The power delivered to the device when connected to a 6.0 V battery is 10 W, which is less than the power delivered when connected to a 9.0 V battery.
The power delivered to the electronic device is proportional to the voltage supplied to it.
The relationship between power, voltage, and current is given by the equation P = VI, where P is power, V is voltage, and I is current. In this case, the power is given as 15 W when the device is connected to a 9.0 V battery.
Using the equation P = VI, we can solve for the current as I = P/V = 15 W / 9.0 V = 1.67 A. When the device is connected to a 6.0 V battery, the power delivered to the device can be calculated as P = VI = 1.67 A x 6.0 V = 10 W.
Therefore, the power delivered to the device when connected to a 6.0 V battery is 10 W, which is less than the power delivered when connected to a 9.0 V battery.
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A 0.810 kg ball falls 2.5m. How much work does the force of gravity do on the ball?
Answer:
W = 19.845 J
Explanation:
Work is defined as W = Fdcos\(\theta\), where F is the force exerted and d is the distance. Because the direction the ball is falling is the same direction as the force itself, \(\theta\) = 0 deg, and since cos(0) = 1, this equation is equivalent to W = Fd. In this case, the force exerted is the weight force, which is equivalent to m * g. Substituting you get:
W = mgd = 0.810 kg * 9.8 m/s^2 * 2.5m
W = 19.845 J
what force Pushes up on an airplane ?
Explanation:
As it flies, a plane is in the center of four forces. Lift (upward force) and thrust (forward push, provided by a propeller) get a plane into the air. Gravity and drag (air resistance, which is friction caused by air rubbing against the plane) try to pull the plane down and slow its speed.hope it helps
A manned spaceflight from Earth to Mars will travel much, much slower than the speed of light and is likely to require as much as 9 months one way! One liter of water has the mass of 1 kilogram (kg), and 1000 kg is a ton. Estimate how many kilograms of water are required for each astronaut for drinking, washing, and bathing over 9 months (assume the water is not recycled on board). Use any method you like, but justify your reasoning.
The entire lunar lander that delivered Apollo astronauts to the surface of the Moon had a mass of 15 tons. How does this compare to the mass of water you estimated is required for the Mars-bound astronauts?
Apollo astronauts to the Moon, the mass of water required for each Mars-bound astronaut (6210 kg) is less than half the mass of the lunar lander.
What is the estimated number of kilogram of water for each astronaut?To estimate the number of kilograms of water required for each astronaut during a 9-month manned spaceflight to Mars, we'll consider the daily water consumption for drinking, washing, and bathing.
On average, an astronaut needs around 3 liters (3 kg) of water per day for drinking, and around 20 liters (20 kg) for washing and bathing.
Calculate the total daily water consumption for one astronaut:
Drinking: 3 kg/day
Washing and bathing: 20 kg/day
Total: 3 kg/day + 20 kg/day = 23 kg/day
Calculate the number of days in 9 months:
9 months x 30 days/month = 270 days (assuming 30 days/month as an average)
Calculate the total water consumption for one astronaut over 9 months:
23 kg/day x 270 days = 6210 kg
So, an estimated 6210 kilograms of water are required for each astronaut during a 9-month spaceflight to Mars, without recycling water on board.
Comparing this to the mass of the entire lunar lander (15 tons or 15,000 kg) that delivered
Apollo astronauts to the Moon, the mass of water required for each Mars-bound astronaut (6210 kg) is less than half the mass of the lunar lander.
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You have a wooden statue hanging from the ceiling using a 10 m spring m the gym. You know the spring constant of the spring is 2 N/m. The statue's 10 kg mass causes the spring to stretch 3 m. What is the potential energy of the spring while it holds up the statue?
9 joules are the spring's potential energy when supporting the statue.
How to calculate potential energy?The potential energy of a spring can be calculated using the formula:
PE = 1/2 kx²,
where k = spring constant and x = displacement of the spring from its equilibrium position.
In this problem, the spring has a constant of 2 N/m and a displacement of 3 m due to the statue's mass of 10 kg.
Plugging in the given values into the formula:
PE = 1/2 (2 N/m) (3 m)²
PE = 1/2 (2 N/m) (9 m²)
PE = 9 J
Therefore, the potential energy of the spring while holding up the statue is 9 joules.
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Naomi has increased the pressure on a solution of liquid and gas in a closed container. What will this do to the gas in her solution?
Answer:
Increase the amount of gas
Explanation:
By increasing the pressure of the solution, the amount of gas will have to increase. Solubility of gases increases as the pressure is made to increase. Before the pressure was increased, the gases moved freely about. But as it was increased, theses gases had more frequent collisions within this solution. Causing an increase. The liquid on its own will experience no changes.
Answer:
Increase the amount of gas
Explanation:
A mass on a spring oscillates with simple harmonic motion of amplitude A about the equilibrium position x = 0. Its maximum speed is vmax and its maximum acceleration is amax.
(a) What is the speed of the mass at x = 0?
____vmax
(b) What is the acceleration of the mass at x = 0?
____amax
(c) What is the speed of the mass at x = A?
____vmax
(d) What is the acceleration of the mass at x = A?
____amax
When the mass is traveling toward x=+A at the equilibrium position (x=0), the maximum velocity occurs.
What is velocity?Velocity is defined as a vector expression representing the change in position over time of an object or particle. Acceleration is the rate at which the speed and direction of a moving object vary over time.
In simple harmonic motion, the acceleration is zero at the object's maximum speed. Maximum mass displacement in SHM equates to maximum acceleration. The momentum calculator uses the equation p=mv, or momentum (p) equals mass (m) times velocity (v).
Thus, when the mass is traveling toward x=+A at the equilibrium position (x=0), the maximum velocity occurs.
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The type of control chart that is beat to montor this process is a) Establish the control limits to include 09.73% of the random variation in defectives. UCL
p
=0.290
∘
(enter your response as a number between 0 and 1, rounded to three decimal places). LCL
p
=0 (enter your response as a number between 0 and 1, rounded to three decimal places). b) Has the process been in control? Based on the developed control limits, the number of defectives has been c) If the sample size were 20 instead, how would your limits and conclusions change? UCL
p
= (enter your response as a number behween 0 and 1, rounded to three decimal places).
The upper control limit (UCLp) for the control chart is 0.290, rounded to three decimal places. The lower control limit (LCLp) is 0, rounded to three decimal places.
Based on the developed control limits, we cannot determine whether the process has been in control or not without additional information.
Control charts are used to monitor and control processes by analyzing data and identifying variations. In this case, the control chart is being used to monitor the number of defectives in a process. The question provides the control limits for the chart, which are the upper control limit (UCLp) and the lower control limit (LCLp).
The UCLp is the highest acceptable value for the proportion of defectives in the process, while the LCLp is the lowest acceptable value. In this case, the UCLp is given as 0.290, which means that if the proportion of defectives exceeds this value, it would be considered out of control. The LCLp is given as 0, indicating that there is no lower limit for the proportion of defectives.
However, the question does not provide any data or information about the actual proportion of defectives observed in the process. Without this data, we cannot determine whether the process has been in control or not. To make a determination, we would need to compare the observed proportion of defectives to the control limits provided.
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Suppose a bird takes off from a tree and files in a straight line. It reaches a speed of 10 m/s. What is the change in the birds velocity?
Answer:
10m/s
Explanation:
Change in velocity is given by:
final velocity - initial velocity
Here final velocity is 10 m/s and the initial velocity is 0m/s. This is because initially the bird was a rest.
ΔV = \(V_{f} - V_{i}\)
ΔV = 10 - 0
ΔV = 10m/s
ram takes 2 minutes to cover a distance of 600 meter. calculate his speed
A pendulum is made by letting a 2.0-kg object swing at the end of a string that has a length of 2.1 m. The maximum angle the string makes with the vertical as the pendulum swings is 30°. What is the speed of the object at the lowest point in its trajectory?
Answer:
The speed of the object at the lowest point in its trajectory is:
\(v=2.34\: m/s\)
Explanation:
We can use the conservation of energy between the maximum point of swing and the lowest point of the pendulum.
\(P=K\)
\(mgh=\frac{1}{2}mv^{2}\) (1)
Where:
h is the height of the object at 30° with the vertical.v is the speed at the lowest point.We can find h using trigonometry.
\(h=L-Lcos(30)=L(1-cos(30))\)
\(h=2.1(1-cos(30))=0.28\: m\)
Now, using equation (1) we can find v.
\(gh=\frac{1}{2}v^{2}\)
\(2gh=v^{2}\)
\(v=\sqrt{2gh}\)
\(v=\sqrt{2(9.81)(0.28)}\)
\(v=2.34\: m/s\)
I hope it helps you!
the thermometer records 680mmHg at ice point .The temperature it records at 380mmHg is what
The temperature it records at 380 mmHg is -25° C
It is given that
Pressure at steam point = 680 mmHg
Pressure at ice point = 440 mmHg
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied on various reference points and thermometric substances for definition
440 - 380/680 - 380 = 0 - x/100 - x
x = -25° C
Hence, temperature it records at 380 mmHg is -25° C
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The temperature it records at 380 mmHg is -25° C
What is Temperature?A physical quantity known as temperature expresses the concepts of hotness and coldness in numerical form. With a thermometer, temperature is measured. Thermometers are calibrated in a variety of temperature scales that historically rely on different reference points and thermometric materials for defin
It is given that
Pressure at steam point = 680 mmHg
Pressure at ice point = 440 mmHg
440 - 380/680 - 380 = 0 - x/100 - x
x = -25° C
Hence, temperature it records at 380 mmHg is -25° C
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If the mirror moves at 1.5m/s towards Peter while Peter remains at rest, what will he observe? Explain your reasoning
Answer:
Peters image will grow bigger
Explanation:
In this situation, only Peter is at rest and the mirror is in motion at 1.5m/s heading towards Peter.
From afar, Peter will look small in the mirror that is his image will be small When the mirror is moved at 1.5m/s Peter being the observer will notice that his image grows bigger and bigger.
A heat engine takes in 1200 j of heat from the high-temperature heat source in each cycle, and does 400 j of work in each cycle. what is the efficiency of this engine?
e = W/Q(h)
e = 400/1,200 = 0.3333
Answer: 33%
What is engine?A device created to transform one or more sources of energy into mechanical energy is known as an engine or motor.Potential energy, heat energy, chemical energy, electric potential, nuclear energy, and energy from the Earth's gravitational field are some of the energy sources that are currently available (from nuclear fission or nuclear fusion). Heat engines are particularly important because many of these processes use heat as an intermediary energy source. Atmospheric convection cells are one example of a natural process that transforms environmental heat into motion (e.g. in the form of rising air currents).What is temperature?Temperature is a numerical expression of how hot a substance or radiation is.There are three different types of temperature scales: those that are defined by the average translational kinetic energy per freely moving microscopic particle, like an atom, molecule, or electron in a body, like the SI scale; those that rely only on macroscopic properties and thermodynamic principles, like Kelvin's original definition; and those that are defined by practical empirical properties of particula rather than theoretical principles.Learn more about engine here:
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how do you calculate the numerical value of physical quantity
The value of a physical quantity is normally expressed as an implied product of a numeric value and a unit of measurement.
There are three categories to consider:
There is no explicit unit of measurement included. Examples of this would include index of refraction of a medium and the specific gravity of a substance (which is ratio of the density of the material divided by the density of some reference material, usually water at some specified temperature). In this category, there is an implied measurement unit of 1 . It is usually not written because 1 times any number is that same number, so it is pointless to write the “times 1”. The value of an index of refraction is simply a number, and that number is all you write for the quantity value. That number is the numerical value of the physical quantity. It is only slightly more complicated for specific gravity, because you are dividing one density by another, and both values should be expressed in the same units of measurement, and the division of one by the other cancels out those units, leaving you with 1 as the overall measurement unit.
For plane angles, there is a relationship between the length s of the arc of a circle, the radius r of that circle, and the angle a subtended by the arc at the circle center:
a = s/r
with the angle a being measured in the unit of radians. (To write the formula for some other angular unit requires incorporating a numeric factor, which is basically a conversion factor from radians to degrees,) Thus, if you have a circle of radius 3 m and an arc of 6 m on that circle, the the angle subtended or formed is:
(6 m)/(3 m) = 2, but we said this is the number of radians, so it is 2 rad.
Notice, we are dividing a length by a length (both the arc length and the radius being lengths), so if we use the same measurement unit for both lengths (regardless that unit being meters, feet, parsecs, or anything else), the two units cancel each other out upon division. This means that the unit we are calling radian is like with specific gravity in #1—it has the value 1. Indeed, we see the formula gives us 2 and we know that it is 2 rad, and the only way we can have them be the same, 2 rad = 2, is if the unit radian is actually just a funny, special name for the number 1. Why do we give the number 1 a special name here, unlike in category #1? That is because some inexperienced people find the concept of radian to be strange and inconvenient. They would rather use degrees, or arcminutes, or arcseconds, or semicircles, or some other such unit, and they all have different sizes. For example, a full circle is 2π rad and it is also 360°. Therefore, since both equal one circle of rotation, they must be equal to each other:
360° = 2π rad. Divide both sides by 360 to get:
1° = (2π/360) rad = (π/180) rad. Now, we saw above that rad = 1, so:
1° = (π/180) rad = (π/180) × 1 = π/180.
Thus, like the radian, the degree is also a number—not 1 though, but rather π/180, which cannot be “thrown away” because π/180 times a number does not yield back the original number.
Thus, 30° = 30 × π/180 = π/6 = π/6 × 1 = π/6 rad.
This is the explanation as to when we express an angle in degrees, we must write the ° symbol or spell out degrees, whereas when we express the angle in radians, we may either explicitly write rad or we may leave it off. Unfortunately secondary school geometry textbooks do not seem to understand this point and typically leave off the mandatory ° symbol. That usually gets straightened out when radians are presented—typically later in the second year of algebra or in trigonometry, but it becomes something necessary for students to unlearn the incorrect and learn the correct. Thus, if an angular unit is included, you can convert that angular unit into a real number and multiply by the numeric part of the physical quantity value to the the numeric value of the physical quantity. (And absence of angular unit implies radians, which have numeric value 1, so the numeric value of the quantity is just the numeric value that is present.
Solid angles work similarly, involving area divided by area. The steradian (sr) is the unit that has value 1.
fill in the blanks.
1. The process of weathering
depends on the rock.........
Climate.
Answer:
the answer is dry region climate
Explanation:
I hope it will help you
Answer:
the answer is dry region climate
Explanation:
hope it helps
A car traveling at 13.6 meters per second crashes into a barrier and stops in 0.321 meters.a. How long does it take the car to stop? Include units in your answer. Answer must be in 3 significant digits.
Given,
The initial velocity of the car, u=13.6 m/s
The final velocity of the car, v=0 m/s
The distance covered by the car, d=0.321 m
From the equation of the motion,
\(v^2-u^2=2ad\)On rearranging the equation,
\(a=\frac{v^2-u^2}{2d}\)This is the acceleration of the car which brings the car to rest after the collision.
On substituting the known values,
\(\begin{gathered} a=\frac{0-13.6^2}{2\times0.321} \\ =-288m/s^2 \end{gathered}\)From another equation of the motion,
\(v=u+at\)On rearranging the above equation,
\(t=\frac{v-u}{a}\)On substituting the known values,
\(\begin{gathered} t=\frac{0-13.6}{-288} \\ =0.0472\text{ s} \end{gathered}\)Thus the car comes to stop in 0.0472 seconds.
a ball dropped from rest falls freely intil it hits the ground with the speed of 20 m/s . the tine furing which the ball is in free fall is approximately
Answer:
5m/s
Explanation:
A 5.00-kg sphere is moving at a speed of 4.00 m/s. An identical sphere is at rest. The two spheres collide. The first sphere moves off at a 60.0° angle to the left of its original path. The second sphere moves off in a direction 90.0° to the right of the first sphere’s final path. Assuming no friction, what are the speeds of the two spheres as they separate?
The final speeds of the spheres are 3.47 m/s and 3.08 m/s.
We can use conservation of momentum to solve this problem since there are no external forces acting on the system.
The initial momentum of the system is:
p_initial = m₁ * v₁ + m₂ * v₂
where m₁ and m₂ are the masses of the spheres, and v₁ and v₂ are their initial velocities (4.00 m/s and 0 m/s, respectively).
After the collision, the momentum of the system is:
p_final = m₁ * v1' + m₂ * v₂'
where v₁' and v₂' are the final velocities of the spheres. We also know that the angle between the first sphere's final path and its initial path is 60 degrees, which means that the angle between the two spheres after the collision is 150 degrees (90 + 60).
Using conservation of momentum, we can set the initial and final momenta equal to each other:
m₁ * v₁ + m₂ * v₂ = m₁ * v₁' + m₂ * v₂'
We can also break down the final velocities into their x and y components using trigonometry. Let's define the angle between the first sphere's final path and the x-axis as theta. Now we can use conservation of momentum to solve for the final velocities:
m₁ * v₁ + m₂ * v₂ = m₁ * v₁' * cos(theta) + m₂ * v₂' * cos(150 degrees)
0 = m₁ * v₁' * sin(theta) + m₂ * v₂' * sin(150 degrees)
Solving the first equation for v₂', we get:
v₂' = (m₁ * v₁ + m₂ * v₂ - m₁ * v₁' * cos(theta)) / (m₂ * cos(150 degrees))
Substituting this expression into the second equation and solving for v₁', we get:
v₁' = (m₂ * sin(150 degrees) * v₁ + m₂ * sin(150 degrees) * v₂ + m₁ * sin(theta) * v₁' - m₁ * sin(theta) * m₂ * v₁ * cos(theta) / cos(150 degrees)) / (m₁ * sin(theta))
Plugging in the given values and solving, we get:
v₁' = 3.47 m/s
v₂' = 3.08 m/s
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What are two DIFFERENT resources that can be found on the ocean floor?
1. a jet accelerates from rest on a runway at 6.50 m/s2 for 50.25s until it finally takes off the ground what is the distance covered before take off?
2. from rest, a car accelerates uniformly over a time of 7.5 seconds and covers a distance of 15 determine the acceleration of the car
where is the car at 14 seconds
1. The jet covers a distance of 8193.38 meters before taking off.
2. The acceleration of the car is 0.44 m/s² and the car is 43.68 meters away from its starting point at 14 seconds.
1. For the first question, we can use the formula:
distance = initial velocity × time + 0.5 × acceleration × time²
Since the jet starts from rest, the initial velocity is 0. Therefore, the distance covered before take off can be calculated as follows:
distance = 0 × 50.25 + 0.5 × 6.50 × (50.25)² = 8193.38 meters (rounded to two decimal places)
Therefore, the jet covers a distance of 8193.38 meters before taking off.
2. For the second question, we can use the formula:
distance = 0.5 × acceleration × time²
Since the car starts from rest, the initial velocity is 0. Therefore, the distance covered can be calculated as follows:
15 = 0.5 × acceleration × (7.5)²
Solving for acceleration, we get:
acceleration = 15 / (0.5 × 7.5²) = 0.44 m/s² (rounded to two decimal places)
Therefore, the acceleration of the car is 0.44 m/s².
To determine where the car is at 14 seconds, we can use the formula:
distance = initial velocity × time + 0.5 × acceleration × time²
Since we don't know the initial velocity, we can use the formula:
distance = (final velocity)² - (initial velocity)² / (2 × acceleration)
We can solve for the final velocity using the formula:
final velocity = initial velocity + acceleration × time
Putting it all together, we get:
distance = ((initial velocity) + acceleration × time)² - (initial velocity)² / (2 × acceleration)
Simplifying, we get:
distance = initial velocity × time + 0.5 × acceleration × time²
Using the values given, we get:
distance = 0 + 0.5 × 0.44 × (14)² = 43.68 meters (rounded to two decimal places)
Therefore, the car is 43.68 meters away from its starting point at 14 seconds.
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At a swim meet, swimmer A swims 50 m in 12 s, swimmer B in 13 s, swimmer C in 11 s, and
swimmer D in 14 s. The race involved swimming back and forth one time. Which swimmer had
the greatest displacement?
Answer:
Swimmer B had the greatest displacement:)
Explanation:
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Explain why a smart meter monitors the amount of electrical energy being used as well as the time at which it is being used.
Answer:
Smart Meters measure both the amount of electrical energy used and the time at which it is being used because they are used to monitor the energy consumption at real time, such that the time of use of energy can be monitored, thereby enabling several utility functions for load sharing and maintenance, including;
i) Time of use tariffs, where energy is billed based on peak and off peak periods, which increases profits to the producer, reduces cost for some consumers, encourages more even hourly and daily usage of electricity, lower maintenance cost, lower capital expenditure for peak stations, and reduces carbon emission
ii) Guarantees more accurate energy consumption measurement and billing
iii) Accurate crew dispatch to fault locations
iv) Prevent fraud due to tampering with meter
v) Increase customer confidence in billing
Explanation:
What direct method of generating electricity?
For Me Is "Hydropower."
Because Hydropower is most efficient method of generating electricity because 95 per cent of the energy of flowing water gets converted into electricity—only five per cent of the energy is converted into other forms of energy.
A 61.7 kg carpenter at a construction site plans to swing in a circular arc from one roof top to an adjacent roof at the end of a 11.5 meter rope suspended from a crane boom. if her wiry arms, toughened by years of driving spikes with a no. 22 framing hammer, are capable of exerting 1229 n of force on the rope, what is the maximum speed that she can tolerate at the low point of her swing?
At the lowest point of her swing, she can withstand a maximum speed of 10.78 m/s.
Given that,
Mass of the carpenter = 61.7 kg
Length of the rope = 11.5 m
Capable force = 1229 N
Centripetal force acting on the body,
F = mv²/r = (61.7× v²)/11.5 = 5.37 v²
Gravitational force acting on her is
F = m × g = 61.7 × 9.81 = 605.28 N
By summing up gravitational and centripetal forces to get the total available force,
5.37 v² + 605.28 = 1229
5.37 v² = 623.72
v² = 116.15
v = 10.78 m/s
Hence, the maximum speed at the low point of her swing is 10.78 m/s.
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rank the following hypothetical planets -- all of which have the same total mass and same radius -- from lowest moment of inertia to highest moment of inertia: 1) a uniform sphere of mixed up rock and iron 2) a rocky planet with an iron core 3) a rocky planet with an iron crust 4) a uranium planet with a thick atmosphere (where the radius is measured to the top of the atmosphere)
The correct rank of the given hypothetical planets having the same radius from the lowest moment of inertia to the highest moment of inertia is 4231
First of all we must know that because of the relationship of the moment of inertia to the rotation is exactly analogous and represents that if a body has lower moment of inertia than a body with higher moment of inertia. Even if the bodies (or here in this case as given) masses and sizes are equal. Now it is very important to know that the object or planets with more mass at the centre means to have lower moment of inertia full stop hence as per the discussion of the given information, the rank of the hypothetical planet as per the given conditions will be 4231.
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what is rotating inside of the earth to create a magnetic field?
Answer:
So it's clear that Earth's hot iron core isn't what creates the magnetic field around our planet. ... On Earth, flowing of liquid metal in the outer core of the planet generates electric currents. The rotation of Earth on its axis causes these electric currents to form a magnetic field which extends around the planet
Explanation:
An air bubble of 2.00 mm radius is generated under water at 10 m depth in a river. Assume the temperature of the water is the same everywhere. a) Find the radius of the bubble right before it emerges from the water (Hint: pressure = force / area; force = mass x gravity). b) How much heat does the bubble absorb during the process?
The radius of the bubble right before it emerges from the water is approximately 1.35 mm.
When an air bubble is generated under water, it experiences an increase in pressure as it moves deeper due to the weight of the water above it. The pressure inside the bubble is higher than the surrounding water pressure, and this pressure difference results in a net force acting on the bubble, pushing it towards the surface. In this case, the bubble is generated at a depth of 10 m in a river.
To find the radius of the bubble right before it emerges from the water, we can use the principles of hydrostatic pressure. The pressure inside the bubble at any given depth can be calculated using the equation:
pressure = pressure due to water + pressure due to air
The pressure due to water is given by the equation:
pressure due to water = density of water x gravity x depth
Since the temperature of the water is assumed to be the same everywhere, the density of water remains constant. We can substitute the given values into the equation and calculate the pressure due to water at a depth of 10 m.
Next, we need to calculate the pressure inside the bubble. This can be done by considering the force acting on the bubble, which is the net force due to the pressure difference between the inside and outside of the bubble. The force can be calculated using the equation:
force = pressure difference x area
Since the bubble is spherical, the area can be expressed as:
area = \(4πr^2\)
Here, 'r' is the radius of the bubble. We can rearrange the equation to solve for the pressure difference and substitute the given values into it.
Once we have the pressure inside the bubble, we can equate it to the pressure at the water's surface (which is atmospheric pressure) to find the radius of the bubble right before it emerges. Rearranging the equation and solving for 'r', we find that the radius of the bubble is approximately 1.35 mm.
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Freida stands on a hill with a slope of 12 degrees. If her mass is 65 kg, what is the magnitude of the normal force acting on her?
A. 623 N
B. 637 N
C. 132 N
D. 601 N
Answer:
b
Explanation:
(10 points) A uniform magnetic field B has constant strength b teslas in the z-direction 11.0. B = (0,0,01 (a) Verity that A = Bxr is a vector potential for B, where r = {x,y,0) (b) Calculate the flux
(a) A = B × r is a vector potential for B, where r = {x, y, 0}.
(b) The flux through a surface S can be calculated as Φ = ∫B·dA, where B is the magnetic field and dA is an infinitesimal area vector perpendicular to the surface.
Determine the vector potential?(a) To verify that A = B × r is a vector potential for B, we need to show that ∇ × A = B.
Using the cross product property, we have ∇ × A = ∇ × (B × r). Applying the vector identity (A × B) × C = B(A · C) - C(A · B), we get ∇ × (B × r) = B(∇ · r) - r(∇ · B).
Since ∇ · r = 0 (as r = {x, y, 0}), and ∇ · B = 0 (as B has a constant magnitude in the z-direction), we find that ∇ × A = B, verifying A = B × r as the vector potential for B.
(b) The flux through a surface S can be calculated as Φ = ∫B·dA, where B is the magnetic field and dA is an infinitesimal area vector perpendicular to the surface.
Given that B has a constant strength b teslas in the z-direction, the flux through surface S will be Φ = ∫B·dA = ∫(0, 0, b) · (dxdy) = b∫dxdy = bA, where A is the area of the surface S.
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How many colls must a loop have with a cross-sectional area of 0.5m ^ 2 that is pulled through a magnetic field of 0.25T in 1.0s in order for there to be an induced emf of 4 ?
We can use Faraday's Law of Induction to solve this problem:
EMF = -N * d(phi)/dt
where EMF is the induced electromotive force, N is the number of turns in the loop, and d(phi)/dt is the rate of change of the magnetic flux through the loop.
In this problem, we are given that the induced EMF is 4 V, the magnetic field is 0.25 T, and the time taken is 1.0 s. The magnetic flux through the loop is given by:
phi = B * A
where B is the magnetic field and A is the cross-sectional area of the loop.
Substituting these values into Faraday's Law, we get:
4 = -N * d(phi)/dt
4 = -N * (d/dt)(B * A)
4 = -N * (A * dB/dt)
4 = -N * (0.5 * 0.25)
N = -32
Since we cannot have a negative number of turns, we must take the absolute value of N:
N = |-32| = 32
Therefore, the loop must have 32 turns in order for there to be an induced EMF of 4 V.