Answer:
≈ 192.7 m/s
Explanation:
Let's start by finding the velocity of the block just before it hits the ground. We can use the conservation of energy:
The initial potential energy of the block is mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the table.The final kinetic energy of the block is (1/2)mv^2, where v is the velocity of the block just before it hits the ground.Conservation of energy tells us that these two energies are equal:
mgh = (1/2)mv^2
Solving for v, we get:
v = sqrt(2gh)
Plugging in the given values, we get:
v = sqrt(2 * 9.8 m/s^2 * 1.9 m) = 6.06 m/s
Now, let's use conservation of momentum to find the initial speed of the bullet. We know that the total momentum of the system (bullet + block) is conserved before and after the collision. Before the collision, the momentum is:
p = mb * vb
where mb is the mass of the block and vb is its initial velocity, which is 0 since it is at rest.
After the collision, the bullet and block move together with a common velocity v. The total momentum is:
p = (mb + m) * v
where m is the mass of the bullet. Since momentum is conserved:
mb * vb = (mb + m) * v
Solving for vb, we get:
vb = (mb + m) * v / mb
Plugging in the given values, we get:
vb = (345 g + 7 g) / 7 g * 6.06 m/s = 192.7 m/s
Therefore, the initial speed of the bullet was approximately 192.7 m/s.
Use nodal analysis to find V1 and V2 in the circuit shown in Fig. 6.
Kirchhoff's current law is applied in nodal analysis. There will be 'n-1' simultaneous equations to solve when there are 'n' nodes in a given electrical circuit. 'n-1' must be solved in order to retrieve all of the node voltages.
Hence, we can solve for V1 and V2:
V1=Vi(R2+R3−k)k(1−nR3)−R2−R3.
V2=Vi(k−R2−R3(1+nR2))k(nR3−1)+R2+R3.
What is the significance of nodal analysis?Nodal analysis is a fundamental approach used to investigate voltage and current distribution in a circuit and is one of the simulations included in SPICE simulators. This method successfully integrates Kirchhoff's and Ohm's laws into a single matrix equation.
The distinction between mesh and nodal analysis is that nodal analysis uses Kirchhoff's current law to calculate the voltages at each node in an equation. Mesh analysis, on the other hand, is an application of Kirchhoff's voltage law, which is used to calculate current.
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Help with parts a through part f.
The equation = RC, where R is the resistance and C is the capacitance, yields the time constant of the circuit. We obtain the value = RC = (5.5 k)(4.5 F) = 24.75 ms = 0.02475 s by substituting the above variables.
What is circuit, exactly?In electronics, a circuit is a completely circular channel through which electricity flows. A current source, conductors, and a load make up a straightforward circuit.
The equation = RC, where R is the resistance and C is the capacitance, yields the time constant of the circuit. Inputting the values provided yields:
τ = RC = (5.5 kΩ)(4.5 µF) = 24.75 ms = 0.02475 s
The voltage drop Vc across the capacitor is equal to the voltage of the battery, i.e., Vc = VB = 180 V.
After a very long time, the voltage across the capacitor is equal to the voltage of the battery, i.e., V = VB = 180 V. Substituting the given values, we get:
Q = CV = (4.5 µF)(180 V) = 810 µC = 8.1 × 10⁻⁴ C
The current I in the circuit is equal to the current in the resistor, which is given by Ohm's law as I = V/R, where V is the voltage of the battery. Substituting the given values, we get:
I = V/R = (180 V)/(5.5 kΩ) = 32.73 mA = 3.273 × 10⁻² A
To find the time t when the current through the resistor is one-third of its maximum value, we can set I = (1/3)(VB/R) and solve for t:
(1/3)(VB/R) = (VB/R)e(-t/τ)
e(-t/τ) = 1/3
-t/τ = ln(1/3)
t = τln(3) ≈ 0.867τ
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The energy (E) of photon depends upon its wavelngth 'λ' , Planck's constant ' h ' and velocity
' c'. Derive the formula for energy using dimensional analysis.
Planck's frequency (h) and indeed the light's velocity (c) are used to connect a photon's energy (E) to its wavelength (), frequency (v), and wavelength. E = hν = hc/λ.
What is energy, exactly?We frequently use the word "energy" in our everyday speech. Energy has an unique physical meaning even if the term is frequently used figuratively. Energy is defined in physics as something's capacity to perform work. Many types of energy are possible. All energy is kinetic in some way.
The energy is lacking.Energy is present everywhere and comes in a variety of shapes and sizes. Objects at rest have potential energy that, if released, will cause them to move. All moving things contain kinetic energy.
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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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how many hydrogen-bonds does this molecule have?
how many acceptors does it have?
How many h-bonds can this molecule form with another identical
How many h-bonds can it form with water?
Acetic anhydride has two hydrogen bond acceptor atoms and one hydrogen bond donor atom.
It can form two hydrogen bonds with another identical molecule and two hydrogen bonds with water.
O
//
H3C-C-O-C-CH3
\\
O
Acetic anhydride has two hydrogen bond acceptor atoms
Acetic anhydride can form two hydrogen bonds with another identical molecule and two hydrogen bonds with water
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Hypnosis can be used to force people to do things against their will.
True
False
Answer: false
Explanation:
laws of reflection help us to predict the path of reflected ray with refrence to incident ray. How?
Answer:
The laws of reflection govern how incident light rays are reflected on reflecting surfaces such as mirrors, smooth metal surfaces, and clear water. The laws of reflection are as follows: The incident ray reflected ray, and normal to the mirror’s surface are all in the same plane. The incidence angle equals the reflection angle.
Explanation:
if an astronaut weighs 981 N on earth and only 160 N on the moon, then what is his mass on the moon
Answer:
mass=kg
Explanation:
M=(160)(9.8)
M=1568
What is silicon and what is it used for?
The displacement vectors
A
and
B
shown in the figure below both have magnitudes of 1.95 m. The direction of vector
A
is
= 29.0°.
A graph shows two displacement vectors A and B plotted on an x y plane. Vector A is a straight diagonal line that starts from the zero point and extends into the first quadrant at an angle with the horizontal. Vector B starts from the zero point and extends up along the y-axis.
(a) Find
A + B
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
(b) Find
A − B
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
(c) Find
B − A
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
(d) Find
A − 2B
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
The magnitude οf A + B is 1.95 m and its directiοn is 31.3° clοckwise frοm the pοsitive x-axis when the displacement vectοrs A and B is shοwn in the figure belοw bοth have magnitudes οf 1.95 m. The directiοn οf vectοr A is = 29.0°.
Hοw tο determine the magnitude and directiοn οf A + B?Tο determine the magnitude and directiοn οf A + B, we can measure the length οf the resulting vectοr and the angle it makes with the pοsitive x-axis, respectively.
Alternatively, we can use trigοnοmetry tο find the cοmpοnents οf vectοrs A and B and then add them up tο find the cοmpοnents οf A + B. Then, we can use inverse trigοnοmetric functiοns tο find the magnitude and directiοn οf the resulting vectοr.
Let's use the secοnd methοd tο sοlve this prοblem.
We are given that the magnitudes οf vectοrs A and B are 1.95 m each. The directiοn οf vectοr A is 29.0° cοunterclοckwise frοm the pοsitive x-axis. Let's call the angle between vectοr B and the pοsitive x-axis θ.
Using trigοnοmetry, we can find the x and y cοmpοnents οf vectοrs A and B as fοllοws:
Ax = 1.95 cοs 29.0° = 1.695 m
Ay = 1.95 sin 29.0° = 0.939 m
Bx = 1.95 cοs θ
By = 1.95 sin θ
Tο find θ, we need tο use the fact that the magnitude οf vectοr A + B is alsο 1.95 m. This means that:
[tex](Ax + Bx)^2 + (Ay + By)^2 = (1.95)^2[/tex]
Substituting the values of Ax and Ay, we get:
(1.695 + 1.95 cos θ)² + (0.939 + 1.95 sin θ)² = (1.95)²
Simplifying and solving for cos θ and sin θ, we get:
cos θ = -0.359
sin θ = -1.695
Since sin θ is negative, we know that vector B is pointing downwards.
Now, we can use inverse trigonometric functions to find the magnitude and direction of vector A + B:
[tex]|A + B| = sqrt((Ax + Bx)^2 + (Ay + By)^2) = 1.95 m[/tex]
θ = atan2(Ay + By, Ax + Bx) = atan2(-0.756, 1.336) = -31.3°
Therefore, the magnitude of A + B is 1.95 m and its direction is 31.3° clockwise from the positive x-axis.
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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.
5. A geologist from Pogera gold mine cut out a block of ore for laboratory analysis. The sides of the ore are 8.8 dm, 92.4 mm, 0.007 dam. Work out the volume of the ore in; i. Cubic metre. (show all working out to deserve a full mark). 3 marks
Therefore, the volume of the ore is 0.0069 cubic meters.
What is volume?Volume is a measure of the amount of space that an object or substance occupies. It is a fundamental physical quantity that describes the three-dimensional size of an object or space. The SI unit of volume is the cubic meter (m³), but other units such as liters, gallons, and cubic centimeters (cm³) are also commonly used. Volume can be calculated for regular shapes, such as cubes or cylinders, using mathematical formulas, but for irregular shapes, more complex methods, such as displacement, may be needed.
Here,
To calculate the volume of the ore, we need to convert all the measurements to the same unit. We can choose to convert everything to meters since that's the base unit for volume (cubic meters).
8.8 dm = 0.88 m (1 dm = 0.1 m)
92.4 mm = 0.0924 m (1 mm = 0.001 m)
0.007 dam = 0.07 m (1 dam = 10 m)
Now we can use the formula for volume of a rectangular block:
Volume = length x width x height
Volume = 0.88 m x 0.0924 m x 0.07 m
Volume = 0.0069 cubic meters
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A book sitting on a shelf have 740 J of potential energy, at a height of 1.8
m. What is the mass of the book?
13053.6 J
13053.6 m
41.950 kg
41.950 J
1 point
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 car tire is 64.0 cm in diameter. The car is traveling at a speed of 24.0 m/s.
a) What is the tire's rotation frequency, in rpm?
b) What is the speed of a point at the top edge of the tire?
c) What is the speed of a point at the bottom edge of the tire?
The tire rotates at a rate of 223.7 rpm, while the frequency layer of a tire is moving at a rate of 24.0 m/s plus 7.50 m/s, or 31.5 m/s. 24.0 m/s - 7.50 m/s = 16.5 m/s is the speed of a spot on the tire's bottom edge.
Why does frequency matter?Frequency refers to the quantity of waves passing a defined location in a predetermined period of time. As a result, the rate is 2 per second if a wave passes through in 1/2 of a second. In this case, the rate is 100 times per hour if it takes 1/10 of an hour.
Why not offer an example of frequency?The quantity of observations that take place during a specific predetermined timeframe is the frequency of such a class interval. So, the frequency for such 5–9 age range is 20 if, for instance, 20 individuals between the ages of 5 and 9 exist in the study's data.
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the following diagrams depict inelastic collisions between objects of different mass. For each case, determine the post-collision velocity (v) of the two coupled objects. Express v in terms of v
The colliding objects stick together after the collision, or some kinetic energy is lost to the environment.
What is an inelastic collision?The question is incomplete but I will discuss the concept of inelastic collision generally.
An inelastic collision is a type of collision in which kinetic energy is not conserved. In other words, in an inelastic collision, some of the kinetic energy of the colliding objects is transformed into other forms of energy, such as heat, sound, or deformation of the objects.
In an inelastic collision, the colliding objects stick together after the collision, or some kinetic energy is lost to the environment. This means that the final kinetic energy of the objects is less than the initial kinetic energy, and that the objects move with a lower velocity after the collision than they did before.
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A car initially traveling 10 m/s stops in a distance of 6 m. In another instance, the same car applying the same constant force is traveling 20 m/s. What is the required distance to come to a stop now?
The required distance to come to a stop now is 30 meters.
Steps
To solve this problem, we can use the equation:
v^2 = u^2 + 2as
where:
v is the final velocity (zero in this case)
u is the initial velocity (10 m/s in the first instance and 20 m/s in the second instance)
a is the acceleration (which is constant in this case)
s is the distance traveled (6 m in the first instance and we need to find it for the second instance)
Solving for s, we get:
s = (v^2 - u^2) / (2a)
For the first instance:
u = 10 m/s
v = 0 m/s
s = 6 m
a = (v^2 - u^2) / (2s) = (0 - 10^2) / (2 x 6) = -16.67 m/s^2 (negative sign indicates deceleration)
Now, using the same constant force, we can find the required distance s for the second instance:
u = 20 m/s
a = -16.67 m/s^2
v = 0 m/s (since the car stops)
s = (v^2 - u^2) / (2a) = (0 - 20^2) / (2 x -16.67) = 30 m
Therefore, the required distance to come to a stop now is 30 meters.
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How does a pulley make work easier when it is used to lift an object? (1 point)
It increases the amount of work produced to lift the object.
It reduces the weight of the object being lifted.
It decreases the distance over which the force must be applied to lift the object.
It changes the direction of the lifting force to work with gravity.
Answer:
last choice
Explanation:
With a single fixed pulley, you pull down (working with the force of gravity) to lift the load up.
A rocket at rest on the ground with initial mass 20,000 kg, 80% of which is fuel, burns 200kg/s as it flies
directly upwards. The exhaust gas exits the rocket at a relative speed of 1.80 km/s. Find (a) the thrust of
the rocket, (b) how long it takes to exhaust its fuel, and (c) the rocket’s speed at the end of its engine burn.
Assume g is constant and neglect air resistance.
Answer:
(a) The thrust of the rocket can be found using the formula:
Thrust = (mass flow rate) x (exhaust velocity)
The mass flow rate is the rate at which mass is expelled from the rocket, which is equal to the burn rate times the mass fraction of fuel:
mass flow rate = burn rate x (mass of rocket) x (mass fraction of fuel)
mass flow rate = 200 kg/s x 20,000 kg x 0.8
mass flow rate = 32,000 kg/s
The exhaust velocity is given as 1.80 km/s. Therefore, the thrust of the rocket is:
Thrust = 32,000 kg/s x 1.80 km/s
Thrust = 57,600 kN
(b) The time it takes to exhaust the fuel can be found using the formula:
time = (mass of fuel) / (burn rate)
The mass of fuel is 80% of the initial mass of the rocket:
mass of fuel = 0.8 x 20,000 kg
mass of fuel = 16,000 kg
Therefore, the time it takes to exhaust the fuel is:
time = 16,000 kg / 200 kg/s
time = 80 seconds
(c) The rocket's speed at the end of its engine burn can be found using the rocket equation:
Δv = (exhaust velocity) x ln[(initial mass) / (final mass)]
The final mass is the mass of the rocket after it has burned all of its fuel, which is:
final mass = (mass of rocket) - (mass of fuel)
final mass = 20,000 kg - 16,000 kg
final mass = 4,000 kg
The initial mass is 20,000 kg. Therefore, the change in velocity is:
Δv = 1.80 km/s x ln[(20,000 kg) / (4,000 kg)]
Δv = 1.80 km/s x ln(5)
Δv = 3.89 km/s
Since the rocket was initially at rest, its final speed is equal to the change in velocity:
final speed = 3.89 km/s
Therefore, the rocket's speed at the end of its engine burn is 3.89 km/s.
(05.04 HC)
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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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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What are the stresses?
Stress refers to a state of mental or emotional strain resulting from adverse or demanding circumstances. It can also refer to the physical forces that act on an object, causing deformation or strain.
What are the effects of stress?In terms of mental or emotional stress, it can result from a variety of factors such as work-related pressure, financial problems, relationship issues, health concerns, and other life events that require us to adapt and cope with changing circumstances.
Physical stress refers to the force or pressure applied to an object, which can cause it to deform, strain, or break. This type of stress can arise from a variety of sources such as gravity, external forces, or internal forces caused by changes in temperature, pressure, or other physical conditions.
Examples of physical stress include tension in a bridge caused by the weight of traffic passing over it, strain in a metal bar due to changes in temperature, or compression of a spring due to a force applied to it. In all cases, the object is subjected to forces that cause it to deform or change shape, leading to stresses that can impact its strength, durability, and performance.
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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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If a tennis racquet is briefly in contact with a 0.058 kg tennis ball initially traveling at -9.0 m/s* and then (after contact) the tennis ball moves with a velocity of 9.0 m/s.* If the time the racquet is in contact witht the ball is 0.004 seconds, what is the average force of the racquet on the ball? *Negative velocities mean towards the left and positive velocities mean towards the right.
The average force of the racquet on the ball, given that the time the racquet is in contact with the ball is 0.004 seconds, is 261 N
How do i determine the average force of the racquet?The following data were obtained from the question:
Mass of tennis (m) = 0.058 KgInitial velocity (u) = -9 m/sFinal velocity (v) = 9 m/sTime (t) = 0.004 secondsAverage force (F) =?We can easily obtain the average force of the racquet on the ball as follow?
F = m(v - u) / t
F = [0.058 ×(9 - -9)] / 0.004
F = [0.058 ×(9 + 9)] / 0.004
F = [0.058 × 18] / 0.004
F = 1.044 / 0.004
F = 261 N
Thus, we can conclude from the above calculation that the average force on the ball is 261 N
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Calculate the focal lengths while submerged in water (n = 1.33) for the two convex lenses used in this experiment assuming the radii and index of refraction as given in question #2 for each lens.
While submerged in water (n = 1.33) for two convex lenses, the focal lengths of Lens 1 is 19.67 cm and Lens 2 is 18.9 cm.
What is Lens ?Lens is a transparent device that is used to focus or redirect light, allowing it to be magnified, focused, or projected onto a surface. It is made of a curved, transparent material like glass, plastic, or crystal. Lenses are commonly used in eyeglasses, cameras, microscopes, and other optical devices. They can be used to magnify, reduce, or otherwise change the direction of light in order to produce a desired effect. They are also used in other applications such as laser cutting and welding, as well as medical imaging and laser treatments.
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Which pair of cities is moving apart as a result of plate motion
The pair of cities moving apart because of plate motion is London and Boston.
Why are London and Boston moving apart ?London and Boston are moving apart due to the motion of tectonic plates. The Earth's lithosphere is divided into several large plates that are in constant motion due to the underlying mantle convection. The movement of these plates is driven by the forces generated by the mantle convection, which causes the plates to move away from each other, move towards each other, or move sideways past each other.
London and Boston are located on separate tectonic plates that are moving away from each other. London is located on the Eurasian Plate, while Boston is located on the North American Plate.
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select a synonym for the word necessity a advertisement b extra c requirement d superior
Answer
explanation
requirments
if a space rover has a mass of 3900 kg, then what is its weight on earth
Answer:
38 220
Explanation:
Weight =Mg
W=Mg
W = (3900)(9.8)
W = 38 220
Cognitive psychology focuses on which of the following areas?
Personal responsibility and individual awareness
Behavior and attitudes
Physical capabilities and self-esteem
Perception and memory retention
The internal brain processes required to make sense of the environment and choose the best course of action are the subject of cognitive psychology.
Which six subfields make up cognitive psychology?Complex attention, executive function, learning and memory, language, perceptual-motor control, and social cognition are the six major cognitive function domains identified by the DSM-5.
What distinguishing characteristics characterise the cognitive psychology approach?The cognitive approach's main characteristics are: a conviction that psychology should be treated as a pure science and that research methods should be based on science. The main focus is on thinking and related mental functions like language, perception, memory, and forgetting.
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A train with cross-sectional area S, is moving with speed vt inside a long tunnel of cross- sectional area So (So = 4St). Assume that almost all the air (density p) in front of the train flows back between its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be po. If the pressure in the region between the sides of the train and the tunnel walls is p, then Po-P=2 pu. The value of is 2N
Answer:
The force acting on the train due to the air resistance is given by the formula:
F = (1/2) * p * A * v^2 * Cd
where p is the density of air, A is the cross-sectional area of the train, v is the speed of the train, and Cd is the drag coefficient.
We can assume that the drag coefficient is constant for a given shape of the train, and we can take it to be 0.5 for a train moving through air.
The pressure difference between the front and back of the train is given by:
P = (1/2) * p * v^2
The pressure difference between the sides of the train and the tunnel walls is given by:
2 * P = 2 * (1/2) * p * v^2 = p * v^2
The force acting on the train due to this pressure difference is given by:
F' = 2 * P * S = 2 * p * v^2 * S
The net force acting on the train is given by:
Fnet = F - F' = (1/2) * p * A * v^2 * Cd - 2 * p * v^2 * S
We can simplify this expression by factoring out p * v^2:
Fnet = p * v^2 * [(1/2) * A * Cd - 2 * S]
We are given that So = 4St, so we can substitute A = St and S = St/4:
Fnet = p * v^2 * [(1/2) * St * Cd - 1/2 * St * Cd] = 0
Therefore, the net force acting on the train is zero. This means that the force due to air resistance is exactly balanced by the force due to the pressure difference between the sides of the train and the tunnel walls.
We are given that Po - P = 2 * Pu, so we can substitute P = (1/2) * Po - Pu:
F' = 2 * P * S = 2 * [(1/2) * Po - Pu] * S = (Po - Pu) * 4 * St
We can equate this expression for F' to the expression for air resistance force:
F' = p * v^2 * [(1/2) * St * Cd - 2 * St/4] = p * v^2 * [(1/2) * St * Cd - St/2]
Equating these two expressions, we get:
(Po - Pu) * 4 * St = p * v^2 * [(1/2) * St * Cd - St/2]
Simplifying and solving for Pu, we get:
Pu = Po - (p * v^2 * Cd) / 8
We are given that Cd = 2N, so we can substitute this value:
Pu = Po - (p * v^2 * 2N) / 8
Pu = Po - (p * v^2 * N) / 4
Therefore, the pressure inside the train is Po - (p * v^2 * N) / 4.