The energy released in the alpha decay reaction is approximately 0.736 MeV.
To determine the energy released in the alpha decay reaction, we can use the mass-energy equivalence principle (E = mc²). The energy released is equal to the difference in the masses of the reactant and the products, multiplied by the speed of light squared (c²).
Given the atomic masses of the reactant and the products:
Mass of 212Bi (m1) = 211.9912857 u
Mass of 208Tl (m2) = 207.9820187 u
Mass of 4He (m3) = 4.002603 u
The mass of the reactant (m1) is greater than the combined masses of the products (m2 + m3) since some mass is converted into energy during the decay process.
Mass difference (Δm) = m1 - (m2 + m3)
Energy released (E) = Δm * c²
To convert the atomic mass units (u) to kilograms (kg), we use the conversion factor:
1 u = 1.66053906660 x \(10^{-27}\) kg
The speed of light (c) is approximately:
c = 2.998 x \(10^{8}\) m/s
Substituting the given values, we can calculate the energy released:
Δm = (211.9912857 - (207.9820187 + 4.002603)) * 1.66053906660 x \(10^{-27}\) kg
= (211.9912857 - 211.9846223) * 1.66053906660 x \(10^{-27}\) kg
= 0.0066634 * 1.66053906660 x \(10^{-27}\) kg
E = Δm * c²
= 0.0066634 * 1.66053906660 x \(10^{-27}\) kg * \((2.998*10^{8}m/s) ^{2}\)
≈ 0.0066634 * 1.66053906660 x \(10^{-27}\) kg * 8.988 x \(10^{16}\) m²/s²
≈ 1.17869 x \(10^{-13}\) kg * m²/s²
= 1.17869 x \(10^{-13}\) Joules
To convert the energy from Joules to MeV (Mega-electron volts), we use the conversion factor:
1 MeV = 1.60218 x \(10^{-13}\) Joules
Energy released (E) in MeV = (1.17869 x \(10^{-13}\) Joules) / (1.60218 x \(10^{-13}\) Joules/MeV)
≈ 0.736 MeV
Therefore, the energy released in the alpha decay reaction is approximately 0.736 MeV.
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I need help Will give five stars please show work please
Answer:
These has anwers and also the solution. You can recheck if you want.
3. With suitable sketch, explain the measuring instrument used
for measuring the Gauge Pressure
Gauge pressure is the pressure measured relative to atmospheric pressure. A commonly used instrument for measuring gauge pressure is the pressure gauge.
A pressure gauge typically consists of a circular dial with a pointer, a pressure sensing element, and a scale. The sensing element, which is usually a diaphragm or a Bourdon tube, is connected to the system or container whose pressure is being measured.
The pressure gauge is usually connected to the system or container through an inlet port. When the pressure in the system or container changes, it exerts a force on the sensing element of the pressure gauge. This force causes the sensing element to deform, which in turn moves the pointer on the dial. The position of the pointer on the pressure scale indicates the gauge pressure.
The pressure scale on the dial is calibrated in units such as psi (pounds per square inch), bar, or kPa (kilopascals), depending on the application and region. The scale allows the user to directly read the gauge pressure value.
It's important to note that the pressure gauge measures the difference between the pressure being measured and the atmospheric pressure. If the system or container is under vacuum (pressure lower than atmospheric pressure), the gauge will indicate negative values.
Pressure gauges are widely used in various industries and applications where monitoring and control of pressure is essential, such as in industrial processes, HVAC systems, pneumatic systems, and hydraulic systems.
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A certain physical quantity, R, is calculated using the formula: R- 4a2(b - c) where a, b, and c are distances. What is the SI unit for R? cm cm^2 m
m^2 m^3
We can assume that a, b, and c are measured in metres as they are distances (m). R = 4(m)2(m - m) = 4m3 as a result. Thus, m3 is the SI unit for R. (cubic meters).
How is the R constant calculated?By calculating the number of moles of a gas that occupy a specific measured volume at a specified pressure and temperature, the ideal gas constant R can be calculated experimentally. In this laboratory, the breakdown of potassium chlorate produces oxygen, which is collected and analysed.
What are the ideal gas equation's units for R?pV = nRT, where n is the number of moles and R is the universal gas constant, is the formula for the ideal gas law. R's value is influenced.
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Which of following are longitudinal waves?
a Electromagnetic waves
b Sound waves
c Both electromagnetic and sound waves
d None of the above
Answer:
The answer is B
Sound waves
The 500-N force F is applied to the vertical pole as shown(1) Determine the scalar components of the force vector F along the x'- and y'-axes. (2) Determine the scalar components of F along the x- and y'-axes.
Solution :
Given :
Force, F = 500 N
Let \($ \vec F = F_x\ \hat i + F_y\ \hat j$\)
\($|\vec F|=\sqrt{F_x^2+F_y^2}$\)
∴ \($F_x=F \cos 60^\circ = 500 \ \cos 60^\circ = 250 \ N$\)
\($F_y=-F \cos 30^\circ = -500 \ \cos 30^\circ = -433.01 \ N$\) (since \($F_y$\) direction is in negative y-axis)
\($F=250 \ \hat i - 433.01 \ \hat j$\)
So scalar components are : 250 N and 433.01 N
vector components are : \($250 \ \hat i$\) and \($-433.01\ \hat j$\)
1. Scalar components along :
x' axis = 500 N, since the force is in this direction.
\($F_{x'}= F \ \cos \theta = 500\ \cos \theta$\)
Here, θ = 0° , since force and axis in the same direction.
So, cos θ = cos 0° = 1
∴ \($F_{x'}=500 \times 1=500\ N$\)
\($F_{y'}= F \ \sin \theta = 500\ \sin 0^\circ=500 \times 0=0$\)
\($F_{y'}=F\ cos \theta$\) but here θ is 90°. So the force ad axis are perpendicular to each other.
\($F_{y'}=F\ \cos 90^\circ= 500 \ \cos 90^\circ = 500 \times 0=0$\)
∴ \($F_{x'}= 500\ N \text{ and}\ F_{y'}=0\ N$\)
2. Scalar components of F along:
x-axis :
\($F_x=F\ \cos \theta$\), here θ is the angle between x-axis and F = 60°.
\($F_x=500 \times \cos60^\circ=250\ N$\)
y'-axis :
\($F_{y'}=F\ \cos \theta$\), here θ is the angle between y'-axis and F = 90°.
\($F_{y'}=500 \times \cos90^\circ=500\times 0=0\ N$\)
∴ \($F_{x}= 250\ N \text{ and}\ F_{y'}=0\ N$\)
comets tend to be ________ than asteroids, and it is estimated that there are far ___________ large comets than large asteroids.A. Crust and MantleB. Faster and MoreC. Hydrogen and HeliumD. Change in climate and core
"Comets tend to be faster than asteroids, and it is estimated that there are far more large comets than large asteroids." Correct option is B.
As comets typically originate from farther out than asteroids do, they move at faster speeds when they cross Earth's orbit: An asteroid would need to be larger than 10 kilometres in diameter, whereas a comet would only need to be about 7 kilometres in diameter to hit Earth with enough energy to form Chicxulub crater.
Two factors that differentiate a comet from an asteroid are shape of the orbit and chemical composition.
There are asteroids that are spherical, curved, and even have satellites. A comet circles the Sun similarly to an asteroid, but unlike an asteroid, it is made of ice and dust. Therefore, a comet's ice and dust composition begin to vaporise as it approaches the Sun. Consequently, a comet looks fuzzy and/or has a tail when viewed through a telescope.
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A flux of 0.6Wb passes through a motor field pole with an area of 120 cm2. Calculate the flux density
We will have that the flux density will be:
\(^{}\rho=\frac{0.6Wb}{120cm^2}\Rightarrow\rho=5\cdot10^{-3}Wb/cm^2\)Ứng dụng ra đầu tiên
Answer:
?
Explanation:
how is charged particles related to electric current, electric circuits, and resistance
Charged particles are fundamental to the behavior of electric currents, electric circuits, and resistance. An electric current is the flow of charged particles, typically electrons, through a conductor.
The flow of charged particles generates an electric field that induces a potential difference, or voltage, across the conductor.Electric circuits are constructed by connecting conductors and electrical components, such as resistors, capacitors, and inductors, in a specific configuration. The arrangement of the components determines how the current flows through the circuit.
The flow of current through the circuit depends on the resistance offered by the components in the circuit and the potential difference across the circuit.Resistance is the property of a conductor that opposes the flow of current. The resistance of a conductor is proportional to the number of charged particles in the conductor, the length of the conductor, and the cross-sectional area of the conductor. The resistance can also be affected by the temperature of the conductor and its material properties.
In summary, charged particles are responsible for generating electric currents that flow through electrical circuits. The behavior of the currents is determined by the arrangement of the components in the circuit and the resistance offered by the conductors and components. Resistance is a fundamental property of a conductor that opposes the flow of charged particles and can be affected by various factors.
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A ball is thrown vertically upward with a speed of 18m/sec from the edge of 85m tall building.
a. What is the maximum height in which the ball reached from the ground?
b. How much later it took the ball to reach the ground?
c. What is the final velocity of the ball as it hits the ground?
Answer:
Explanation:
Using the formula to calculate the maximum height
H = u²/2g
u is the initial velocity = 18m/s
g is the acceleration due to gravity = 9.81
H = 18²/2(9.81)
H = 324/19.62
H = 16.51m
The maximum height in which the ball reached from the ground = 85m + 16.51m = 101.5m
b) Time of fight = 2u/g
T = 2(18)/g
T = 36/9.81
T = 3.67s
It took the ball 3.67s later to reach the ground
3) To get the final velocity of the ball as it hits the ground, we need to calculate the horizontal component of the velocity,
Ux = Ucosθ
ux = 18cos 90 (angle of launch is 90 since the ball is thrown vertically upwards)
Ux = 18(0)
Ux = 0m/s
Hence the final velocity of the ball as it hits the ground is 0m/s
Astronomers can now report that active star formation was going on at a time when the universe was only 20% as old as it is today. When astronomers make such a statement, how can they know what was happening inside galaxies way back then
Answer:
First, as you may know, the light travels at a given velocity.
In vaccum, this velocity is c = 3x10^8 m/s.
And we know that:
distance = velocity*time
Now, if some object (like a star ) is really far away, the light that comes from that star may take years to reach the Earth.
This means that the images that the astronomers see today, actually happened years and years ago (So the night sky is like a picture of the "past" of the universe)
Also, for example, if an astronomer sees some particular thing, he can apply a model (a "simplification" of some phenomena that is used to simplify it an explain it) and with the model, the scientist can infer the information of the given thing some time before it was seen.
The astronomers could know what was happening inside galaxies way back then by the fact that;
they examine the spectra of galaxies (or the overall colors of galaxies) with the highest redshifts they can find
Astronomers Measure the wavelength of the light that is stretched, so the light is seen as 'shifted' towards the red part of the spectrum by using spectroscopy. This measure is also called redshift.
This invokes a ray of light through a triangular prism that splits the light into various components known as spectrum.
The way the astronomers could use this concept to know what was happening in the galaxies before is by examining the spectra of galaxies that have the highest redshifts.
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HELP!! An illustration of a pendulum at 3 positions of a pendulum. The equilibrium position is labeled B. The other two positions are the maximum displacement of the pendulum labeled A and C. In between A and B are 3 lighter colored pendulum sketches equally spaced. In between B and C are 3 lighter colored pendulum sketches equally spaced.
At which point(s) does the pendulum have the greatest potential energy?
A only
B only
C only
both A and C
Answer
the answer is A and c
Explanation:
i got it right on edge
Answer:
Both A and C is correct
Explanation:
A student is in class 400 minutes every day for 5 days each week. How many seconds is this?
Answer:
120,000seconds
Explanation:
400 minutes x 5= 2000minutes (2000minutes x 60)seconds =120,000seconds.
btw :
stay safe! :3
Answer:
12000
Explanation:
5 x 400 = 2000, 2000 x 60 = 12000
average method and it reports the tollowing unit data tor the rorming department. Units completed in the torming department are transferred to the painting department. Production cost information for the forming department follows. . Calculate the equivalent units of production for both direct materials and conversion for the Forming department. o. Calculate the costs per equivalent unit of production for both direct materials and conversion for the Forming department c. Using the weighted average method, assign costs to the forming department's output-specifically, its units transferred to painting and its endina work in brocess inventorv. Calculate the costs per equivalent unit of production for both direct materials and conversion for the For Jsing the weighted average method, assign costs to the forming department's output-specifically, its 4 d its ending work in process inventory. Complete this question by entering your answers in the tabs below. Calculate the equivalent units of production for both direct materials and conversion for the forming department. a. Calculate the equivalent units of production for both direct materials and conversion for the Forming departm b. Calculate the costs per equivalent unit of production for both direct materials and conversion for the Forming c. Using the weighted average method, assign costs to the forming department's output-specifically, its units tra and its ending work in process inventory. Complete this question by entering your answers in the tabs below. Calculate the costs per equivalent unit of production for both direct materials and conversion for the forming department Required information Using the weighted average method, assign costs to the forming department's output-specifically, its units trar painting and its ending work in process inventory.
Given information: The average method reports the following unit data for the forming department. Units completed in the forming department are transferred to the painting department. Production cost information for the forming department follows.
Direct materials:
Units completed during the period = 45,000 units
Ending work in process inventory = 5,000 units
Direct materials cost = $202,500
Conversion costs:
Units completed during the period = 45,000 units
Ending work in process inventory = 5,000 units
Conversion cost = $189,000
a. Calculation of equivalent units of production for both direct materials and conversion for the forming department:
Equivalent units of production = Units completed during the period + (Ending work in process inventory * Degree of completion)
Direct materials:
Equivalent units of production = 45,000 + (5,000 * 50%) = 47,500 units
Conversion costs:
Equivalent units of production = 45,000 + (5,000 * 60%) = 48,000 units
b. Calculation of the cost per equivalent unit of production for both direct materials and conversion for the forming department:
Cost per equivalent unit of production = Total cost for the period / Equivalent units of production
Direct materials:
Cost per equivalent unit of production = $202,500 / 47,500 units = $4.26 per unit
Conversion costs:
Cost per equivalent unit of production = $189,000 / 48,000 units = $3.94 per unit
c. Calculation of the cost assigned to the forming department's output using the weighted average method:
Total cost = Cost of units transferred out + Cost of ending work in process inventory
Cost of units transferred out = Number of units transferred out * Cost per equivalent unit of production
Cost of ending work in process inventory = Number of units in ending work in process inventory * Cost per equivalent unit of production
Direct materials:
Cost of units transferred out = 40,000 * $4.26 per unit = $170,400
Cost of ending work in process inventory = 5,000 * $4.26 per unit = $21,300
Total cost = $170,400 + $21,300 = $191,700
Conversion costs:
Cost of units transferred out = 40,000 * $3.94 per unit = $157,600
Cost of ending work in process inventory = 5,000 * $3.94 per unit = $19,700
Total cost = $157,600 + $19,700 = $177,300
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12) A road has a round hump 12.0 m in radius. What is the minimum speed at which a car can leave the road at the top
of the hump?
The minimum speed at which a car can leave the road at the top is 10.84 m/s.
The minimum speed
The minimum speed at which the car can leave the road is calculated as follows;
\(F_c = F_n\\\\\frac{mv^2}{r} = mg\\\\\frac{v^2}{r} = g\\\\v^2 = rg\\\\v = \sqrt{rg} \\\\\)
where;
r is the radius of the curved road = 12 mg is acceleration due to gravity = 9.8 m/s².\(v = \sqrt{12 \times 9.8} \\\\v = 10.84 \ m/s\)
Thus, the minimum speed at which a car can leave the road at the top is 10.84 m/s.
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Please help! Will give brainliest!
A cyclist changes its speed going down hill from 22 m/s to 37 m/s in 2 seconds. Calculate the acceleration of the cyclist.
Answer:
7 1/2m/s/s
Explanation:
37-22=15
15/2=7 1/2
suppose you and your sister travel at different speeds in space and you note a slowing of her clock. compared with her clock your sister will notice that your clock runs group of answer choices slower. the same. faster. need more information
It is to be noted that suppose you and your sister travel at different speeds in space and you note a slowing of her clock, compared with her clock your sister will notice that your clock runs "slower" (Option B). The theory that explains this is called the Theory of Relativity.
What is the Theory of Relativity and why is it important?
The theory of relativity, developed by Albert Einstein beginning in 1905, describes the behavior of objects in space and time and may be used to predict things like the presence of black holes, light bending due to gravity, and the behavior of planets in their orbits.
It's essentially a gravity hypothesis. Gravity, rather than being an invisible force that draws objects to one another, is a bending or warping of space. The greater the bulk of an item, the more warped the space around it.
The special theory of relativity is important because it helps us comprehend time and space better. The special theory of relativity defines how two observers perceive each other's motion when gravity is not a factor.
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Please help, I will give brainly.
The specific latent heat of vaporization of water is 2300 kj/kg.
What is the specific latent heat of vapourization?
Specific latent heat of vapourization is the quantity of heat required to convert unit mass of a substance from liquid to vapour state without change of temperature.
We have...
Q = heat energy = 69 kj
m = mass = 0.030 kg
L = Specific heat
The formula is given by:
Q = mL
L = Q / m
L = 69 / 0.030
L = 2300 kj / kg
When would an objects average speed and average velocity be different?
Answer:
the motion of an object is along a straight line and in the same direction, the magnitude of displacement is equal to the total path length. In that case, the magnitude of the average velocity is equal to the average speed.
f) if the red laser has a wavelength of 633 nm, what is the speed and wavelength of the red light in the plastic?
The speed of light in a medium, such as plastic, is given by the equation v = c/n, where v is the speed of light in the medium, c is the speed of light in vacuum (approximately 3 x 10^8 m/s), and n is the refractive index of the medium. To determine the speed of red light in plastic, the refractive index of the specific plastic material must be known.
The wavelength of light in a medium can be determined using the equation λ = λ0/n, where λ is the wavelength of light in the medium, λ0 is the wavelength of light in vacuum, and n is the refractive index of the medium. Given that the red laser has a wavelength of 633 nm (633 x 10^-9 m) in vacuum, the wavelength of red light in plastic can be calculated using the refractive index of the plastic material.
In conclusion, to determine the speed and wavelength of red light in plastic, the specific refractive index of the plastic material needs to be known.
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if 50.0 cm of copper wire (diameter 1.00 mm) is formed into a circular loop and placed perpendicular to a uniform magnetic field that is increasing at the constant rate of 10.0 mt/s, at what rate is thermal energy generated in the loop?
The required rate at which thermal energy is generated in the loop is calculated to be 3.66× 10⁻⁸ W.
Length of the copper wire is given as 50 cm.
The relation between radius and length is given as,
r = L/2π = 50/(2×3.14) = 50/6.28 = 7.96 cm
The loop's area can be expressed as,
A = π r² = 3.14(7.96)² = 198.95 cm²
Change in magnetic field is calculated as,
⇒ dB/dt = 0.01 T/s
Induced EMF is given as,
e = A × dB/dt = 198.95 × 0.01 = 1.98 × 10⁻⁵ V
Resistivity of copper wire is given as,
ρ = 1.69 × 10⁻⁸ Ω m
Diameter d = 1 mm
Radius = d/2 = 0.5 mm = 0.5 × 10⁻³ m
The wire's resistance is determined by,
R = ρL/πr² = (1.69 × 10⁻⁸× 50 ×10⁻²)/π ×(0.5 × 10⁻³)² =(84.5× 10⁻¹⁰) /(0.785× 10⁻⁶) = 107.64 × 10⁻⁴ = 1.07 × 10⁻² ohm
Power is given by the relation,
P = e²/R = (1.98 × 10⁻⁵)²/(1.07 × 10⁻²) = (3.92 × 10⁻¹⁰)/(1.07 × 10⁻²) = 3.66× 10⁻⁸ W
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How is the interaction of electrons with the nucleus of an atom similar to the interaction of two magnets?
Answer:
One of the harder ideas to grasp in fusion is that nuclei, which, because of their electric charge, strongly repel at long range
(compared to the size of a nucleus), can strongly attract at short range. This activity allows students to explore a similar situation in
which
the magnetic interaction provides the repulsion (similar to the electric interaction within
the nucleus) and Velcro provides an attractive force at short range (similar to the nuclear
strong interaction).
Explanation:
Brainliest Answer pls
If the pressure head in the aquifer is 100 ft., calculate the effective stress (N/m") in the aquifer.
If the aquifer is pumped and the hydraulic head at some point is reduce by 12 ft., what will be the resulting changes in the pressure head (m), the effective stress (N/m*), the fluid pressure (N/m*), and the total stress (N/m? ?
The resulting changes will be:
1. Pressure head: 88 ft (or 26.82 m)
2. Effective stress: No change, assuming no other factors affect it
3. Fluid pressure: No change
4. Total stress: Decreased by the same amount as the effective stress
To calculate the effective stress in the aquifer, we need to subtract the fluid pressure from the total stress.
Given:
Pressure head in the aquifer = 100 ft (or 30.48 m)
The pressure head in the aquifer is directly proportional to the fluid pressure, which can be calculated using the formula:
Fluid pressure (P) = ρ * g * h
Where:
ρ = density of the fluid (water) = approximately 1000 kg/m³
g = acceleration due to gravity = 9.8 m/s²
h = pressure head
Fluid pressure = 1000 kg/m³ * 9.8 m/s² * 30.48 m ≈ 298,440 N/m² (or Pa)
The total stress in the aquifer is the sum of the fluid pressure and the effective stress. Therefore, the effective stress can be calculated by subtracting the fluid pressure from the total stress.
Now, let's consider the changes in the hydraulic head due to pumping:
Change in hydraulic head = -12 ft (or -3.66 m)
The resulting changes in each parameter will be as follows:
1. Pressure head:
The pressure head will be reduced by 12 ft, so the new pressure head will be 100 ft - 12 ft = 88 ft (or 26.82 m).
2. Fluid pressure:
The fluid pressure does not change, as it depends on the density of the fluid and the acceleration due to gravity, which remain constant.
3. Effective stress:
The effective stress can be calculated as the total stress minus the fluid pressure. Since the fluid pressure remains constant, the effective stress will also remain constant unless there are other factors affecting it.
4. Total stress:
The total stress is the sum of the fluid pressure and the effective stress. As mentioned earlier, the fluid pressure remains constant, so the total stress will decrease by the same amount as the effective stress, assuming no other factors affect the total stress.
Therefore, the resulting changes will be:
1. Pressure head: 88 ft (or 26.82 m)
2. Effective stress: No change, assuming no other factors affect it
3. Fluid pressure: No change
4. Total stress: Decreased by the same amount as the effective stress
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How might viral diseases be prevented?
Answer:
There are antiviral medicines to treat some viral infections. Vaccines can help prevent you from getting many viral diseases.
A ball is thrown straight up into the air, with an initial speed of 28.2 m/s.
How fast is it moving after 1.00 s?
Martin likes to make flower bouquets that have 333 daffodils and 444 tulips per vase. A daffodil has a mass of ddd grams, a tulip has a mass of ttt grams, and the vase has a mass of vvv grams.
Mass of a bouquet = v + 3d + 4t
Calculation:Given,
Mass of daffodil = d gm
Mass of Tulip = t gm
Mass of vase = v gm
No. of daffodils = 3
No. of tulips = 4
To find,
Weight of flower bouquet =?
According to the question the equation will be
Mass of a bouquet = mass of vase + Mass of 3 daffodils + Mass of 4 tulips
Mass of 3 daffodils = 3d
Mass of 4 tulips = 4t
Now put in the equation,
Mass of a bouquet = v + 3d + 4t
Hence, the weight of flower bouquet is v + 3d + 4t.
I understand the question you are looking for is this:
Martin likes to make flower bouquets that have 3 daffodils and 4 tulips per vase. A daffodil has a mass of d grams, a tulip has a mass of t grams, and the vase has a mass of v grams. Find the total weight of the bouquet.
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particle travels in a circle of radius 26 m at a constant speed of 14 m/s. what is the magnitude of the acceleration (in m/s2)?
The magnitude of acceleration is 7.44 m/s²
Given data:
Radius of the circle, r = 26 m,
Speed of the particle, v = 14 m/s.
Acceleration of the particle is given by the formula: a = v²/r
Where, v is the velocity of the particle and r is the radius of the circle on which the particle is moving.
Substitute the given values in the formula of acceleration.
a = v²/r
= (14 m/s)²/26 m
= 7.44 m/s² (rounded off to two decimal places)
Therefore, the magnitude of acceleration is 7.44 m/s².
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a spring has a relaxed length of 5 cm and a stiffness of 150 n/m. how much work must you do to change its length from 7 cm to 12 cm? n·m
The amount of work you must do to change the length of the spring from 7 cm to 12 cm is 0.3375 N·m.
To find the work required to change the spring's length from 7 cm to 12 cm, we'll use the formula for work done on a spring, which is W = (1/2)k(x₂² - x₁²), where W is the work, k is the stiffness or spring constant, x₂ is the final length, and x₁ is the initial length.
In this case, the stiffness (k) is 150 N/m, the initial length (x₁) is 7 cm - 5 cm = 2 cm (0.02 m), and the final length (x₂) is 12 cm - 5 cm = 7 cm (0.07 m).
Plug these values into the formula: W = (1/2)(150)(0.07² - 0.02²) = (1/2)(150)(0.0049 - 0.0004) = 75(0.0045) = 0.3375 N·m
So, you must do 0.3375 N·m of work to change the spring's length from 7 cm to 12 cm.
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Knowing that an 8-mm-diameter hole has been drilled through each of the shafts AB,BC, and CD, determine (a) the shaft in which the maximum shearing stress occurs, (b) the magnitude of that stress.
Knowing that an 8-mm-diameter hole has been drilled through each of the shafts AB,BC, and CD, Without specific details about the applied load, material properties, and shaft geometry, it is not possible to provide a conclusive answer regarding
To determine the shaft in which the maximum shearing stress occurs and the magnitude of that stress, we need additional information such as the applied load, material properties, and geometry of the shafts. Without these details, it is not possible to provide a specific answer. However, I can provide a general explanation of the concept. In general, the shearing stress in a shaft is related to the applied torque and the shaft's geometry. The shearing stress can be calculated using the formula:
τ = T * r / J
where τ is the shearing stress, T is the applied torque, r is the radius of the shaft, and J is the polar moment of inertia of the shaft.
The polar moment of inertia (J) depends on the shape and dimensions of the shaft. In the case of a solid circular shaft, J is equal to (π/32) * d^4, where d is the diameter of the shaft.
To determine the maximum shearing stress, we would need to compare the values of τ in each shaft by considering the applied torques and the shaft dimensions. The shaft with the highest shearing stress would have the maximum value.
Without specific details about the applied load, material properties, and shaft geometry, it is not possible to provide a conclusive answer regarding the shaft in which the maximum shearing stress occurs or the magnitude of that stress.
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Betelgeuse is a supergiant star that will eventually supernova, which means that by mass it is classified as
Betelgeuse is a supergiant star that by mass is classified as a high-mass star.
What is a celestial body:
Celestial bodies are natural objects that are a part of the massive universe. Even though the universe has vast expanses of empty space, it is inhibited by them. The following are the 7 categories in which the celestial bodies are classified in:
Thus, as Betelgeuse is a supergiant star that will eventually result in a supernova it is classified as a high-mass star.
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