The drag on the hull of a ship depends in part on the height of the water waves produced by the hull. The potential energy associated with these waves therefore depends on the acceleration of gravity $g$. Hence, we can state that the wave drag on the hull is $D=f\leftrho_{\infty}, V_{\infty}, c, g\right)$ where $c$ is a length scale associated with the hull, say, the maximum width of the hull. Define the drag coefficient as $C_D \equiv D / q_{\infty} c^2$. Also, define a similarity parameter called the Froude number, ${Fr}=V / \sqrt{g c}$. Using Buckingham's pi theorem, prove that $C_D=f({Fr})$.
Answers
Using Buckingham's Pi theorem, we can analyze the variables in the problem and determine the dimensionless groups that govern the relationship between them.
Let's consider the following variables:
- Drag on the hull (D)
- Density of the fluid (ρ∞)
- Velocity of the ship (V∞)
- Length scale associated with the hull (c)
- Acceleration due to gravity (g)
We have 5 variables and 3 fundamental dimensions: mass (M), length (L), and time (T). Therefore, we can form 5 - 3 = 2 dimensionless groups.
Let's choose the following dimensionless groups:
1. Drag coefficient (CD) = D / (ρ∞ V∞² c²)
2. Froude number (Fr) = V∞ / √(g c)
Now, let's check if these dimensionless groups can fully describe the problem.
The dimension of each variable in terms of M, L, and T is as follows:
- Drag on the hull (D) = [M L T⁻²]
- Density of the fluid (ρ∞) = [M L⁻³]
- Velocity of the ship (V∞) = [L T⁻¹]
- Length scale associated with the hull (c) = [L]
- Acceleration due to gravity (g) = [L T⁻²]
By substituting these dimensions into the dimensionless groups, we get:
- Drag coefficient (CD) = [D] / ([M L⁻³] [L T⁻¹]² [L²]) = [M L T⁻²] / [M L⁻³ L² T⁻²] = [L⁻¹]
- Froude number (Fr) = [L T⁻¹] / √([L T⁻²] [L]) = [L T⁻¹] / [L T⁻¹] = [1]
Both dimensionless groups are dimensionally consistent and independent, and they can fully describe the problem. Therefore, according to Buckingham's Pi theorem, the relationship between CD and Fr can be expressed as a function:
CD = f(Fr)
This shows that the drag coefficient is a function of the Froude number, which is consistent with the statement to be proved.
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Related Questions
True/false: a polarized material must have a nonzero net electric charge.
Answers
The answer is False. A polarized material does not need to have a nonzero net electric charge. Polarization occurs when the positive and negative charges within a material are displaced relative to each other, creating an electric dipole moment.
This can happen in materials such as dielectrics or insulators, which do not conduct electricity. The net electric charge of a polarized material can still be zero, as the overall positive and negative charges remain balanced, but the charges are spatially separated. Polarization plays an important role in phenomena such as capacitance, dielectric constant, and polarization-induced electric fields.
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A sound wave travels to a high wall which is 225m away from the source and is then reflected back to is initial position If the speed of sound in air as 340ms", calculate the time it takes to hear the echo.
Answers
Answer:
1.32 (3sf)
Explanation:
total distance the sound wave travel= 225 x 2= 450m
450 ÷ 340= 1.32s
A small insect smashes into the windshield of your car while you are zooming down the interstate. Which exerts the larger force; the bug on the car or the car on the bug?
Answers
Force is directly proportional to the mass of the body. The small insects weight so small thus the force exerted by the insect will be smaller. Thus the force exerted by the car is greater.
What is force?Force is an external agent acts on a body to change it from the state of rest or motion. Various kinds of forces include magnetic force, frictional force, nuclear force, gravitational force etc.
In physics, force is the product of mass and the acceleration. Thus force has the expression F = ma. Therefore, the force exerted from a massive body is greater than the force exerted from a lighter body.
The car is very large in comparison to the insect and it weighs a lot where, the weight of the insect and the force exerted by it is negligible. Hence, the force exerted by the massive body that is car is larger than that by the small insect.
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A light rod of length 2L has 2 small heavy masses (each with mass m) attached at the end and the middle. The axis of rotation is at one end, as shown. If the bar is released from rest what is the magnitude of the initial angular acceleration?
Answers
To determine the magnitude of the initial angular acceleration of the system, we can use the principles of rotational dynamics and the equation for the torque.
When the rod is released from rest, the two masses will start to fall due to gravity, creating a torque that causes the rod to rotate. The magnitude of the torque can be calculated using the equation:
τ = I * α
where:
τ is the torque,
I is the moment of inertia of the system,
α is the angular acceleration.
The moment of inertia of the system can be calculated as the sum of the individual moments of inertia of the masses with respect to the axis of rotation.
For the mass at the end of the rod, the moment of inertia is given by:
I1 = m * L^2
For the mass at the middle of the rod, the moment of inertia is given by:
I2 = (1/4) * m * L^2
The total moment of inertia of the system is the sum of these two:
I = I1 + I2 = m * L^2 + (1/4) * m * L^2 = (5/4) * m * L^2
Substituting this into the torque equation, we have:
τ = (5/4) * m * L^2 * α
The torque created by the falling masses is due to the force of gravity acting on them. The magnitude of the torque is given by:
τ = F * d
where F is the force of gravity on one of the masses and d is the lever arm, which is L for the mass at the end of the rod and L/2 for the mass at the middle of the rod.
The force of gravity on one of the masses is given by:
F = m * g
where g is the acceleration due to gravity.
Substituting these values into the torque equation, we have:
(5/4) * m * L^2 * α = m * g * L + (1/2) * m * g * (L/2)
Simplifying the equation:
(5/4) * L * α = g * L + (1/2) * g * (L/2)
(5/4) * α = g + (1/2) * (g/2)
(5/4) * α = g + (1/4) * g
(5/4) * α = (5/4) * g
α = g
Therefore, the magnitude of the initial angular acceleration is equal to the acceleration due to gravity, g.
which type of energy is released when a nucleus is split apart?
a. kinetic energy
b. elastic energy
c. chemical energy
d. nuclear energy
Answers
Answer:
D. Nuclear energy
Explanation:
A nucleus is the result of nuclear energy if it is split into an other the same result shall happen it being nuclear energy.
A ball is thrown vertically upward.It's velocity at the highest point is?
A. 10 ms^-1
B. Zero
C. 10 ms^-2
D. None of these
Answers
B
Explanation:
BECAUSE IT WAS GOING UPWORD THEN IT'S VELOCITY WAS DECREASING -10MS¹
Answer:
Explanation:
From physics, which is directly related to math (especially when it comes to parabolic motion!), we learn that at the very top of the parabola the object has to stop for a millisecond so it can turn around and fall back to earth. This translates to a velocity of 0 at its highest point. So B.
When a 15.00 kg mass is attached to a vertical spring, the spring is stretched 2.0 m such that the mass is 6.0 m above the table. The spring constant is 400.0N/m? What is the total potential energy associated with this system?
Answers
Answer:
idk
Explanation:
idk
a car having a mass of 10kg accelerates from 10m/s square to 16 m/s square in t seconds? What is the force exerted by the car?
Answers
using F=ma (force = mass * acceleration), the force needed would be 10 kg * 16
10 * 16 = 160, so the force would be 160N.
Answer:
The answer is 160 N
Explanation:
I did the test
Hope this helps :)
Refer to Scenario 119. 52. When properly connected to a 480-volt circuit, the boiler will supply ___ watts of power
Answers
Scenario 119 in relation to the question is not provided. In an AC circuit, the formula to determine the power is given as:P = V x I x cos θwhere: P is the power in watts, V is the voltage in volts, I is the current in amperes, and cos θ is the power factor.
However, the voltage is given in the question, which is 480 V, and there is no current or power factor provided in the question. Hence, the answer will be a which is equal to the power of the boiler in watts when it is connected to a 480-volt circuit.
In an AC circuit, power is defined as:P = V x I x cos θFor this question, the voltage (V) is given as 480V. However, the current (I) and the power factor (cos θ) are not provided. Hence, we cannot directly calculate the power from the equation given above.
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the image of a shoplifter in a department store is viewed in a convex (diverging) mirror. the image is
Answers
The image of a shoplifter in a department store being viewed in a convex (diverging) mirror so the image of the shoplifter will appear smaller, upright, and virtual. This is because convex mirrors are designed to provide a wider field of view, making it easier for store staff to monitor potential shoplifters.
If the cut part of the hollow sphere is painted from the inside, then its outer surface becomes the reflecting surface. This kind of mirror is known as a convex mirror.
A convex mirror is also known as a diverging mirror as this mirror diverges light rays when they strike its reflecting surface.Virtual, erect, and diminished images are always formed with convex mirrors, irrespective of the distance between the object and the mirror.
So, convex mirrors are designed to provide a wider field of view, making it easier for store staff to monitor potential shoplifters.
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explain the difference in how particles are arranged in a solid,liquids and gases
Answers
Answer:
hope this helps
Explanation:
solid particles are arranged according to the size of the object
while liquid particles are arranged how they move freely together in the object they are in.
while gas particles are arranged scatterly like they spread.
please help
Newton second law of motion is F =ma
Answers
Answer: ma is the formula of Newton's Second Law of Motion. Newton's Second Law of Motion is defined as Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.
Explanation: Newton's second law of motion is F = ma, or force is equal to mass times acceleration.
Hi there!
Using Newton's Second Law:
\(F = ma\)
F = Net Force (60 N)
m = mass (30 kg)
a = acceleration (m/s²)
Solve for acceleration given the other values.
\(60 = 30a\\\\a = \frac{60}{30} = \boxed{2 \frac{m}{s^2}}\)
If the net force increases (while the mass is held constant), the acceleration will INCREASE.
If the mass of the object increases (while the net force is held constant), then the acceleration will DECREASE.
the energy produced by the internal motion of atoms? electrical , thermal, chemical, nuclear
Answers
Answer:
Thermal energy, or heat, is the energy that comes from the movement of atoms and molecules in a substance. Heat increases when these particles move faster. Geothermal energy is the thermal energy in the earth. Motion energy is energy stored in the movement of objects. so the answer is thermal energy
Most metallic elements, such as copper
and iron, have high melting points. This
is a useful property because
F. it keeps cars made of metal from
becoming hot on summer days
G. it enables people to use pots and pans
made of metal to cook food
H. it prevents machine parts made of
metal from rusting
J. it makes metals easier to melt so they
can be poured into molds to make
precision tools
Answers
Answer:
G. it enables people to use pots and pans made of metal to cook food
Explanation:
Metals are known to be substances with a relative high melting point, which means that it takes a very high temperature to melt them. As used in this question, copper (Cu) and iron (Fe) at metallic elements that have high melting points.
One advantage of this property based on the options provided is that "it enables people to use pots and pans made of metal to cook food". This is because cooking food requires subjecting them to a constant temperature from a heat source e.g cooker or stove.
The material used to hold the food being cooked must possess a very high melting point to withstand the heat, hence, the importance of these metallic substances. Most pots and pans are made of steel, an alloy of iron, hence, they have high melting point.
Una persona pesa 700 N al nivel del mar. ¿Cuándo sube a un avión a
10000 m de altura pesará más, igual o menos? Bien explicado por favor
Answers
Answer:
The weight of the person decreases.
Explanation:
Weight of person at sea level = 700 N
height = 10000m
We know that the weight is given by product of mass and the acceleration due to gravity.
The acceleration due to gravity at height is given by
\(g' =g\times \left ( \frac{R}{R+h} \right )^2\)
Where, R is the radius of earth and h is the height.
Now, as we go on heights , the acceleration due to gravity decreases, so the weight also decreases as we go on heights.
Physics assignment <3 [100 points]
![Physics assignment <3 [100 points]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/YWDZhXWgd2Q6gQ7TmhEDa6fl0e6nRqsm.jpeg)
Answers
Case B: All of the forces that have been applied on this object are in balance because they all cancel each other out. In conclusion it means that the object is not moving.
Case C: The forces that have been applied to this object are unbalanced. Therefore the object will move to the right because it has a force of 2N
unknown12367 Can you see it? And will you help me? Sorry if its too much
I got 6 more left
Answers
.......................
What do you think is the main advantage of the Scientific Method approach to understand the physical world and an alternative like astrology? Please explain.
Answers
The main advantage of the scientific method is that it is a systematic and objective way to acquire knowledge. The scientific method is a process for acquiring knowledge that has been used to great success in understanding the physical world. Astrology, on the other hand, is based on subjective interpretations of the positions of the stars and planets.
The scientific method is a process for acquiring knowledge that has been used to great success in understanding the physical world. It is based on the following steps:
1. **Observation:** The scientist observes a phenomenon and asks questions about it.
2. **Hypothesis:** The scientist proposes a hypothesis, or a possible explanation for the phenomenon.
3. **Experimentation:** The scientist designs experiments to test the hypothesis.
4. **Data analysis:** The scientist collects data from the experiments and analyzes it.
5. **Conclusion:** The scientist draws a conclusion about the hypothesis based on the data analysis.
The scientific method is an iterative process, meaning that the scientist may go back and forth between the different steps as needed.
Astrology, on the other hand, is a system of divination that attempts to predict future events by interpreting the positions of the stars and planets. Astrology is not based on the scientific method, and there is no evidence that it is a reliable way to predict the future.
The main advantage of the scientific method is that it is a systematic and objective way to acquire knowledge. The steps of the scientific method are designed to minimize bias and to ensure that the results of the experiments are repeatable. This makes the scientific method a reliable way to learn about the physical world.
Astrology, on the other hand, is based on subjective interpretations of the positions of the stars and planets. There is no scientific evidence to support the claims of astrology, and the results of astrological predictions are not repeatable.
In conclusion, the scientific method is a more reliable way to understand the physical world than astrology. The scientific method is based on a systematic and objective approach to acquiring knowledge, while astrology is based on subjective interpretations of the positions of the stars and planets.
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When a 9.00 V voltage is applied to a resistor, it drives 0.325 A of current through the resistor. How much power does the resistor use? (Unit = W)
Can someone please explain how to do this question.
Answers
Answer: 2.925
Explanation: :)
Answer:
2.925
Explanation:
a helicopter drops a care package to stranded climbers as it is ascending at 8m/s. the package hits the ground 4 seconds later
Answers
d = 8 * 4
d = 32 m
PLS HELPP
Rowan is at an all-you-can-eat breakfast. He has a pancake on his plate and is going to put another pancake on top of it. Which one of these other pancakes would make the bottom pancake the warmest? Explain how the energy and temperature of both the bottom pancake and your chosen top pancake will change after they’ve been touching for a while, and why.
Answers
The other pancakes are at various temperatures and Conduction refers to the mode of transfer of thermal energy that arise when the two bodies are in close contact.
Briefing:The other pancakes are presumably at different temperatures in this scenario. If this is the case, then due to the thermal energy transfer, the pancake with the highest temperature should be the warmest at the bottom. Conduction is the process through which thermal energy is transferred when two bodies are in close proximity to one another.
How is temperature measure?Thermometers are used to measure the air's temperature. Common thermometers have a glass rod inside of which is a very thin tube. A liquid is delivered to the tube from a reservoir, or "bulb," at the thermometer's base. Sometimes the liquid is reddish alcohol, and other times it is mercury.
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when two or more cars arrive at an intersection at approximately the same time, who goes first?
Answers
When two or more cars arrive at an intersection at approximately the same time, the general rule is that the car on the right has the right of way.
However, if the cars are directly across from each other and there is no clear right or left, then the car that is already in the intersection has the right of way. In situations where there is still confusion, it is always best to proceed with caution and communicate with other drivers to ensure a safe and orderly flow of traffic.
When two or more cars arrive at an intersection at approximately the same time, the question of "who goes first?" depends on several factors.
1. Check for traffic signs or signals: Follow the rules indicated by stop signs, yield signs, or traffic signals to determine the right of way.
2. Right of way at a four-way stop: If it is a four-way stop, the first car to come to a complete stop has the right to proceed. If multiple cars stop at the same time, the car furthest to the right has the right of way.
3. Right of way at a T-intersection: If it is a T-intersection (three-way stop), the car on the through road has priority over the car on the terminating road.
Remember, always prioritize safety and ensure all drivers are aware of their turn before proceeding through the intersection.
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The graphic organizer compares energy transfer in two layers of the Sun. A venn diagram of 2 intersecting circles with the left circle labeled convection zone and the right circle labeled radiative zone. There is an X in the convection zone circle. There is a Y in the radiative zone. Which labels belong in the regions marked X and Y? X: Absorbs energy from the core Y: Takes longer for photons to move through X: Releases energy to the photosphere Y: Takes longer for photons to move through X: Takes longer for photons to move through Y: Absorbs energy from the core X: Takes longer for photons to move through Y: Releases energy to the photosphere
Answers
Answer:
X: Absorbs energy from the core.
Y: Releases energy to the photosphere.
Explanation:
Convection is a mode of heat transfer through fluids (liquids or gas), and it requires material medium for its propagation.
The energy absorbed from the core of the Sun, is transferred through X (convection zone) by convectional process, and it flows to Y (radiative zone). Since the regions X and Y have different functions, the heat propagates from X causing photons to traverse through Y where it get released into the photosphere or the Sun's surface.
Therefore;
X: Absorbs energy from the core.
Y: Releases energy to the photosphere.
Answer:
X: Takes longer for photons to move through
Y: Releases energy to the photosphere
Explanation:
Dos resistencias de 30 y 20 Ω se conectan en seria a un generador que tiene una diferencia de potencial de 20 V entre sus bornes. a. Determina la resistencia equivalente de la asociación b. Dibuja el circuito y coloca un amperímetro que indique el valor de la intensidad de la corriente y unos voltímetros que muestren la diferencia de potencial entre los extremos de las resistencias ¿Qué valores muestran estos aparatos?
Answers
Answer:
V = 12V, V = 8V
Explanation:
a) In this series circuit the equivalent resistance is
Req - R1 + R2
Req = 30 + 20
Eeq = 50 Ω
b) see attached
c) the circuit current is
i = V / Req
i = 20/50
i = 0.4 A
voltages are>
V = 0.4 30
V = 12V
V = 0.4 20
V = 8V
A student shoots a basketball in gym class. What pair of forces are acting on the ball and student? What
happens to the ball, and the student?
Answers
The pair of forces acting on the ball and student are the action and reaction forces.
What is a Force?This causes an object with mass to change its velocity. The pair of forces are the action and reaction forces.
The student exerts the force on the basketball and the ground with a corresponding reaction force from both acting on the student too.
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The magnetic field on Earth is due primarily
a) iron and nickel sinking into the core
b) magnesium diffusing through the mantle
c) aluminum remaining in the crust
d) silicates rising to the surface
Answers
The magnetic field on Earth is due primarily to iron and nickel sinking into the core. Option A is correct.
A magnetic field is a region in space where a magnetic force is experienced by a magnetic object or a moving charged particle. It is created by the motion of electric charges, such as electrons in atoms, or the movement of current in a wire.
The Earth's core is composed mainly of iron and nickel, and the movement of these metals in the liquid outer core generates a magnetic field through a process known as dynamo action.
The flow of liquid metal in the outer core generates electric currents, which in turn create the magnetic field that surrounds the Earth. This magnetic field is important for protecting the Earth from harmful solar radiation and is also responsible for phenomena such as the aurora borealis.
Hence, A. is the correct option.
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How is speed calculated? multiply velocity by displacement divide velocity by displacement multiply distance by time divide distance by time
Answers
Answer:
\(\huge\boxed{Divide\ distance \ by \ time}\)
Explanation:
Speed = Distance / Time
So, to find distance, we actually divide distance by rime.
Answer:
\(\large \boxed{\mathrm{divide \ distance \ by \ time}}\)
Explanation:
Using the formula to calculate speed:
\(\displaystyle \sf speed =\frac{distance}{time}\)
We divide the distance by the time taken to get the average speed.
a roller-coaster car is moving at 20 m/s along a straight horizontal track. what will its speed be after climbing the 15-m hill shown in the figure, if friction is ignored?
Answers
The speed of the roller-coaster car after climbing the 15-m hill will be less than 20 m/s if friction is ignored.
When the roller-coaster car climbs the hill, it gains potential energy at the expense of its kinetic energy. Ignoring friction, the total mechanical energy of the car is conserved. At the bottom of the hill, the car has both kinetic and potential energy.
As it climbs the hill, the potential energy increases while the kinetic energy decreases. At the top of the hill, all of the initial kinetic energy is converted into potential energy. According to the law of conservation of energy, the sum of the potential energy and kinetic energy will remain constant.
Since the car started with an initial speed of 20 m/s and has climbed a 15-m hill, the potential energy gained at the top of the hill will be equal to the initial kinetic energy.
Therefore, at the top of the hill, the car's speed will be zero. The initial kinetic energy has been completely converted into potential energy.
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A sport car starts from rest with an acceleration of 12 m/s2 . Calculate its final velocity after 7 s.
Answers
Answer:
Final velocity= 84 m/s
Explanation:
V final= V initial + a * t
Vf = 0+ 12 (7)
Vf= 84 m/s
if the cat has a mass of 3.4 kg , how far to the right of sawhorse b can it walk before the plank begins to tip?
Answers
The cat can walk up to 0.617 m to the right of sawhorse B before the plank begins to tip.
To determine how far to the right of sawhorse B the cat can walk before the plank begins to tip, we need to consider the balance of forces and torques acting on the plank. Let's assume that the plank has a mass of negligible amount compared to the cat and that it is in equilibrium before the cat steps on it.
The torque caused by the weight of the cat can be calculated as the product of the weight force and the distance from the pivot point (which is at the position of sawhorse A). This torque needs to be balanced by the torque caused by the weight of the plank, which is acting at its center of mass, and the torque caused by the normal forces exerted by the sawhorses.
Assuming that the sawhorses are at the same height, the normal forces exerted by them on the plank are equal in magnitude and opposite in direction, which means that they cancel out each other's torque. Therefore, the only torque that needs to be balanced is the one caused by the cat's weight.
Using the equation for torque balance, we can write:
(distance from sawhorse B to cat's position) x (cat's weight) = (distance from center of mass to pivot point) x (plank's weight)
We know the cat's mass, which we can convert to weight using the acceleration due to gravity \((9.8 m/s^2)\), and we can assume that the plank's weight acts at its center (which is the midpoint of the plank). We also know the length of the plank and the position of the pivot point (which is at the position of sawhorse A).
Using these values, we can solve for the distance from sawhorse B to the cat's position:
(distance from sawhorse B to cat's position) = [(distance from center of mass to pivot point) x (plank's weight)] / (cat's weight)
Plugging in the values, we get:
(distance from sawhorse B to cat's position) = \([(1/2 x 1.5 m) x (9.8 m/s^2 x 4 kg)] / (3.4 kg x 9.8 m/s^2)\)
Simplifying the equation, we get:
(distance from sawhorse B to cat's position) = 0.617 m
Therefore, the cat can walk up to 0.617 m to the right of sawhorse B before the plank begins to tip.
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Before the plank starts to tip, the cat can move up to 2.1 metres to the right of sawhorse B.
The weight distribution on each side of the fulcrum determines where a plank will tip. The fulcrum is located in the middle of the plank, assuming the sawhorses are evenly distanced from it. To prevent tilting, the entire weight on the fulcrum's two sides must be equal.
The total weight on the left side of the fulcrum is 8 kg, made up of the 3.4 kg of the cat and 4.6 kg of the plank. The total weight on the right side of the fulcrum must likewise be 8 kg in order to prevent tilting.
We may determine the cat's speed by applying the torque formula (T = F x d), where T is torque, F is force, and d is distance. can cross the plank up to 2.1 metres to the right of sawhorse B without it tipping.
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