_source = 1 - 0.44
T_sink_new / T_source = 0.56
Now we can set up an equation to find the new temperature of the sink:
0.56 = T_sink_new / T_source
T_sink_new = 0.56T_source
To find the temperature difference between the old and new sink temperatures, we can subtract the two equations we have derived:
T_sink_new - T_sink = 0.6T_source - 0.56T_source
T_sink_new - T_sink = 0.04T_source
Finally, we can substitute the given efficiency of 40% to find the source temperature:
0.4 = 1 - T_sink / T_source
T_source = T_sink / (1 - 0.4)
T_source = T_sink / 0.6
Substituting this expression for T_source into the equation for the temperature difference, we get:
T_sink_new - T_sink = 0.04(T_sink / 0.6)
Simplifying, we get:
T_sink_new - T_sink = 0.067T_sink
Multiplying both sides by 100, we get:
(T_sink_new - T_sink) * 100 = 6.7T_sink
Therefore, if the temperature of the sink is lowered by 6.7%, the efficiency of the Carnot engine will increase by 10%.
Some roads have signs that specify a maximum load for the vehicles that travel on them. Why might this be?
Answer: Applying a weight limit to a road is often done in an attempt to protect a roadway's appearance in particular. It also aims to protect the character and environment of rural areas, villages, and residential estates. Restricting overweight freights may just prevent damages like pot holes and cracks in the road.
Explanation:
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Larry finds a lens and shows it to his friends, Mirez and Sherly. All three look through it. Larry looks at the window across the room with the lens and says the window looks upside down. Mirez said that he must be using it incorrectly, because when he looks at his thumb through the lens, it is definitely not upside down. Sherly says that she thinks it is broken, because when she looks through it, everything just looks blurry.
Using your understanding about image formation, explain each of their observations.
The explanation of each of their observations can be found below.
Explanation of observationsLarry observed the window appearing upside down when viewed through the lens. This is because the lens creates an inverted image of the object being viewed. The light rays from the object are refracted by the lens and converge at a point behind the lens to form an inverted real image.Mirez observed that his thumb appeared normal when viewed through the lens. This is because the lens he used is a convex lens and it can create both real and virtual images, depending on the position of the object relative to the lens. For objects placed closer than the focal length of the lens, convex lenses produce virtual images that are upright, magnified, and on the same side of the lens as the object.Sherly observed that everything appeared blurry when viewed through the lens. This might be because the lens is either scratched or dirty, which can cause aberrations in the image formation. Also, the lens might not be properly focused or the object is placed too far or too close to the lens, causing the image to be out of focus.More on observations can be found here: https://brainly.com/question/28041973
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Sergio saw an angle that measures greater than 0° and less than 90°.What type of angle did he see
B) Show that the equation for pressure p=F/ A' is dimensionally correct.
P = [M1 L1 T-2] × [L2]-1 = M1 L-1 T -2. Therefore, the pressure is dimensionally represented as M1 L-1 T -2.
You have learned that the pressure from a fluid at a certain depth is given by the equation P = ρgh + Patm. You have also learned that the buoyant force is due to the difference in pressure between the top and bottom of an object. Derive the equation for the buoyant force from these two ideas. (Hint: In your derivation, use a simple submerged object, such as a perfect cube with sides of length s.) (3 points)
To derive the equation for the buoyant force, we can start with the equation for the pressure from a fluid at a certain depth:
P = ρgh + Patm
where P is the pressure at a depth h, ρ is the density of the fluid, g is the acceleration due to gravity, and Patm is the atmospheric pressure at the surface of the fluid.
Now, let's consider a simple submerged object, such as a perfect cube with sides of length s, as the hint suggests. The object is fully submerged in the fluid, so it experiences a pressure difference between the top and bottom surfaces. The pressure at the top surface of the object is Ptop = ρghtop + Patm, where htop is the depth of the top surface below the surface of the fluid. The pressure at the bottom surface of the object is Pbottom = ρghbottom + Patm, where hbottom is the depth of the bottom surface below the surface of the fluid. Since the object is at rest in the fluid, the net force acting on the object must be zero. Therefore, the buoyant force must be equal and opposite to the weight of the object:
Buoyant force = Weight of object
The weight of the object is given by its mass multiplied by the acceleration due to gravity:
Weight of object = mg
where m is the mass of the object and g is the acceleration due to gravity.
To find the buoyant force, we need to find the difference between the pressure at the top and bottom surfaces of the object, and then multiply that difference by the surface area of the object:
Buoyant force = Pressure difference × Surface area
The pressure difference is given by:
Pressure difference = Pbottom - Ptop
= (ρghbottom + Patm) - (ρghtop + Patm)
= ρg(hbottom - htop)
Therefore, the buoyant force is:
Buoyant force = ρg(hbottom - htop) × Surface area
For a perfect cube with sides of length s, the surface area is given by A = 6s^2. Therefore, the buoyant force on the cube is:
Buoyant force = ρg(hbottom - htop) × 6s^2
This is the equation for the buoyant force on a submerged object, derived from the equation for the pressure from a fluid at a certain depth and the concept of the buoyant force being due to the pressure difference between the top and bottom of an object.
Two friends are rock climbing on a cliff face. They are 18 m above the
ground. The two friends have a combined mass of 150 kg. Use
9 = 9.8 m/s².
Calculate the gravitational potential energy of the two climbers.
Round your answer to the nearest thousand.
J
The gravitational potential energy of the two climbers would be 26,460 J.
Gravitational potential energy calculationThe gravitational potential energy (PE) of an object is given by the formula:
PE = mgh
where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above some reference point.
In this case, the combined mass of the two climbers is 150 kg, and they are 18 m above the ground. Using g = 9.8 m/s², we can calculate their gravitational potential energy as:
PE = (150 kg) x (9.8 m/s²) x (18 m) = 26,460 J
Rounded to the nearest thousand, the gravitational potential energy of the two climbers is 26,000 J.
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What is the relationship of the wavelength of a
particle and its mass?
a
The wavelength of a particle cannot
be measured.
b They are directly related.
C
The mass of a particle does not affect
its wavelength.
d They are inversely related.
The relationship of the wavelength of a particle and its mass is they are inversely related.
Option D is correct.
What is de Broglie frequency condition?The link between a particle's mass and wavelength is provided by the de Broglie wavelength equation: = h/p,
where is the wavelength, h is the Planck constant, and p is the particle's momentum.
This condition shows that a molecule's energy is contrarily relative to its frequency. Because momentum (p = mv) is defined as the product of mass and velocity, we can also say that a particle's wavelength is inversely proportional to its mass.
What is the Wavelength?A wavelength is the distance between two identical points (adjacent crests) in consecutive cycles of a waveform signal that travels in space or down a wire. In wireless systems, its length is typically measured in meters (m), centimeters (cm), or millimeters (mm).
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It takes 80 pounds of force to
stretch a particular spring 2
inches. How much work is done
in stretching it from its relaxed
state a total of 4 inches?
[?] inch - pounds
Answer: 240 inch-lbs.
Explanation:
The spring constant, k, is given by:
k = (F/x)
where F is the force, x is the displacement, and k is the spring constant.
Using the given information, we can calculate the spring constant as:
k = (80 lbs / 2 in) = 40 lbs/in
To find the work done in stretching the spring from its relaxed state to a total of 4 inches, we need to integrate the force over the displacement:
W = ∫F dx
Since the force required to stretch the spring varies with displacement, we need to break up the integration into two parts: one from 0 to 2 inches, and another from 2 to 4 inches.
W = ∫0^2 F dx + ∫2^4 F dx
The first integral is:
∫0^2 F dx = ∫0^2 (kx) dx = (1/2)kx^2 = (1/2)(40 lbs/in)(2 in)^2 = 80 inch-lbs
The second integral is:
∫2^4 F dx = ∫2^4 (2k) dx = 2kx = 2(40 lbs/in)(4 in - 2 in) = 160 inch-lbs
Therefore, the total work done in stretching the spring from its relaxed state to a total of 4 inches is:
W = ∫0^2 F dx + ∫2^4 F dx = 80 inch-lbs + 160 inch-lbs = 240 inch-lbs
So, the work done in stretching the spring from its relaxed state a total of 4 inches is 240 inch-lbs.
A container with a height of 7.7 inches with an open top has a 5.6 inch diameter and is open to the atmosphere. The container is filled with water. The bottom of the container has a 0.87 inch diameter hole. Calculate ρgh at the top of the container if the datum is set at the bottom of the container.
This is the pressure at the top of the container due to the height of the water. The pressure at the bottom of the container due to the height of the water is 0 Pa since the datum was set at the bottom.
What is pressure?Pressure is a physical quantity used to measure the force applied by an object to another object or by an object to a surface. It can be expressed as the force per unit area and is typically measured in units such as pounds per square inch (psi) or pascals (Pa). Pressure can be applied to gases, liquids, and solids, and is generated by the weight of the atmosphere, the force of gravity, and by the movement of air or liquids. Pressure can also be created by mechanical devices such as pumps and compressors, as well as by chemical reactions.
ρ = density of water = 1000 kg/m3
g = acceleration due to gravity = 9.81 m/s2
h = height of the container = 7.7 in = 0.198 m
Using the equation ρgh = density x gravity x height, we can calculate the pressure at the top of the container to be:
ρgh = (1000 kg/m3)(9.81 m/s2)(0.198 m) = 1960.38 Pa
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A body of mass 1 kg is pushed at a constant speed against a vertically placed wall, with a constant force F, which forms an angle of 45 degrees with the horizontal, as in the picture. The sliding friction coefficient is 0.2. What is the intensity of the force F? For the acceleration of the heavier force, take g=10 m/s2.
The intensity of the force F is calculated to be approximately 2.83 N.
What is sliding friction coefficient?Coefficient of sliding friction is a value that measures force of sliding friction for particular surface type.
Weight = mg = 1 kg x 10 m/s² = 10 N (acting downwards)
F_vertical - Weight = 0
F_vertical = 10 N
As Frictional force = coefficient of friction x normal force
Frictional force = 0.2 x 10 N = 2 N (acting to the left)
F_horizontal = F x cos(45) = F / √2
F_horizontal - frictional force = 0
F_horizontal = frictional force = 2 N
F / √2 = 2 N
F = 2 N x √2
F ≈ 2.83 N
Therefore, the intensity of the force F is approximately 2.83 N.
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A power transistor is a solid-state electronic device. Assume that energy entering the device at the rate of 1.00 W by electrical transmission causes the internal energy of the device to increase. The surface area of the transistor is so small that it tends to overheat. To prevent overheating, the transistor is attached to a larger metal heat sink with fins. The temperature of the heat sink remains constant at 35.0°C under steady-state conditions. The transistor is electrically insulated from the heat sink by a rectangular sheet of mica measuring 8.25 mm by 6.25 mm, and 0.0852 mm thick. The thermal conductivity of mica is equal to 0.0753 W/m·°C. What is the operating temperature of the transistor?
Answer:
Explanation:
The rate of heat transfer from the transistor to the heat sink through the mica sheet can be calculated using Fourier’s Law of heat conduction. The formula for this law is Q = kA(T1 - T2)/d where Q is the rate of heat transfer, k is the thermal conductivity of the material, A is the cross-sectional area through which heat is transferred, T1 and T2 are the temperatures at either end of the material and d is its thickness.
In this case, we know that Q = 1.00 W (the rate at which energy enters the device), k = 0.0753 W/m·°C (the thermal conductivity of mica), A = 8.25 mm * 6.25 mm = 5.15625e-5 m² (the cross-sectional area of the mica sheet), T2 = 35°C (the temperature of the heat sink) and d = 0.0852 mm = 8.52e-5 m (the thickness of the mica sheet).
Substituting these values into Fourier’s Law gives us:
1.00 W = (0.0753 W/m·°C)(5.15625e-5 m²)(T1 - 35°C)/(8.52e-5 m)
Solving for T1 gives us:
T1 ≈ 35 + (1 / ((0.0753 * 5.15625e-5) / 8.52e-5)) ≈ 35 + 22 ≈ 57°C
So under steady-state conditions with an energy input rate of 1 W and a heat sink temperature of 35°C, we can expect that the operating temperature of this power transistor would be approximately 57°C.
A block of mass m = 1.9 kg is attached to a string that is wrapped around the circumference of a wheel of radius R = 8.1 cm. The wheel rotates freely about its axis and the string wraps around its circumference without slipping. Initially, the wheel rotates with an angular speed ω, causing the block to rise with a linear speed v = 0.43m/s
Find the moment of inertia of the wheel if the block rises to a height of h
= 7.5 cm before momentarily coming to rest.
The moment of inertia of the wheel if the block rises to a height of h is 7.5 cm before momentarily coming to rest is 0.068 kg m².
We can use the conservation of mechanical energy to solve for the moment of inertia of the wheel. Initially, the system has kinetic energy, which is converted to potential energy at the highest point of the block's trajectory. Therefore, we can write:
Initial kinetic energy = Final potential energy
At the start, the wheel and block have kinetic energy due to the motion of the block:
KE i = 0.5 * m * v²
At the highest point of the block's trajectory, all of the kinetic energy is converted to potential energy due to the block's height above the ground:
PE_f = m * g * h
where g is the acceleration due to gravity.
Since the string is wrapped around the circumference of the wheel, the distance that the block moves upwards is equal to the distance that the string moves around the wheel, which is equal to the circumference of the wheel:
h = 2 * pi * R
Substituting this into the expression for potential energy:
PE_f = m * g * 2 * π * R
Equating initial kinetic energy with final potential energy:
0.5 * m * v² = m * g * 2 * π * R
Simplifying and solving for the moment of inertia of the wheel, I:
I = (m * v²) / (2 * g * π * R)
Substituting the given values:
I = (1.9 kg * 0.43 m/s)² / (2 * 9.81 m/s² * π * 0.081 m)
I = 0.068 kg m²
Therefore, the moment of inertia of the wheel is 0.068 kg m².
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