With a vacuum wavelength of 488 nm and an electron mass of 9.11*10^-31 kg, an electron travelling at 1490.45 m/s has the same momentum as a photon.
The pace at which the distance a moving item travels changes is measured as speed. Since speed is a scalar, it has magnitude but no direction as a unit of measurement. Speed is the rate at which anything moves over a predetermined distance. The elementary electric charge of the electron, sometimes known as the symbol e or, is a negative one. Given that they have no known components and are part of the first generation of lepton particles, electrons are frequently regarded as being elementary particles to its wavelength.
E = mc^2
mc^2 = hc/(lamda)
v = h/m(lamda)
v = 6.626*10^-34/9.11*10^-31*488*10^-9
v = 1490.45 m/s
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When moving a 100 kg couch, you apply a 55 N force and experience a frictional force or 10 N, what is the couch's
acceleration?
25N
Answer:
0.45 m/s²
Explanation:
Fnet = 55N - 10N = 45N
Force of friction is in opposite direction of the applied force.
a = Fnet/m = 45N/100 kg = 0.45 m/s²
Energy from the sun sets in motion extraordinary interactions between the atmosphere,
organisms and minerals,
energy from the earth's core profoundly affects the
shape of the ground we walk on.
A Consequently
B Meanwhile
C In conclusion
D For example
Energy from the sun sets in motion extraordinary interactions between the atmosphere, In option C In conclusion, organisms and minerals, energy from the earth's core profoundly affects the shape of the ground we walk on.
Why choose option C?C In conclusion is the best option to use in this sentence. This is because the sentence presents a summary or conclusion of the information that has been presented in the paragraph or passage. The phrase "In conclusion" signals to the reader that the author is wrapping up their thoughts on the topic and is a common way to signal the end of a presentation or discussion.
Option A "Consequently" could also be a good choice if the preceding information discussed the consequences or results of the interactions between the atmosphere, organisms, minerals, and energy from the earth's core.
Option B "Meanwhile" would not be a good choice because it suggests that there is some kind of parallel or contrasting action occurring at the same time, which is not the case in this sentence.
Lastly, Option D "For example" would not be a good choice because it introduces an example to illustrate a point, but the sentence does not present an example.
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what is the delta u for a system which has the following two steps: step 1: the system absorbs 60 j of heat while 40 j of work are performed on it
The delta Internal energy u for a system which has the following two steps is zero.
E = q + w
where q = heat and w = work completed
Q is positive when the system absorbs heat.
Q is negative when the system emits heat.
When the mechanism is functioning, w is negative.
The system performs better when work is done on it.
Step 1
E1 = 60 KJ + 40 KJ = 100 KJ.
E2 = (30 KJ + 70 KJ = (-100 KJ)
E1+E2=100KJ+(-100)KJ = 0KJ
Internal energy is the total internal energy of a thermodynamic system. It consists of both internal kinetic and potential energy contributions and is the energy needed to create or prepare the system in its internal state at the time. It keeps track of the system's energy gains and losses as a result of adjustments to its internal condition. [1][2] Both the system's total kinetic energy of motion and any external energies from the surrounding force fields are excluded. The cornerstone of the first law of thermodynamics, the law of conservation of energy, is the notion that the internal energy of an isolated system remains constant. Internal energy has a wide range of facets.
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if a 15-foot seesaw had a child weighing 100 pounds on the side where the seat was 10 feet away from the fulcrum, and the child on the opposite side weighed 200 pounds and was 5 feet away from the fulcrum, which formula would be correct to figure out if they were in static equilibrium?
The formula used to figure out if the two sides of the seesaw are in static equilibrium is force* perpendicular distance from the fulcrum.
The principle of moments is used to determine the seesaw's balancing point.
According to the principle of moments, the clockwise moment around a point equals the anti-clockwise moment.
The moment on one side of the seesaw = 100 pounds* 10 ft
⇒ 1000 pound-ft
The moment on the other side of the seesaw = 200 pounds* 5
⇒ 1000 pound-ft
Here, moment on one side of the seesaw = moment on the other side of the seesaw = 1000 pound-ft
So, according to the principle of moments, the seesaw is in static equilibrium.
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a circular coil of radius 15 cm is placed in a uniform magnetic field of strength 0.70 t. the direction of the magnetic field is at an angle of 20o with the normal of the coil. what is the magnetic flux through the coil?
The magnetic flux through the coil is 667.38 mWb. Magnetic flux is an important concept in electromagnetism and is used to calculate the force on a conductor in a magnetic field
Magnetic flux is a measure of the strength of a magnetic field passing through a surface. It is defined as the product of the surface area and the component of the magnetic field perpendicular to that surface.
The unit of magnetic flux is the weber (Wb), which is defined as the amount of magnetic flux that produces an electromotive force of one volt in a conductor that is completely enclosing a flux of one weber.
The magnetic flux through the coil is given by the equation:
φ = BAcosθ
where φ is the magnetic flux, B is the strength of the magnetic field, A is the area of the coil, and θ is the angle between the magnetic field and the normal to the surface of the coil.
In this case, the magnetic flux is given by:
φ = (0.70 T) * (π * (15 cm)^2) * cos(20o)
= 667.38 mWb
Note that the magnetic field strength is in tesla (T), the radius of the coil is in centimeters (cm), and the magnetic flux is in milliwebers (mWb).
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a foot ladder is resting in a wall and start slipping along the wall at a rate of m/sec. how fast is the based of the ladder moving away from the wall when the ladder is at the high meters?.
A foot ladder is resting in a wall and start slipping along the wall at a rate of m/sec. Along the diameter of the ladder, fast is the based of the ladder moving away from the wall when the ladder is at the high meters.
Velocity is the direction at which an object is moving and serves as a measure of the rate at which its position is changing as seen from a specific point of view and as measured by a specific unit of time (for example, 60 km/h northbound). In kinematics, the area of classical mechanics that deals with the motion of bodies, velocity is a fundamental idea. A physical vector quantity called velocity must have both a magnitude and a direction in order to be defined. Speed is the scalar absolute value (magnitude) of velocity; it is a coherent derived unit whose quantity is measured in metres per second (m/s or m/s1) in the SI (metric system). In order to stress the difference between the instantaneous velocity and average velocity, velocity is defined as the rate of change of location with regard to time. The average velocity of an object, or the constant velocity that would produce the same resultant displacement as a variable velocity in the same time interval, v(t), over some time period t, may be required in various applications. Always, an object's average velocity is less than or equal to its average speed.
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Determine the force in member DE of the truss, and state if the member is in tension or compression. Take P = 1745 lb .
The tension or compression of F CD = 3375 lb (G), F HI = 5625 lb (G), F CJ = 6750 lb (G)
Latin roots for the verb "to stretch" give us the word "tension." testing a portion of the force, such as a particular type of pull force. Any two physically connected objects may apply forces to one another. Depending on the kinds of things in contact, this contact forces different names. The force tensions are what we refer to when one of the items applying the force is a rope, string, chain, or cable. The force that results from compressing a material or object is called the compression force. Compression forces are the result of shearing forces aligning into one another. From hand tools to compression brakes, the compression force is employed to power everything. An essential engineering aspect is the compressive strength of materials and structures.
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The complete question:
Determine the force in members CD of the truss, and state if the member is in tension or compression. Take P = 1570lb. Determine the force in members HI of the truss, and state if the member is in tension or compression. Take P = 1570lb . Determine the force in members CJ of the truss, and state if the member is in tension or compression. Take P = 1570lb .
A box with a passenger inside is launched straight up into the air by a giant rubber band. Before launch, the passenger stood on a scale and weighed 750 N.Once the box has left the rubber band but is still moving upward, is the passenger's weight more than 750 N, 750 N, less than 750 N but not zero, or zero?
The passengers weight will be zero according to the box, but their true weight is still 750 N.
If the passenger was standing on a scale in the box, the scale would be at zero. This is because the passenger, box, and scale are all in free fall. The passenger still has mass, though and is still in a gravitational field, therefore it has a true weight of 750 N, which is mass X acceleration due to gravity, mg. Technically something can only have weight if it a normal force exists between the mass and the surface of another object, such as a scale.
Freefall is defined as a situation when a body is moving only under the influence of the earth's gravity. Since external force is acting on the ball, the motion will be accelerated. This free-fall acceleration is also known as acceleration due to gravity.
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an ultrasound system is set at 0 db and is transmitting at full intensity. what is the output power when the system is transmitting at 50% of full intensity?
the output power when the system is transmitting at 50% of full intensity -3dB .
In telecommunications, transmission is the act of transmitting or relaying analog or digital signals over wired, wireless, or fiber optic media. [1][2]
Transmission techniques are usually associated with physical layer protocol tasks such as modulation, demodulation, line coding, equalization, error control, bit synchronization and multiplexing, but also include higher layer protocol tasks. There are cases. B. Digitization and data compression of analog signals.
The transmission of digital messages or digitized analog signals is called data transmission.
An example of a transmission is the transmission of a signal of limited duration. Blocks or packets of data, phone calls, or emails
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a force of 20 n causes a spring to stretch 5 cm. what is the spring constant? group of answer choices 1 n/m 20 n/m 400 n/m 2 n/m
A force of 20 n causes a spring to stretch 5 cm. The spring constant is 400 N/m. So the correct option is (c) 400 N/m.
The spring constant is a measure of how much force is required to stretch the spring a certain distance. To calculate the spring constant, we must use the equation F = kx, where F is the applied force, k is the spring constant, and x is the distance the spring is stretched.
In this problem, we are given the applied force (F) of 20 N and the distance the spring is stretched (x) of 5 cm. To solve, we can rearrange the equation to solve for k:
k = F/x
k = 20 N/5 cm
k = 4 N/cm
We can also express this in newtons per meter (N/m) by multiplying by 100 to convert cm to m:
k = 400 N/m
Therefore, the spring constant is 400 N/m.
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what is the sequence of the anticodon, from the 3\' to 5\' end, of the trna in the a site?
The sequence of the anticodon, from the 3' to 5' end, of the trna in the a site is UGC.
'What is tRNA?'
A unique type of RNA molecule is called a transfer RNA (tRNA). Matching an mRNA codon to the amino acid it codes for is its responsibility. It functions as a sort of molecular "bridge" between the two, if you will.
An anticodon is a group of three nucleotides found in each tRNA. One or more distinct mRNA codons can bind to the anticodon of a particular tRNA. The amino acid encoded by the codons to which the tRNA binds is carried by the tRNA molecule as well.
A cell contains a wide variety of tRNAs, each of which has a unique anticodon and corresponding amino acid. In actuality, depending on the species, there are often 404040 to 606060 various varieties.
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identify the stage in star life cycle in which hydrogen is the primary fuel for nuclear fusion?
The stage in star life cycle where hydrogen is the primary fuel for nuclear fusion is called the main sequence star.
The star life cycle comprises of different stages. All stars are formed from nebula, which is a huge cloud of gas. The different stages in a star's life are
1. Protostar - They are massive clumps of cloud and dust and are not hot enough to achieve fusion.
2. Main sequence star - This is where the fusion takes place. Hydrogen undergo nuclear fusion to become helium and emits a great amount of energy. As long as there is hydrogen for nuclear fusion, the star remains as main sequence.
3. Red giants- After the star run out of hydrogen, they becomes much larger than the size when they were Main sequence. These stars will be much cooler. Here fusion takes place between helium and carbon.
Even though all stars starts the same the end will be based on the mass of the star. Smaller stars form a white dwarf. Big stars can become super giants and explode as supernova. Massive stars becomes neutron stars or black holes.
Life cycle of star where Hydrogen fusion is the main source of energy is Main sequence star.
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True or false :if there is a net force acting on an object it means there is an unbalanced force.
Answer:
true
Explanation:
The object will always accelerate if it has an unbalanced force acting on it in that direction
how may kilometers would you have to go above the surface of the earth for our weight to decrease to half of what it was at the surface
We have to go above 2651 kilometers of the earth for our weight to decrease to half of what it was at the surface
Geophysics applies the concepts of physics to the take a look at of the Earth. It deals with things like the motion of the Earth's crust and the temperatures of its interior.
Geology : is the medical take a look at of the earth- the material of which it is made, the methods that act on those materials, the products shaped, and the history of the planet and its existence paperwork due to the fact starting place. Geology now includes the take a look at of other planets as nicely.
We defile the earth via thinking about other people as our enemies, outsiders and foreigners; by dividing our earth into international locations and by developing enmity in opposition to any other institution of people.
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the captain of a plane wishes to proceed due west. the cruising speed of the plane is 246 m/s relative to the air. a weather report indicates that a 35.1-m/s wind is blowing from the south to the north. in what direction, measured with respect to due west, should the pilot head the plane?
The pilot of the plane should move 7.96° due west in order to proceed west direction.
According to the question the relative speed of plane with respect to air is 246 m/s. The speed of the wind is 35.1 m/s and the direction of the wind is from south to north. Now if we consider the velocity of plane with respect to ground as V m/s then in the west direction the components of this velocity will be
V cosθ = 246 m/s .....(1)
V sinθ = 35.1 m/s .....(2)
Dividing equation (2) by equation (1)
tanθ = 35.1/246
tanθ = 0.14
θ = tan⁻1(0.14)
θ = 7.96° which is the required value.
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part a a calorimeter consists of an aluminum cup inside of an insulated container. the cup is weighed on a top-loading balance and is found to have a mass of 31.91 g. a reaction is conducted in the calorimeter, raising the temperature from 21.2 c to 26.1 c what is the change in heat q for the aluminum cup in units of j? aluminum has a specific heat of 0.903 j 1 ? 1 write your answer to the correct number of significant figures.
The change in heat for the aluminum cup is 141.19 Joule.
What is specific heat?The amount of heat needed to raise a substance's temperature by one degree Celsius per gram is known as its specific heat. Typically, calories or joules per gram per degree Celsius are used as the units of specific heat.
Given that: mass of the aluminum cup: m = 31.91 g
Initial temperature: t = 21.2° C.
Final temperature: T = 26.1° C.
specific heat of aluminum: s = 0.903 J/g/° C.
Hence, the change in heat for the aluminum cup = ms (T-t)
= 31.91 g × 0.903 J/kg/° C × ( 26.1° C - 21.2° C)
= 141.19 Joule.
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)how far beyond its natural length (in cm) will a force of 50 n keep the spring stretched? (round your answer one decimal place.)
The spring will stretch beyond its natural length by 1.5 cm when a force of 50 N is applied.
The amount of stretching a spring experiences when a force of 50 N is applied to it is determined by Hooke's Law. According to Hooke's Law, the force applied to the spring and the extension of the spring are proportional. This means that the greater the force applied to the spring, the greater the extension.
Using Hooke's Law, the amount of extension of the spring when a force of 50 N is applied can be calculated using the following formula:
Extension = Force/Spring Constant
Where the spring constant is a measure of how stiff the spring is.
To calculate how far beyond its natural length (in cm) the spring will be stretched when a force of 50 N is applied, we first need to determine the spring constant of the spring in question. This can be done by measuring the natural length of the spring and then measuring how far it stretches with a known force. Once we have determined the spring constant, we can enter it into the formula above and solve for the extension.
For example, if the natural length of the spring is 15 cm and it extends to 18 cm with a force of 50 N, the spring constant would be 33.33 N/cm.
Using this spring constant, the extension of the spring when a force of 50 N is applied would be 1.50 cm
50/33.33 = 1.50.
Therefore, the spring will stretch beyond its natural length by 1.50 or 1.5 cm when a force of 50 N is applied.
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how is momentum related to the pressure exerted by a gas? explain on the molecular level, considering the behavior of molecules.
The momentum is p = m v . You can see from the equation that momentum is at once proportional to the object's mass (m) and velocity (v).
Therefore, the extra an object's mass or the extra its velocity, the extra its momentum.From equation (1), whilst the common velocity of the fueloline is increased, the momentum of the fueloline will growth too.
This will make the stress exerted via way of means of the fueloline will increase too. And, whilst the quantity of the molecules is increased, this could growth the full mass of the fueloline and the momentum of the fueloline will growth too.
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for which of the following values of p is the value of p(1 - p) maximized?
p(1 - p) value can be a maximum of 0.5. A p-value is nothing but a probability value which is a numerical representation of likelihood.
The likelihood that the null hypothesis is true is represented by the p-value. The possibility that the alternative hypothesis is accurate is (1 - p value). Replicable outcomes are indicated by a low p-value. A large effect or a significant result with significant theoretical, clinical, or practical implications are indicated by a low p-value.
A statistical test employing your data is used to determine the likelihood of your test statistic, which is the result of the test.
A p-value of 0.05 or less (usually 0.05) indicates statistical significance. Strong evidence is presented against the null hypothesis.
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A 1200kg elevator i upported by a cable in which the maximum afe tenion i 14. 000N
A. What i the greatet upward acceleration of the devetor
B. The greatet downward acceleration
(a)The greatest upward acceleration of the elevator with 1200 kg mass and specified maximum tension is 11.67 m/s².
(b) The greatest downward acceleration is 9.8 m/s².
(a) Given that,
Mass of the elevator = 1200 kg
Tension = 14000 N
Acceleration is the pace at which the speed and direction of a moving object alter over time.
We know the formula to calculate force as, F = m* a
Making a as subject, we have a = F /m
Putting the values in the equation,
a = F /m = 14000/1200 = 11.67 m/s²
Hence, the upward acceleration of the system is 11.67 m/s²
(b) The greatest downward acceleration is nothing but the acceleration due to gravity.
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A bowling ball rolls without slipping up a ramp that slopes upward at an angle β to the horizontal. Treat the ball as a uniform, solid sphere, ignoring the finger holes.
Part A:
What is the acceleration of the center of mass of the ball?
Express your answer in terms of the variable β and appropriate constants.
Part B:
What minimum coefficient of static friction is needed to prevent slipping?
Express your answer in terms of the variable β and appropriate constants.
Friction is an opposing force that works on a body's surface and tries to stop it from moving. Newton (N) is its unit.
What is the friction force?
Friction is the force created when two surfaces of two things come into contact and slide against one another.
It is described mathematically as the product of the normal reaction and the coefficient of friction.
The equation becomes balanced once the provided force and acceleration in the various components have been resolved. elements moving in the x-direction
To find acceleration on an inclined plane
Ma(sin∅) - F = ma
mg(cos∅) = R
F = μR
To prevent slippage, the frictional force must be less than the maximum static friction force. We'll use constants to represent the ratio of the ramp's opposite and adjacent sides.
At this point, the frictional force equals ma. It was previously discovered that a=gsin
The frictional force is thus mgsin∅. The maximum static friction force, or normal force, is defined as kmgcos∅, where k is the minimal static friction coefficient.
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four inductors, each having an inductance of 0.6 h, are connected in series. what is the total inductance of the circuit?
A series connection is made between four inductors, each of which has an inductance of 0.6 h. so the circuit's overall inductance is 2.4h.
Since the current change through each coil is the same, the inductance of inductors that are connected in series is computed as the sum of the individual inductances of each coil. L di/dt = V. Accordingly, the individual inductances of each inductor are added to determine the overall inductance of the series connection.
Let the four inductors be L1 = L2= L3= L4 = 0.6h
Given that inductance of each inductor = 0.6h
We are aware that LTotal = L1 + L2 + L3 +... + Ln is the formula for the total inductance of a series.
LTotal = L1+L2+L3+L4 = 0.6+0.6+0.6+0.6 = 2.4h is the total inductance.
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Tom has a mass of 70.8 kg and Sally has a
mass of 48.1 kg. Tom and Sally are standing
31.3 m apart on a massless dance floor. Sally
looks up and she sees Tom. She feels an
attraction.
If the attraction is gravitation, find its magnitude. Assume both can be replaced by point
masses and that the gravitational constant is
6.67259 × 10^−11 N · m^2
/kg^2
Answer in units of N.
Answer:
The Gravitational Attraction of Tom and Sally is 28.4631292 N.
Explanation:
The gravitational force formula is
gravitational force = (gravitationalconstant)(massofobject1)(massofobject2)/(distancebetweenobjects)^2
So if you plug in the values given, you get 28.4631292.
the power plant comprises one-piston engine of 230 hp at sea level. calculate the maximum velocity of the airplane at sea lev
The maximum velocity of aircraft will be between 200- 300 ft.
What is velocity ?
Velocity is the rate at which something is travelling in a specific direction. An object's velocity can either be constant or variable. The object's speed, direction of travel, or both can be altered.
What is sea level ?
On Earth, sea level serves as the reference point for determining elevation and depth. Since the ocean is one continuous body of water, its surface tries to seek uniformity everywhere it is.
b= 35.8 ft
S= 174 ft2
W= 2950lb
fuel capacity= 65
cp₁₀= 0.025
e=0.8
p=0.8
powerplant= one piston engine of 230hp of sea-level
V= ?
Let us assume v= 200ft/s
G= W/ 1/2 lr v²s = 2950/ 1/2 *0.0002377 * (200)² *177
= 0.357
Aspect ratio b³/3 = (35.8)²/ 17 a
=7.37
=0.025+ (0.357)²/π (0.07) (7.37)²
=0.0319
L/D = 0.357/ 0.0319 = 11.2
T= W/ L/D = 2950/ 11.2 = 263lb
PR=TRV = 263lb* 200
= 52600lb/fts²
This engine has power of 230 hp
230*550lb
= 126500 lb/fts²
so it can flow more at velocity of sea level
Hence, the maximum velocity of aircraft will be between 200- 300 ft.
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one block 3 of 3kg is next to a 5kg block, 47 newtons is being applid to the first block. what is the force between the blockws
The calculated answer is 196 N. The 2 kg block applies a typical response force of 16 N to the 3 kg block.
Newton's second law of motion states that the force applied by an object equals its mass times its acceleration: F = m ⨉ a. To apply this formula, you must use SI units for force (newtons), mass (kilograms), and acceleration (meters per second squared). Multiply the block's height and breadth to find its area. By the block area, divide your wall space. It is determined by multiplying the force's intensity by the distance the object moves in the force's direction.
F = mg = (20 kg)(9.8 m/s2)
= 196 N
in the aforementioned case, and
W = (196 N)(1.5 m)
= 294 Nm.
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a car increases its speed, changing its kinetic energy from 60,000 j to 80,000 j. assuming no friction, how much work is done by the car’s engine to cause this change?
The work done by the car engine to cause the car to increase its speed, hence, changing its kinetic energy from 60,000 j to 80,000 is 20000 J
What is work done?Work done is the product of the force applied and the distance moved by the applied force in the direction of the applied force.
Mathematically;
Work done = force * distance
The unit for measurement of work done is Joules.
The work done by the car engine to cause the car to increase its speed, hence, changing its kinetic energy from 60,000 j to 80,000 is the difference between the initial kinetic energy of the car and the final kinetic energy of the car.
The work done by the car engine = final kinetic energy - initial kinetic energyThe work done by the car engine = 80000 J - 60000 J
The work done by the car engine = 20000 J
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what happens to a moving object here on earth that keeps it's kinetic energy less than potential energy?
Answer:
If a moving object on Earth has less kinetic energy than potential energy, it means that its speed is not enough to overcome the force of gravity.As a result, the object will slow down and eventually come to a stop.If it is moving uphill, it will roll back down, and if it is moving horizontally, it will eventually come to a halt due to friction with the ground.In either case, the object will eventually reach a state where its kinetic energy is equal to its potential energy, at which point it will stop moving.A body which moves from rest with a uniform acceleration travels 18m during the third second. What will be its velocity at the end of the eighth second?
air flows through this tube at a rate of 1100 cm3/s . assume that air is an ideal fluid.
The height h=0.369cm of mercury in the right side of the U-tube.
As per the data given in the above question are as bellow,
Air flows through this tube at a rate of [tex]1100 cm^3/s[/tex]
Air is an ideal fluid.
Use the bernouli's equation, we get
[tex]p_1+\frac{1}{2} \rho v_1^2 & =p_2+\frac{1}{2} \rho v_2^2 \\p_1-p_2 & =\frac{1}{2} \rho\left(v_1^2-v_2^2\right)[/tex]
Use the continuity equation:
[tex]A_1 v_1 & =A_2 v_2 \\v_1 & =\frac{A_2 v_2}{A_1} \\& =\frac{A_2 v_2}{\pi\left(\frac{r_1}{2}\right)^2}[/tex]
That the rate of in the tube is
[tex]A_1 v_1=A_2 v_2=1100 \mathrm{~cm}^3 / \mathrm{s}[/tex]
Substitute the numerical value in the above equation we get
[tex]v_1 & =\frac{1100 \mathrm{~cm}^3 / \mathrm{s}}{\pi\left(\frac{2.0 \mathrm{~cm}}{2}\right)^2} \\& =350.14 \mathrm{~cm} / \mathrm{s} \\& =3.50 \mathrm{~m} / \mathrm{s}[/tex]
Similarly,
[tex]v_2 & =\frac{A_1 v_1}{A_2} \\& =\frac{1100 \mathrm{~cm}^3 / \mathrm{s}}{\pi\left(\frac{4.0 \mathrm{~mm}}{2}\right)^2} \\& =\frac{1100 \mathrm{~cm}^3 / \mathrm{s}}{\pi(0.2 \mathrm{~cm})^2} \\& =8753.5 \mathrm{~cm} / \mathrm{s} \\& =87.5 \mathrm{~m} / \mathrm{s}[/tex]
The pressure difference in the u shaped tube is
[tex]p_1-p_2=\rho^{\prime} g h[/tex]
Here, [tex]$\rho^{\prime}$[/tex] is the density of mercury.
From the above equation we get
[tex]h & =\frac{p_1-p_2}{\rho^{\prime} g} \\& =\frac{\frac{1}{2} \rho\left(v_1^2-v_2^2\right)}{\rho^{\prime} g} \quad\left(\text { Since } p_1-p_2=\frac{1}{2} \rho\left(v_1^2-v_2^2\right)\right)[/tex]
Substitute the numerical values in the above equation we get
[tex]h & =\frac{\frac{1}{2} \rho\left(v_1^2-v_2^2\right)}{\rho^{\prime} g} \\& =\frac{\frac{1}{2}\left(1.29 \mathrm{~kg} / \mathrm{m}^3\right)\left((87.5 \mathrm{~m} / \mathrm{s})^2-(3.50 \mathrm{~m} / \mathrm{s})^2\right)}{\left(13.6 \times 10^3 \mathrm{~kg} / \mathrm{m}^3\right)\left(9.8 \mathrm{~m} / \mathrm{s}^2\right)} \\& =0.0369 \mathrm{~m} \\& =0.0369 \mathrm{~m}\left(\frac{1 \mathrm{~cm}}{10^{-2} \mathrm{~m}}\right) \\[/tex]
=0.369cm
Height is 0.369cm
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Note:- The correct question could be as follow,
Air flows through this tube at a rate of 1100 cm3/s . assume that air is an ideal fluid.
What is the height h of mercury in the right side of the U-tube?
a 1.5-v alkaline d battery can provide about 43100 j of electric energy. if a curreny of 0.5 a flows through two d batteries while theyre in a circuit of a flashlight, how long will the batteries be able to provide power to the flashlight
The batteries will be able to provide power to the flashlight for 15.96 hours with specified voltage, energy and current.
Given that,
Energy E = 43100 J
Voltage v = 1.5 V
Current i = 0.5 A
Let t be the time for which batteries provide power to the flashlight.
The relation between energy, time, voltage and current is Energy = v* i* t
where, v is voltage
i is current
t is time
By placing the values in the formula above,
43100 = 1.5* 0.5* t
t = 43100/(1.5* 0.5) = 57466.67 s = 957.78 minutes = 15.96 hours
Thus, the time upto which the batteries provide power to the flashlight is 15.96 hours.
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