The speed with which m must move from M to stay at rest is √Mgr/m m/sec .Centripetal Force is responsible for the speed of mass m.
We are given that final state of mass M is rest. It means its velocity is zero. If velocity is zero it means that force acts on the mass M is balanced. When forces are balanced ,body will remain at rest as component of force and gravity cancel each other.
So, if mass M is at rest we need to identify what force are acting on the mass M.
Since mass M is directly perpendicular to acceleration due to gravity, therefore gravity will act some force on it.
Since mass M is moving in circle, due to its movement mass M feels centripetal force.
Therefore, centripetal force due to mass m=Force due to gravity
=>m×(v²)/r=Mg
=>v² = (Mg×r)/m
=>v=√Mgr/m
Hence, speed of mass m is √Mgr/m,
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(Complete question) is:
a mass m on a frictionless table is attached to a hanging mass M by a cord through a hole in the table. find the speed with which m must move for M to stay at rest.
for what scattering angle (in degrees) will the wavelength shift of x-rays be exactly double that found in part (a)?
The wavelength shift of x-rays be exactly double that found in part (a), if the scattering angle is 84.26°
Δλ = h ( 1 - cos θ ) / me c
Δλ = Wavelength shift
h = Planck's constant
θ = Scattering angle
me = Mass of an electron
c = Speed of light
h = 6.626 * 10⁻³⁴ J s
me = 9.1 * 10⁻³¹ kg
c = 3 * 10⁸ m / s
Δλ' = 6.9 * 10⁻¹⁴ m
Δλ = 2 Δλ'
Δλ = 2 * 6.9 * 10⁻¹⁴
Δλ = 13.8 * 10⁻¹⁴ m
13.8 * 10⁻¹⁴ = 6.626 * 10⁻³⁴ ( 1 - cos θ ) / 9.1 * 10⁻³¹ * 3 * 10⁸
13.8 * 10⁻¹⁴ = 0.2427 * 10⁻¹¹ ( 1 - cos θ )
1 - cos θ = 56.86 * 10⁻³
cos θ = 56.859 * 10⁻³
θ = 84.26°
The given question is incomplete. The complete question is:
for what scattering angle (in degrees) will the wavelength shift of x-rays be exactly double that found in part (a) which is 6.9 * 10⁻¹⁴ m.
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use the 1st law of thermodynamics to derive a simplified equation for a turbine that explains its performance based on inlet (1) and outlet (2) conditions.
Energy can neither be created nor destroyed, but it can be transferred. First law of thermodynamics.
What is energy?This is the ability or capacity to do work. we know that the first law of thermodynamics explains energy conservation. thus, energy can neither be created nor destroyed.
Also, Zeroth's law of thermodynamics talks about the thermal equilibrium of two or more bodies. thus, if body A and Body B are in thermal equilibrium with body C. that body A, B, and C are all in thermal equilibrium with each other.
Again, the second law of thermodynamics says more about heat direction.
Therefore, the thermodynamics supports that the heat cannot be transferred from a colder to a hotter body.
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A baseball player pitches a 0.14-kg baseball at 30 m/s.
–Calculate the kinetic energy for the baseball.
–How much work did the player do on the ball to give it this energy?
The kinetic energy of the baseball be 63 joule.
The player had to work of 63 joule on the ball to give it this energy.
What is kinetic energy?According to the definition of kinetic energy in physics, it is the amount of work that an item may accomplish while in motion.
As a scalar quantity, kinetic energy can only be fully defined by its magnitude.
Given that:
Mass of the baseball: m = 0.14 kg.
Speed of the baseball: v = 30 m/s.
So, kinetic energy of the baseball= 1/2×0.14×30² joule = 63 joule.
Hence, the player had to work of 63 joule on the ball to give it this energy.
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g 13. how fast is a 500 g ball that has a kinetic energy of 4.0 j? a) 4.0 m/s b) 0.13 m/s c) 2.0 m/s d) 1.6 m/s e) 20 m/s
The 500g ball with 4.0 J of kinetic energy, v = √(2*4.0 J/500g) = 2.0 m/s.
What is kinetic energy?
Kinetic energy is the energy associated with movement. It is the energy an object has due to its motion. Kinetic energy can be either potential or kinetic. Potential energy is stored energy and is the energy an object has due to its position or state. Kinetic energy is the energy of movement, and is the energy an object has due to its velocity. Kinetic energy is a function of the mass and velocity of an object. The kinetic energy of an object is equal to one half of its mass multiplied by the square of its velocity. Kinetic energy can be converted into other forms of energy, such as heat, sound, and light. Kinetic energy can also be converted into work, such as when a car accelerates or brakes. Ultimately, kinetic energy is the energy of motion and can be used to do work.
Kinetic energy (KE) of a moving object is equal to 1⁄2 its mass (m) multiplied by its velocity (v) squared.
KE = 1/2 mv2.
Rearranging this equation, we can calculate the velocity of an object given its mass and its kinetic energy.
v = √(2KE/m).
Thus, for the 500g ball with 4.0 J of kinetic energy, v = √(2*4.0 J/500g) = 2.0 m/s.
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given 2 spheres. big sphere diameter is 50% more than smaller one. weight of smaller one is 8 kg. what's the weight of the smaller one?
The weight of the larger mass will therefore be 27 kg. When you know the radius, you may use the formula volume = (4/3) r3 to calculate the sphere's volume or mass.
Then, using the formula mass = volume * density, you can calculate the mass by multiplying the volume by the density: mass = volume density. The formula mass = (4/3) r3 density can also be used.
The new radius can be expressed as r + 0.5r = 1.5r if the radius is increased by 50%. As a result, the new volume is 337.5% larger than the original. In other words, the new mass is 337.5% of the old mass.
The new mass will therefore be 27kg.
Furthermore, the area and circumference of the circle grow as the circle's diameter rises.
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Therefore, the greater mass will weigh 27 kg. When you are aware of the radius, you can determine the volume or mass of the sphere using the formula volume = (4/3) r3.
The mass can then be determined by multiplying the volume by the density using the formula mass = volume*density. It is also possible to apply the formula mass = (4/3)r3 density.
If the radius is expanded by 50%, the new radius may be written as r + 0.5r = 1.5r. The new volume is therefore 337.5% bigger than the old one. The new mass is therefore 337.5% of the original mass.
Therefore, the new mass will be 27kg.
Furthermore, as the circle's diameter increases, so do its surface area and circumference.
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while observing a truck with an alternator cable that is burnt and has many fuses and fusible links blown, technician a says that the battery was connected in reverse polarity. technician b says that batteries were likely deeply discharged and charged at a high current rate. who is correct?
Technician It is accurate to state that the battery was connected with the wrong polarity.
What is battery ?
A battery is a device that transforms chemical energy into electrical energy. It can include one or more electrical cells. Like many other common energy sources, batteries store energy through chemistry in the form of chemical potential.An electric circuit is used in this kind of reaction to transmit electrons from one material to another.
The heat created by the battery's reverse polarity may result in hydrogen gas (ignitable), which could blow the battery's casing up. The battery's damaged cover might allow acid to enter, melting delicate equipment and potentially inflicting serious injury. When you use a battery-powered device while it is plugged in, the entire circuit will be energised, which increases the risk of an electrical shock. Although the damage may be difficult to observe, reverse polarity can result in PCB damage and even PCB failure. Your appliances may be damaged or short-circuited by reversed polarity. Household appliances may overheat as a result of this outlet wiring error, which could also harm the wiring and internal circuitry.
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a refrigerator is an example of a . a refrigerator is an example of a . hot reservoir heat engine cold reservoir reversible process heat pump
A refrigerator is an example of a: Heat Pump
What is second law of thermodynamics?
According to Clausius' statement on the second law of thermodynamics, it is impossible to build a system that operates in a cyclical process, in which heat moves from areas of lower temperature to areas of higher temperature without working on it.
This statement applies to systems that transfer heat from a cold reservoir to a hot reservoir. Refrigerators and heat pumps do the same thing.
Refrigerators give off heat from the freezer to the atmosphere (exhaust air at the back of the refrigerator) even though the temperature inside the freezer is always lower than the temperature of the atmosphere.
Similarly, a heat pump transfers heat from a room to the outside air, cooling the room, which is cooler than the outside air.
A refrigerator is an example of a: Heat Pump
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what transmitter power would be needed for a cellphone to communicate reliably with the cell tower, if the phone is 7.9 kmkm from the tower?
By nation, technology, and urban density, there are vast differences. To connect to the cell tower in a trustworthy manner, use a cellphone.
Uses for transmitters.An object that generates radio waves that radiate from an antenna is referred to as a transmitter in the field of telecommunications. A transmitter is a device used in process control that transforms a sensor's output signal into a signal that can be used to measure and regulate a process variable.
What do receiver and transmitter mean?All electrical gadgets, including mobile phones, television stations, ships, etc., require a transmitter as a basic component. In addition, they are utilized for navigation. A receiver is an electrical gadget that picks up radio waves and messages that the transmitter transmits.
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a flatbed truck is carrying a heavy crate the coefficient of static friction between the crate and the bed of the truck 0.75 what is the maximum rate at which the driver can decelerate and still avoid having the crate slide agaainst the cab of the truck
The box must not slide, thus it is crucial for us to determine when the force of deceleration and the force of friction are equal. ma = mg, a = 0.75 * 9.8 m/s2, which is 7.35 m/s2. The driver may therefore safely decelerate at around 7.2 m/s2.
Friction is a type of force.The force produced when two surfaces glide against and touch one another is referred to as frictional force. There are a few things that impact the frictional force: The surface roughness of these forces and the amount of force pressing them together have the biggest impact.
Exactly what generates friction?Friction is believed to be created by the interactions between the microscopic bumps on surfaces when they rub against one other, however scientists are still unsure of its exact mechanism.
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Atomic Clock Transition The global standard for time is based on a transition in cesium atoms that occurs when a microwave photon of frequency 9,192,631,770 Hz is absorbed. What is the energy difference in eV between the two levels of cesium that correspond with this transition?
Atomic Clock Transition The global standard for time is based on a transition in cesium atoms that occurs when a microwave photon of frequency 9,192,631,770 Hz is absorbed, then the energy difference between the two levels of cesium that correspond with this transition is 38.06 x 10-¹⁴eV
When Cesium atoms are bombarded with microwaves of a certain frequency, this 55th electron goes from one of these hyperfine energy states to the other but then it comes back to the slightly lower energy state and when it does it emits electromagnetic radiation with the exact frequency of 9,192,631,770 Hertz. The time interval in which this wave completes these many cycles is defined as a second. The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.
As we know, energy difference is equal to-
∆E = hf
where h = Planck's constant i.e. 6.626x10-³⁴
f = frequency i.e. 9,192,631,770
∆E = (6.626 x 10-³⁴) * (9,192,631,770)
∆E = 60.91 x 10-³³Joule
To convert joule to electron volt (eV)
1eV = 1.6*10-¹⁹J
∆E = 60.91 x 10-³³/1.6 x 10-¹⁹
∆E = 38.06 x 10-¹⁴eV
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. In the figure, charge q₁ = 3.1 x 10-6 C is placed at the origin and charge q2 = -8.7 x 10-6 C is placed on the x-axis, at x = -0.2 m. Where along the x-axis can a third charge Q = -8.3 µC be placed such that the resultant force on this third charge is zero?
0.296 m along the x-axis can a third charge Q = -8.3 µC be placed such that the resultant force on this third charge is zero.
What is charge?Electric charge is a characteristic shared by many basic, or subatomic, particles of matter. For instance, protons have a positive charge and electrons have a negative charge, and neutrons have no charge.
Given that,
q₁ = 3.1 x 10⁻⁶ C
q₂ = - 8.7 x 10⁻⁶ C
x = - 0.2 m
Q = - 8.3 µC
Let, the charge is kept at r.
The force due to first charge:
F₁ = k × q₁ × Q / r²
The force due to second charge:
F₂ = k × q₂ × Q / (r -x)²
The net force acting on the third charge is zero.
F₁ + F₂ = 0
k × q₁ × Q / r² = k × q₂ × Q / (r -x)²
Hence, the position of charge on x-axis:
r = x / ( 1 - [tex]\sqrt{q_2 /q_1}[/tex])
r = -0.20 m / (1 - [tex]\sqrt{(8.6 *10^-6 /3.1 *10^-6}[/tex])
r = 0.296 m
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from the third rule you know that if a rope passes over a pulley, the tension in the rope is unaffected. with this observation in mind, what is the magnitude of the tension in the second rope?add the forces acting on the block to find the magnitude, t2 , of the tension in rope 2. express your answer in terms of some or all of the variables f , mb and g .
According to the third rule, a rope's tension remains unaffected if it passes over a pulley. The second rope's second rope's tension in magnitude is W strong (weight of the block).
A force throughout a medium's length is known as tension, particularly a force carried by a flexible medium like a rope or cable. An action-reaction pair of forces acting at each end of the mentioned elements is what is referred to as tension. The greatest size and direction of an object are referred to as its magnitude. Both vector and scalar values use magnitude as a common factor. We know that scalar quantities are those that have magnitude and nothing else by definition.
Whenever a system is in equilibrium,
T1 = F
T1 = mb*G+T2
T2 = F - MG
0R
T2 = W(weight of the block)
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In Figure, a climber leans out against a vertical ice wall that has negligible friction. The distance a is 0.914 m and distance L is 2.10 m. His center of mass is distance d=0.940 m from the feet–ground contact point. If he is on the verge of sliding, what is the coefficient of static frition is?
The static friction is the frictional force applied on the opposite of the direction of body to keep it from sliding.
We know that the weight of the body will be mg.
The force F(N) from x-axis will be vertically upwards.
mgd cos θ = F.L Sinθ
F = mgd cosθ / L.sinθ = f
F(not) = 0
F(N) = mg
F = f
Then the frictional force is
f = μ.F(N)
μ = f / F(N)
μ = [ (mgd cosθ / L.sinθ ) / mg ]
= d cosθ/ L sinθ
μ = 1.85/ 2.1 = 0.88
Therefore, the coefficient of static friction is 0.88.
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If gravity is the only force that plays a role in the evolution of the universe, and the mass density is less than the critical mass density, which plot correctly shows the evolution of the universe?.
Plot B correctly shows the evolution of the universe because it shows a steady/constant incline.
The correct option is B.
Evolution of the universe?
Our universe has been known to begin with an explosion of space itself called the Big Bang. Starting from extremely high density and temperature, space expanded, the universe cooled, and the simplest elements formed. Gravity gradually drew matter together to form the first stars and the first galaxies.
The nature of the universe is such that it underwent several stages of evolution, during its lifetime. These major stages include :
the radiation era, recombination eraepoch era and reionization eraOverall, a steady/constant incline will represent the various steady changes the universe has undergone in its development.
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complete question:
If gravity is the only force that plays a role in the evolution of the universe, and the mass density is less than the critical mass density, which plot correctly shows the evolution of the universe?
Plot A: a curved incline
Plot B: a steady/constant incline
Plot C: a very curved decline
A 0. 200-kg mass attached to the end of a spring causes it to stretch 5. 0 cm. If another 0. 200-kg mass is added to the spring, the potential energy of the spring will be.
The potential energy of the spring will be 4 times as much.
What is potential energy?
Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is squeezed or extended, its potential energy increases. If a steel ball is lifted above the ground as opposed to falling to the ground, it has higher potential energy.
In the first question, we have to caculate the constant of the spring with this equation:
[tex]$$m * g=k * x$$[/tex]
Getting the k :
[tex]k=\frac{m * g}{x}=\frac{0,2[k g] * 9,81\left[\frac{m}{*^2}\right]}{0,05[\mathrm{~m}]}=39,24\left[\frac{N}{m}\right]$$[/tex]
Then we can calculate how much the spring stretch whith the another mass of [tex]$0,2 \mathrm{~kg}$[/tex] :
[tex]x=\frac{m * g}{k}=\frac{0,4[k g] * g, 81\left[\frac{m}{a^2}\right]}{39,24\left[\frac{N}{m}\right]}=0,1[m]$$[/tex]
The energy of a spring:
[tex]E=\frac{1}{2} * k * x^2$$[/tex]
For the first case:
[tex]E=\frac{1}{2} * 39,24\left[\frac{N}{m}\right] *(0,05[m])^2=0,049[J]$$[/tex]
For the second case:
[tex]E=\frac{1}{2} * 39,24\left[\frac{N}{m}\right] *(0,1[m])^2=0,0196[J]$$[/tex]
If you take the relation [tex]$\mathrm{E} 2 / \mathrm{E} 1=4$[/tex].
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what is the maximum speed of a 330 kg car if the spring is compressed the full amount? express your answer with the appropriate units.
The maximum speed of a completely compressed spring is 4.993m/s .
The Mass of spring is 330 kg .
As per Kinetic theory , Molecules of every system is randomly oriented. Every molecule has its own radial and angular components.
As per theory root mean square concept is introduced computing energy leakage of any system.
Zero current in electronics is such an example calculating parameters of dissipation of energy.
[tex]K.E=\frac{3RT}{2} -----[1]\\\\K.E=\frac{mv^2}{2}-----[2] \\\\eq[1]=eq[2][/tex]
comparing
[tex]3RT=mv^2\\\\v^2=3RT/m\\\\T/m=1---[Reason:-compression]\\\\v=\sqrt{3R} \\\\v=\sqrt{3* 8.31} \\=4.993m/s[/tex]
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what is the speed of the 0.100 kg sphere when it has moved 0.400 m to the right from its initial position? express your answer with the appropriate units.
The speed of the sphere is 2√2m/s when its displaces off at 0.400 m .
Mass of a spherical object is 0.100 kg displaced by 0.400m
According to Einstein's equation E=mc2, "mass" is a fundamental characteristic of all the energy that we perceive or feel. If you have any kind of energy, it must have some "mass," according to the equation. It results from the Higgs field's interactions with subatomic particles.
The Higgs interaction gave an object its intrinsic mass, which we refer to as rest mass, if it is not moving in relation to you. As you start to accelerate an object, its kinetic energy rises. In other words, if the kinetic energy is rising, then the energy must be manifesting itself in the form of mass. This is because more energy means more inertia content, which equals more mass.
[tex]V^2-u^2=2as\\\\u=0 \\\\V^2=2as\\[/tex]
[tex]V=\sqrt{2as}[/tex] -[1][tex]V=\sqrt{2s\frac{F}{m} }[/tex] -[2]Calculations-
[tex]V=\sqrt{0.8\frac{1}{0.100} }[/tex]
[tex]V=\sqrt{\frac{8000}{1000} } \\\\V=\sqrt{8} =2\sqrt{2}m/s[/tex]
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when tuning his guitar, a music student notices that the string is not vibrating at the desired frequency of 195 hz, so he tightens the string by 16.4% to get this frequency. at what frequency was the string vibrating when he first started the tuning process?
When he started the tuning process the string vibrating frequency was 180Hz.
Frequency in a stretched string as a function of Tension(T) and linear mass density μ is given as:
f = [tex]\frac{1}{2L}[/tex] [tex]\sqrt{\frac{T}{} }[/tex]μ
where L is the length of string
Now in first case let f be the frequency
f = [tex]\frac{1}{2L}[/tex] [tex]\sqrt{\frac{T}{} }[/tex]μ (i)
After the string was tightened by 16.4% the tension in string will increase by 16.4% while all the other parameter will remain same. The new frequency which is equal to 195Hz is given by:
⇒ f₂ = 195 = [tex]\frac{1}{2L}[/tex] [tex]\sqrt{1.164T[/tex] / μ
⇒ 195 = [tex]\frac{1}{2L}[/tex] [tex]\sqrt{1.164T}[/tex]/μ (ii)
Dividing equation (i) by equation (ii), we get;
⇒[tex]\frac{f}{195}[/tex] = [tex]\sqrt{\frac{T}{1.164T} }[/tex]
⇒f = 195 [tex]\sqrt{\frac{1}{1.164} }[/tex]
⇒ f ≈ 180Hz
What is a string's natural frequency?
The length, mass, and degree of stretching a string is used to calculate its natural frequency. Giving a system a brief shock and seeing (or listening to) its reaction is the quickest technique to establish its natural frequency.
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hat is the period of small-angle oscillations of a simple pendulum with a mass of 0.6 kg at the end of a string of length 5 m?
4.49 sec
Given
Mass of simple pendulum = 0.6 kg
String of simple pendulum with length = 5m
Equation used:- T = 2 π (L / g)^1/2
T = period of oscillations
L = length of the pendulum
g = acceleration of gravity
T = 6.28 (5 m / 9.80 m/s^2)^1/2
T = 4.49 sec (the period is not dependent on mass)
A simple pendulum is defined to be a point mass or bob (taking up no space) that is suspended from a weightless string or rod. Such a pendulum moves in a harmonic motion
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calculate the energy and wavelength of the characteristic x-ray produced when a k-shell electron is replaced by an m-shell electron in tungsten.
The electron in tungsten's energy is 66 eV and wavelength is 1.89 x 10⁻¹¹m.
What is energy and wavelength of electron?The wavelength of any wave is the distance between one crest and the next. The wavelength is commonly represented by the symbol.The amount of energy is proportional to the electromagnetic frequency of the photon and thus inversely proportional to the wavelength. The higher the frequency of a photon, the greater its energy. The longer the wavelength of a photon, the lower its energy.The mean energy of the energy spectrum is a critical parameter for therapeutic electron beam dosimetry. It is frequently assumed that the mean energy of such beams remains constant across the beam and that only its degradation with depth is taken into account.To learn more about wavelength refer to :
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During its final days as a red giant, the Sun will reach a peak luminosity of about 3000LSun. Earth will therefore absorb about 3,000 times as much solar energy as it does now, and it will need to radiate 3,000 times as much thermal energy to keep its surface temperature in balance.
Estimate the temperature Earth's surface will need to attain in order to radiate that much thermal energy. You will need to use the formula for emitted power per unit area. (Assume that Earth's temperature today is around 300 K.)
Earth's surface would need to attain a temperature of 12,742 K in order to radiate 3,000 times as much thermal energy
The emitted power per unit area of a black body is given by:P = σT^4 Where is the σ Stefan-Boltzmann constant and T is the temperature in Kelvin.
Therefore, we can solve for the temperature that Earth's surface would need to attain in order to radiate 3,000 times as much thermal energy by rearranging the equation to solve for T:
T = (P/σ)^1/4
T = (3000/σ)^1/4
T = (3000/5.67x10^-8)^1/4
T = 12,742 K
Therefore, Earth's surface would need to attain a temperature of 12,742 K in order to radiate 3,000 times as much thermal energy.
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(b) at what time is the mechanical energy of the bucket-earth system at a minimum? explain your reasoning.
Plants are promoting both mechanical energy and chemical watering process but inhibit erosion of soil always of to the roots.
What is mechanical energy?
Mechanical energy (kinetic energy or potential energy) is one of the energy that is either an object in the motion or to the energy that is very stored in to the objects by their own position. Mechanical energy is also vary the driver of renewable of the energy. Many forms of the renewable energy is rely on mechanical energy to the adequately produce power or the convert energy. As we all know roots of the plant grow Deep its undergoes rock causing mechanical watering process so the mechanical watering process is the important for plants. When when plants roots undergoes the soil through The rocks mechanical watering process is must needed for growth of the plants.
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if it rotates through 8.00 revolutions in the first 2.50 s, what is the wheel’s angular acceleration?
The wheel rotate through 64 revolutions in the next 5.00 s
Using 2nd rotational kinematic equation:
\theta = wi*t + (1/2)*\alpha*t^2
From the question, we have
t = 2.50 sec, \theta = 8.00 rev = 8.00*2*pi rad,
wi = initial angular velocity = 0 rad/sec
So,
16.00*pi = 0*2.50 + (1/2)*\alpha*2.50^2
\alpha = 2*16.00*pi/2.50^2 = 16.08 rad/sec^2
Now in t = 7.50 sec (next 5.00 sec)
number of revolutions will be:
\theta1 = 0*7.50 + (1/2)*16.08*7.50^2 = 452.25 rad
So revolutions will be:
\theta1 = 452.25/(2*pi) = 72.0 rev
revolutions = \theta1 - \theta = 72.0 - 8.00 = 64.0 rev
Multiplication:
It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication.
Complete question:
A wheel rotates from rest with constant angular acceleration. If it rotates through 8.00 revolutions in the first 2.50 s, how many more revolutions will it rotate through in the next 5.00 s?
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an applied 25 n force pushes on a 5.0 kg object resting on a frictionless horizontal surface. the force is directed downward at a 20 degree angle
An applied 25 n force pushes on a 5.0 kg object resting on a frictionless horizontal surface. the force is directed downward at a 20 degree angle is 23.49N
X- component = 25cos20° = 23.49 N
All objects with mass or energy are attracted to one another by gravity, which derives from the Latin word for "weight" (gravitas). By far the weakest of the four fundamental interactions, gravity is 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force, and 1029 times weaker than the weak interaction. As a result, it has no discernible impact on the level of subatomic particles. The motion of planets, stars, galaxies, and even light are all governed by gravity, which is the most important interaction between objects at the macroscopic level.
On Earth, gravity lends weight to physical objects, and the Moon's gravity is what causes sublunar tides in the oceans (the analogous antipodal tide is brought on by the Earth's inertia).
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A liquid of density 1330 kg/m3 flows steadily through a pipe of varying diameter and height. at location 1 along the pipe, the flow speed is 9.85 m/s and the pipe diameter ????1 is 10.1 cm. at location 2, the pipe diameter ????2 is 17.5 cm. at location 1, the pipe is δy=9.15 m higher than it is at location 2. ignoring viscosity, calculate the difference δP between the fluid pressure at location 2 and the fluid pressure at location 1.
The difference between the fluid pressure at location 2 and the fluid pressure at location 1 is 119 kPa.
What is the equation of continuity?The mass balance of a fluid moving through a stationary volume element is all that the equation of continuity is about. It says that the rate of mass inflow less outflow equals the rate of mass buildup in this volume element.
According to equation of continuity:
[tex]A_{1} v_{1} =A_{2} v_{2} \\[/tex]
A₁ = Region 1 cross-sectional area
v₁ = flow velocity of region 1
A₂ = Region 2 cross-sectional area
v₂ = flow velocity of region 2
Here, [tex]A_{1} =\frac{\pi d_{1}^{2} }{4}[/tex] , [tex]A_{2} =\frac{\pi d_{2}^{2} }{4}[/tex]
Now, putting the values in the above equation we get,
[tex]v_{2} =\frac{A_{1} }{A_{2} } v_{1} \\[/tex]
[tex]=\frac{\frac{\pi d_{1}^{2} }{4}}{\frac{\pi d_{2}^{2} }{4}} v_{1}[/tex]
[tex]v_{2} =\frac{d_{1}^{2} }{d_{2}^{2} } v_{1}[/tex]
Using Bernoulli's equation, we get,
[tex]P_{2} + \rho gz_{2} +\frac{\rho v_{2 }^{2} }{2}= P_{1} + \rho gz_{1} +\frac{\rho v_{1 }^{2} }{2}[/tex]
The difference between the location 2 fluid pressure and the location 1 fluid pressure is :
[tex]P_{2}-P_{1} =\rho g(z_{1}-z_{2} )+\frac{\rho (v_{1}^{2}-v_{2}^{2}) }{2} =\rho g(z_{1}-z_{2} )+\frac{1}{2}\rho v_{1} ^{2} (1-(\frac{d_{1} }{d_{2} } )^{4} )[/tex]
[tex]P_{2}-P_{1} = 1330*9.81*9.15+\frac{1}{2} *1330*9.85^{2} (1-(\frac{10.1}{17.5} )^{2} )[/tex]
[tex]P_{2}-P_{1} = 1.19*10^5} Pa\\P_{2}-P_{1} = 119 kPa[/tex]
Hence, the difference between the fluid pressure at location 2 and the fluid pressure at location 1 is 119 kPa.
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g what is the magnitude of the tension ta in rope a? a. 500 n b. 3200 n c. 370 n d. 130 n e. 100 n f. 400 n value: 10 if the axis of rotation is placed on rope a, then the torques of f
To find the magnitude of the tension in rope A, we need to consider the forces and torques acting on the system.
In this problem, the forces acting on the system are the weight of the block and the tensions in ropes A and B. The torques are the forces acting on the ropes multiplied by their distances from the axis of rotation.
We can use the concept of equilibrium to solve this problem. When an object is in equilibrium, the sum of the forces and the sum of the torques must be zero. In this case, the forces on the system are balanced, so the sum of the forces is zero. We can write this as:
$$T_A + T_B - W = 0$$
where $T_A$ and $T_B$ are the tensions in ropes A and B, and $W$ is the weight of the block. We are given that $T_B = 3200 \text{ N}$ and $W = 500 \text{ N}$.
Next, we need to consider the torques on the system. If the axis of rotation is placed on rope A, the only torque acting on the system will be the torque due to the tension in rope B.
The torque due to the tension in rope B is given by the equation $\tau = rT$, where $\tau$ is the torque, $r$ is the distance from the axis of rotation to the point where the force is applied, and $T$ is the force.
In this case, the distance from the axis of rotation to the point where the force is applied is $r = 10 \text{ m}$, and the force is the tension in rope B, $T = 3200 \text{ N}$. The torque due to the tension in rope B is therefore $\tau = 10 \text{ m} \times 3200 \text{ N} = 32000 \text{ Nm}$.
Since the system is in equilibrium, the sum of the torques must be zero. We can write this as:
$$\tau = 0$$
Substituting the value of the torque due to the tension in rope B, we get:
$$32000 \text{ Nm} = 0$$
This equation is satisfied, so the system is in equilibrium.
Finally, we can use the equation for the sum of the forces to solve for
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if your body has a density of 976 kg/m3, what percent of you will be submerged when floating gently in the following liquids? (a) freshwater % (b) salt water, which has a density of 1,030 kg/m3
If your body has a density of 976 kg/m3, 97% 0f the body will sink while gently floating in fresh water, and 95% will sink if it has a density of 1,030 kg/m3
The net force from buoyancy must match the weight when a body is partially submerged in fresh water. When a body is partially submerged in salt water, the net force due to buoyancy must equal the weight.
Fraction of body submerged (f sub) = density of body/density of fluid
Given that density of fresh water = 1000 kg/m3
density of salt water = 1027kg/m3
density of body = 976 kg/m3
Fraction of body submerged in fresh water = (976/1000)x100 = 97%
Fraction of body submerged in salt water = (976/1027)x100 = 95%
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explain why lasers can be used to perform surgery and cut through metal while incandescent light cannot.
The phrase LASER is an acronym of mild Amplification by way of stimulated Emission of Radiation. it's miles a device to provide a sturdy, monochromatic, collimated and tremendously coherent beam of mild. it really works in the phenomenon of 'stimulated emission'.
Laser light is exceptionally monochromatic.
The laser light is a beam of monochromatic mild due to the fact all photons in the laser light have identical power, big hnu = E_2-E_1, identical frequency, large nu = frac{E_2-E_1}{h} and additionally same wavelength, big lambda = frac{hc}{E_2-E_1}.
(ii) Laser light is fairly coherent.
since the emission of all photons are in section, the laser beam is coherent.
(iii) Laser mild is relatively extreme
The depth of laser beam may be very high due to the fact all the photons within the beam are coherent.
(iv) Laser light is highly directional.
A laser beam is fantastically directional. mild from other assets can be made parallel beam by using a lens or a reflect,but the beam divergance is an awful lot more than that for laser light.
Those properties of laser mild enables it for use in surgical treatment and cut via metals.
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a metal wire has a resistance of 10.0 ω at a temperature of 20oc. at 90oc, its resistance increases to 10.5 ω. what is the temperature coefficient of resistivity of this metal?
The temperature coefficient of resistivity of metal
10 = r0(1 + 20k)
10.5 = r0(1 + 90k);
10.5/10 = (1 + 90k)/(1 + 20k);
10.5 + 210k = 10 + 900k
k = 0.5/690 = 7.25·10-4 1/C
The primary unit of temperature within the worldwide gadget of units (SI) is the kelvin. It has the sign K . For normal programs, it's far often handy to use the Celsius scale, in which 0 °C corresponds very carefully to the freezing factor of water and a 100 °C is its boiling factor at sea level.
Temperature is a measure of the common kinetic energy of the debris in an object. While the temperature increases, the movement of those particles also will increase. Temperature is measured with the thermometer or calorimeter.
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an object is hung from a spring scale while it is immersed in water. the scale reads 5.6 n. the mass of the object is 0.75 kg. what is the density in [x103 kg/m3] of the object?
The density of object is 3.33*10³
How to calculate density of object ?The gravitational force draws any two mass-containing objects together. The gravitational force is referred to. According to the formula F=Gm1m2r2, the force will always be applied along the line connecting the two masses in the direction of the other mass. It is a force of attraction in nature.
Given,
gravitational force = 5.00N
Mass of the object = 0.5kg
reading when submerged in water = 3.5 N
The loss in weight = 5 - 3.5
= 1.5 N
This loss in water due to buoyancy in water
Loss in weight of water = weight of displaced water
So ww = 1.5 N
Weight of displaced water = w *v * g
Density of water = 10³kg/m³
Thus , 1.5=10³ * v* 10
V = 1.5/10³ * 10 m³
Let density be m/v
=0.5/1.5*10*10³
= 3.33*10³
Therefore density of object is 3.33*10³
The complete question is : The gravitational force exerted on a solid object is 5.00 N. When the object is suspended from a spring scale and submerged in water, the scale reads 3.50 N. Find the density of the object.
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