Answer: In order for an object to move at a constant speed or to accelerate or decelerate, the applied (horizontal) force and the frictional force must be unequal.
Explanation: How does the frictional force compare to the applied force?
Frictional force serves to keep the crate in place by acting in the opposite direction as the applied force. The term for this rubbing force is static friction. If you push harder, the frictional force will rise until it achieves its maximum value as a result of the increased applied force.
Do we have even or uneven friction?
Friction was the driving force that kept the bucket in place. It absorbed the tiny force applied to the bucket and offset it. a move
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what range of spring constant values will cause the motion of the system to have damped oscillation?
The system's behavior becomes more elastic when the spring constant, k, is increased, as is the Q factor
How might one raise the spring constant?Since a spring's constant k and its length are inversely related, when a spring is divided into n parts, the length increases by 1n, making the spring constant k/(1/n)=nk.
How do mass and the spring constant relate?The square root of the mass and the spring constant have opposite relationships with respect to the period of a spring-mass system.
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a student performs three trials of a standard two-slit interference experiment. in each trial the material and hence the index of refraction in the region between the barrier and the screen is
Between the barrier and the screen in each trial, the material and consequently the index of refraction are 487.8 nm.
Light waves alter in speed when two materials with different densities, like air and glass, come into contact. The resulting change in direction is referred to as refraction.
With D=2.05, d=5,
m=1,Y1=20cm
In our case, d sin = m.
λ=dYn/mD=
5*10⁻⁶*20*10⁻²/1*2.05
λ=487.8 nm
Refraction in physics is the change in direction that results from a wave's change in speed when it travels through one medium and enters another. For instance, waves move faster in deep water than they do in shallow water.
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The Carnot cycle is calculated using this law or modifications of it, and Daniel Bernoulli derived it with Newton's laws of motion. Independently discovered by Edme Mariotte, credit for it is most often given to the author of (*) The Skeptical Chymist. It is part of the combined gas law, with Gay-Lussac's Law and Charles' Law. For 10 points, identify this law that states that at a fixed temperature, pressure and volume of a gas are inversely proportional.
Boyle's law states that the volume of a given quantity of gas sustained at a fixed temperature is inversely proportional to the measurement's measurement of pressure.
Describe Newton's law.The motion of an item is related to the forces operating on it by Newton's equations of motion. According to the first law, until a force strikes on an item, it will not alter its motion. According to the second law, an object's force is determined by multiplying its mass by its acceleration. According to the third law, when two objects interact, they exert equal-sized and opposite-direction pressures upon one another.
Bernoulli equation: what is it?Static pressure plus dynamic pressure equals total pressure is a simple way to express Bernoulli's equation. Each point Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own unique static pressure p and dynamic pressure q.
What is Gay-Lussac's Law and Charles' Law?Joseph-Louis Gay-Lussac investigated the expansion of gases as the temperature is increased. His data helped establishCharles' law, which says, in its modern form, that the volume of a gas is directly proportional to the absolute temperature.
Now we need to say which law is there which state that at a fixed temperature, pressure and volume of a gas are inversely proportional.
The law that states this is Boyle's law.
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Consider a proton, an electron, and a helium nucleus (alpha particle) moving at the same speed vv. List their de broglie wavelengths from largest to smallest.
The sequence for de broglie wavelengths from largest to smallest is electron > proton > helium.
de broglie wavelength is an important concept to study various phenomenon in quantum mechanics.
Mathematically, de broglie wavelength equation is λ = h/p (p=mv)Where, h is the Plank's constant
m is the mass of the particle
v is the velocity of particle.
mass of proton = mp = 1.6 x [tex]10^{-27}[/tex] kg
mass of electron, me = 9.1 x [tex]10^{-31}[/tex] kg
mass of helium nucleus, mHe = 6.6 x [tex]10^{-27}[/tex] kg
As the velocity of all the three elements are same as v.
According to the de Broglie wavelength formula, since v is same for all λ is inversely proportional to the mass of the element.
Lesser the mass more will be the de broglie wavelength.
Here, mass of electron < mass of proton < mass of helium nucleus.
So, de broglie wavelength of electron > de broglie wavelength of proton > de broglie wavelength of helium nucleus.
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At a hydroelectric power plant, water is directed at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine be designed so that the water is brought to a dead stop, or so that the water rebounds? If only an external force can change the momentum of the center of mass of an object, how can the internal force of the engine accelerate a car?
Ideally, the water bounces off the turbine blades, maximizing electricity era. when water splashes, momentum changes extra than while you are simply status.
Also, if the change in momentum of the water is greater than the alternate in momentum of the blade, the blade will spin faster. Consistent with the laws of movement, the momentum of the center of gravity of an object can most effective be changed by the movement of an external force.
But, because of the frictional force generated while the tires contact the ground, the internal force of the engine is added, allowing the automobile to accelerate.
Hydro turbines convert the strength of flowing water into mechanical energy. A hydroelectric generator converts this mechanical power into energy. A high stress water jet is pressed towards the turbine blades. The route of flow modifications. The ensuing change in momentum exerts a force on the turbine blades, inflicting the turbine to rotate.
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Two power lines run parallel for a distance of 270 m and are separated by a distance of 40.0 cm. If the current in each of the two lines is 140 A and if they run in opposite directions, determine the magnitude and direction of the force each wire exerts on the other.
Answers:
magnitude: _____ N
direction: towards eachother, or away from eachother
The force exerted by each wire on the other is 2.646N and it is away from each other.
The parallel electricity lines are 270 meters long and spaced 40 centimeters apart.
The power line's current is 140A.
In order to exert force on one power line owing to another,
F = uI1I2L/2r.
Where,
The line's current is I₁ and I₂, respectively.
L is the wire's length.
The distance between them is r.
Assigning values,
F = 4 x π x 10⁻⁷ x 140 x 140 x 270/2 x π x 0.4.
Continuing to solve,
F = 2.646 N.
Because the current is flowing in the same direction, the force will be in the opposite direction. Regardless of the current's direction, the force's magnitude will not change.
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In comparing two unequal forces on a rigid body, is it possible to have the larger force produce less torque than the smaller force?.
Yes It is conceivable for a force to produce less torque when it is greater than a force that is smaller.
What occurs when there are unequal forces?An object's motion can be altered by unbalanced forces.Two things cause this.An object will move if an imbalanced force pushes and pulls on it while it is at rest.Unbalanced forces also can cause an item in motion to shift its speed or direction.
What impact do uneven forces have on motion?Students are aware that unbalanced forces can cause objects to accelerate, decelerate, or change direction during their motion.
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what is the typical hydrogen content (by mass) of stars that are forming right now in the vicinity of the sun? (a) 100% hydrogen (b) 75% hydrogen (c) 50% hydrogen
The typical hydrogen content (by mass) of stars that are forming right now in the vicinity of the sun is 75% hydrogen.
What is hydrogen?
The chemical element hydrogen is represented by the letter H as well as atomic number 1. The lightest element is hydrogen. Under normal circumstances, hydrogen is a gas made up of diatomic molecules with the formula H2. It is non-toxic, tasteless, colourless, odourless, and highly combustible. In the universe, hydrogen is by far the most prevalent chemical, making up about 75% of all ordinary matter. Plasma hydrogen makes up the majority of stars like the Sun. On Earth, hydrogen mostly takes the form of molecules like water and biological compounds. Each atom of hydrogen's most prevalent isotope, 1H, contains a single proton, one electron, and also no neutrons.
This is because the interstellar medium contains mostly hydrogen, which is the most abundant element in the universe. When these clouds of gas and dust collapse, they become denser and hotter, and the hydrogen atoms begin to fuse together, creating helium and other elements in the process. The resulting star is composed mostly of hydrogen, with the remaining 25% being composed of helium and other elements.
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an object is launched upward with an initial velocity of 64 feet per second from a platform 80 feet height. a. what is the maximum height of the object? b. how many seconds until the object hits the ground?\
a) Object maximum height is : 144 feet
b) object hits the ground in : 5.74 seconds
a) t = - [tex]\frac{b}{2a}[/tex]
t = - [tex]\frac{-64}{2(-16)}[/tex]
t = 2 second
h(t) = -16[tex]t^{2}[/tex] + 64t + 80
h(2) = -16([tex]2^{2}[/tex]) + 64(2) + 80
h = -64 + 128 + 80
h = 144 feet
b) Time to maximum height = 2 seconds
Maximum height = 144 ft
Displacement when it hits the ground = -80
-80 = -16[tex]t^{2}[/tex] + 64t + 80
solve for t :
t = 5.74 seconds
A displacement simple definition is what?
A change in an object's position is referred to as "displacement." It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial location to the ending place. For instance, if an object shifts from location A to position B, its position changes.
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I understand that the question you are looking for is:
A object is launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. The equation that models this is given by h(t) = -16[tex]t^{2}[/tex] + 64t + 80.
a) What will the objects maximum height ?
b) How many seconds until the object hits the ground?
During a tug-of-war, team a pulls on team b by applying a force of 1100 n to the rope between them. The rope remains parallel to the ground. How much work does team a do if they pull team b toward them a distance of 2. 0 m?.
Work done by team A while pulling team B is 2200 J.
What is work done?
The work done by a force is defined to be the product of the component of the force in the direction of the displacement and the magnitude of this displacement. Formula. Work can be calculated by multiplying Force and Distance in the direction of force as follows. W = F × d.
What is cos theta in work done?
Work done in physics is defined as a dot product of a force vector and displacement vector. W = F.S.cos θ where cos θ is the angle between the force vector and displacement vector.
What force is applied during tug of war?
Tug-of-war is a game that uses friction as the driving force.
What happens in a tug of war if both teams apply equal force?
In a tug of war, if the two teams are applying equal force on the rope then the net force acting on the rope is zero and hence the rope stays at the same place.
Force F= 1100 N
Displacement caused by the applied force S = 2 m
Force and displacement are in the same direction the angle between them is zero.
Work done is calculated as
[tex]W=F * S * cos theta\\W=1100 * 2 * cos 0\\W=2200 J[/tex]
Thus, the work done by team A to pull is 2200J.
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two vectors vector a and vector b, each located in a different position in the plane, have equal magnitude and the same direction. what can be said about the relationship of vector a and vector b? (select all that apply.)
Two vectors vector a and vector b, each located in a different position in the plane, have equal magnitude and the same direction, both vectors are considered to be parallel to each other.
Two vectors are said to be parallel if and as it were in case the angle between them is degrees. Parallel vectors are too known as collinear vectors, that is two parallel vectors will be continuously parallel to the same line but they can be either within the same direction or within the exact inverse direction. The cross product of any two parallel vectors could be a zero vector. For any two parallel vectors a and b, their dot product is equal to the product of their magnitudes.
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how much time in seconds will it take a cart to reach the bottom of the track?assume the cart starts from rest, the track is 1.5 m long and the distance covered by the cart is 1.5 m.
Around 80 times we should expect it to land on B.
What is time?Time is basically a measure of non-stop, consistent change in our own surroundings. Usually we can see through a specific point of view. Concept of time is self-evident and intuitive. Describing the fundamental nature of time is quite difficult.
The general time formula of the any kind of task that is given as [Time = Distance ÷ Speed]. for SI unit of time is seconds (s).
As per the given condition-
Spin circle=3
Time = 120 sec
the total is 3
the red and orange equals to 2
2/3 times 120
240/3
=80 times
Thus, the correct answer is 80 times.
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In comparing two unequal forces on a rigid body, is it possible to have the larger force produce less torque than the smaller force?.
Yes, it is possible to have the larger force produce less torque than the smaller force. It is possible for the larger force to be applied closely enough to the center of mass of the rigid body due to which its resulting torque is smaller than that of a smaller force applied at a point far from the center of mass.
What is force?Force is an external cause due to which a body tends to modify or change its state. Due to application of force, the body can also change its size, shape, and direction. Force has both direction and magnitude.
Force = mass × acceleration
What is torque?The force that can cause an object to rotate along an axis is measured as torque.
[tex]\tau = rF\sin\theta[/tex]
Here, [tex]\tau \\[/tex] = Torque
r = radius
F = force
[tex]\theta[/tex] = the angle between the F and the lever arm
In the given question, lets assume the following,
F = Large force
d = Distance from the point of application of the large force to center of mass
f = Small force
D = Distance from the point of application the of small force to center of mass
Now,
Assuming D > d (i.e, D is greater than d).
The torque caused by the large force is Fd, and the torque caused by the little force is fD if the forces are applied perpendicular to the body's axis. Hence, depending on the values of F, f, D, and d, we can have Fd < fD.
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Suppose we use a baseball to represent Earth. On this scale, the other terrestrial worlds (Mercury, Venus, the Moon, and Mars) would range in size approximately from that of _________.
a golf ball to a baseball
The other terrestrial worlds (Mercury, Venus, the Moon, and Mars) would range in size approximately from that of a golf ball to a baseball.
Define solar system.
The Sun and the things that circle it make up the gravitationally bound solar system. It was created 4.6 billion years ago when a massive interstellar molecular cloud collapsed because to gravity. The Sun is home to the great majority (99.86%) of the system's mass, with Jupiter holding the lion's share of the remaining mass. Mercury, Venus, Earth, and Mars are the four planets in the inner solar system. These terrestrial planets are mostly made of rock and metal.
We consider the size of the earth to be that of a golf ball. This scale would allow us to squeeze 1.3 million golf ball-sized earths inside of the Sun, which would be over 15 feet wide. That is equivalent to two full school buses' worth of golf balls.
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a rope of mass m and length ` hangs from the ceiling. (i) what is the wave speed on the rope a distance y above the lower end?
From a ceiling, a rope with the mass m and length L hangs. Demonstrate that v =√gy is the wave speed on the rope at a distance of y above the lower end.
Explain about the wave speed?The amount of space a wave covers in a certain amount of time, such as the number of meters it covers in a second, is known as its wave speed. Speed = Wavelength x Frequency is an equation that describes how wave speed relates to wave wavelength and wave frequency. When the wavelength and frequency are known, this equation can be used to determine the wave speed. Wave frequency (f) is recorded in hertz, while wave speed (v) is measured in meters per second (m/s) (Hz)
Although technically, velocity means both speed and direction, wave velocity is most often used to refer to speed. A wave's velocity is independent of its intensity and equal to the product of its wavelength and frequency (number of vibrations per second).
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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 energy and wavelength of the characteristic x-ray produced is 66KeV and 0.192А° respectively.
What is energy of electrons in a shell?
The energy level of each electron shell varies, with the electron shells nearest to the nucleus having a lower energy level than those farthest from the nucleus. If the electron jumps from the second energy level down to the first energy level, it must give off some energy by emitting light.
What is wavelength and how to calculate it?
Wavelength can be defined as the distance between two successive crests or troughs of a wave. It is measured in the direction of the wave.
Rydberg's Formula for calculating the wavelength:
1 / λ = R(Z - [tex]1^2[/tex]) [tex][\frac{1}{1} - \frac{1}{n^2} ][/tex]
Energy associated with the electron in the K-shell is approximately
[tex]E_k = -(74-1)^2(13.6eV) = -72474eV[/tex]
The number of electrons in the n = 1 and n = 2 states, which act as a shield between the M electrons and the nucleus. M electrons are protected from the nucleus by about nine electrons because there are currently eight electrons in the n = 2 state and one electron in the n = 1 state.
[tex]Z_eff = z - 9[/tex]
Consequently, the energy of an electron in the M shell is
[tex]E_m = \frac{-13.6 z_eff^2}{3^2}[/tex]eV = [tex]E_m = \frac{13.6 (z-9)^2}{3^2}[/tex]
[tex]E_M =[/tex] -6384eV
Therefore, emitted X-ray has an energy equal to
[tex]E_m - E_k = {-6384-(-72474)}eV[/tex]
= 66090eV = 66KeV
To calculate wavelength,
For an electron in the Kshell, σ=1.
Thus, Zeff = Z−σ = Z−1
Here, as electron drops from Mshell(n=3) → Kshell(n=1), we call the radiated emission Kβ X-ray and from is given as
1 / λ[tex]_{kb}[/tex] = R(Z-[tex]1^2[/tex])[tex][\frac{1}{1^2} -\frac{1}{3^2} ][/tex]
λ[tex]_{kb}[/tex] = 10967800 × (74 - [tex]1^2[/tex]) [tex][\frac{8}{9}][/tex]
λ[tex]_{kb}[/tex] = 0.192А°
The energy and wavelength of the characteristic x-ray produced is 66KeV and 0.192А° respectively.
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6. A 1400 kg car is also traveling in a straight line. Its momentum is equal to that *
of the truck in the previous question. What is the velocity of the car? ROUND TO
THE NEAREST HUNDREDTHS (2 DECIMAL PLACES)
Answer:
V = 2.86 m/s
Explanation:
Given:
m = 1400 kg
p = 4000 kg·m/s
_________________
V- ?
Momentum:
p = m·V
Velocity:
V = p / m
V = 4000 / 1400 ≈ 2.86 m/s
The reason padded dashboards are used in cars is that they _____.
a. change the impulse in a collision
b. increase the time it takes the person to come to a complete stop
c. change the momentum of a collision
d. increase the force on the person as they come to a final stop
The reason padded dashboards are used in cars is that they a.) change the impulse in a collision. Therefore option a) is correct.
Why are padded dashboards used in cars?Padded dashboards make automobiles safer as they increase the time taken to decrease the momentum of impacting body to zero, which also decreases the impact. Therefore, force acting on the padded dashboards is small.
If the driver or passenger hits the dashboard, then the force and time required to stop the momentum is exerted by the dashboard. Padded dashboards serve to extend the time duration of the impact, hence minimizing the effect of the force.
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which has the lowest heat capacity? (values of heat capacities and calculations are unnecessary). which has the lowest heat capacity? (values of heat capacities and calculations are unnecessary). 3 kg of iron 10 g of liquid water 30 kg of ice 1 g of gold
Answer:
3kg of iron
Explanation:
an intoxicated clockmaker produces a grandfather clock whose pendulum has a period of 3.5\;\mathrm{s}3.5s. what is the length of the pendulum?
The length of the pendulum is equal to 1.35 m.
What is a simple pendulum?A simple pendulum can be described as a mechanical arrangement that exhibits periodic motion. The simple pendulum is made of a small bob of mass ‘m’ suspended by a thin thread hung at its upper end of length L.
The simple pendulum moves in an oscillatory motion and the motion occurs in a vertical plane which is driven by the gravitational force.
The time period of the pendulum is given by:
T = 2π√(L/g)
Where L is the length and g is the gravitational acceleration.
Given, the time period of a pendulum, T = 3.5 s
Then the length of the pendulum can be calculated as:
[tex]{\displaystyle 3.5 = 3\times 3.14 \sqrt{\frac{L}{9.8} }[/tex]
(0.37)² = L/9.8
L = 1.35 m
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a figure skater is rotating with her arms stretched out away from her body. as she pulls her arms in towards her body, what happens to her angular velocity?
She draws her arms close to her body, decreasing her moment of inertia, to quicken the rotational velocity of her spin. Due to the conservation of angular momentum, rotational velocity will increase,
What are Rotational Velocity ?The angular velocity (w), a vector quantity in uniform circular motion, is determined by dividing the angular displacement (ΔФ a vector quantity), also a vector quantity, by the change in time (t). Speed is equal to the arc length travelled (S) divided by the change in time (Δ), which is also equal to ||R.
According to the above given information
We got to know that
She draws her arms close to her body, decreasing her moment of inertia, to quicken the rotational velocity of her spin. Due to the conservation of angular momentum, rotational velocity will increase.
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analysis of an interference effect in a clear solid shows that the wavelength of light in the solid is 329 nm. knowing this light comes from a he-ne laser and has a wavelength of 633 nm in air, is the substance zircon or diamond?
The substance is zircon, of which interference analysis is done.
Wavelength of light in solid = λ = 329 nm
Wavelength of light from he-ne laser = λ' = 633 nm
Interference effect = n =
= n = λ' / λ
= n = 633 / 329
= n = 1.92
The interference, in physics, is the net effect of the combination of two or more wave trains moving on intersecting or coincident paths. The effect is that of the addition of the amplitudes of the individual waves at each point affected by more than one wave.
Thus the substance is zircon.
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Determine the output voltage Vo in the circuit given below using nodal analysis, where the dependent source A-0.2Vo Please report your answer so the magnitude is positive and all angles are in the range of negative 180 degrees to positive 180 degrees. j2Ω 12/0°V 4Ω The output voltage of the circuit is V.-n/r n/r
It is given that:
dependent source = A-0.2Vo
Nuclear decay occurs according to first-order kinetics. How long will it take for a sample of chromium-51 to decay from 35. 0 grams to 10. 0 grams? the half-life of chromium-51 is 28 days.
50 dayss long will it take for a sample of chromium-51 to decay from 35. 0 grams to 10. 0 grams
What purpose does chromium-51 serve?Observationally stable chromium isotopes include chromium Cr-51.
It is utilized as a diagnostic radiopharmaceutical agent when injected intravenously to calculate the volume or mass of red blood cells, research red blood cell survival, and assess blood loss.
what The half-life of chromium-51 is what?Introduction.With a half-life of 27.7 days and gamma rays with a maximum energy of 0.320 MeV, chromium-51 is a widely utilized radionuclide
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A liquid of constant density rho and constant viscosity μ flows down a wide, long inclined flat plate. The plate makes an angle θ with the horizontal. The velocity components do not change in the direction of the plate, and the fluid depth, h, normal to the plate is constant. There is negligible shear stress by the air on the fluid. Find the velocity profile u(y), where u is the velocity parallel to the plate and y is measured perpendicular to the plate. Write an expression for the volume flow rate per unit width of the plate.
The velocity profile u(y) is defined as V = (alpha)*g*sin(alpha)*h^3/3M, where u is the velocity measured parallel to the plate and y is measured perpendicular to the plate. The air just slightly shear stresses the fluid.
Velocity is a vector measurement of an object's rate of motion and direction of motion. The magnitude and direction must therefore be understood in order to calculate the velocity according to this criterion. It is possible to describe shearing stress, also known as shear stress, as "a type of stress that acts coplanar with cross section of material." Shear forces resulted in shear stress. They are a pair of forces that have the same magnitude and are directed in the opposite direction and operate on opposite sides of a body. A vector quantity is shear stress.
Alpha = g*sin(alpha)*h2/2M [y - y^3/3h^2]
V = (alpha)*g*sin(alpha)*h2/2M
Alpha = g*sin(alpha)*h^3/3M
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what speed (as a ratio with respect to the speed of light) must a canister be shot from one ship towards the other ship in order for the canister to approach the other ship at 0.999c as seen by the other ship?
The speed of the canister relative to the ship firing it must be 0.999c since the speed of light is the same in all inertial reference frames.
Relative velocity is the vector difference between the velocities of two objects in motion relative to each other. It is the velocity of an object in relation to the velocity of the other object. Since the speed of the canister must be 0.999c relative to the ship firing it, the speed of the canister relative to the other ship must be 0.999c + (the relative velocity of the two ships).
So, if the relative velocity of the two ships is v, the speed of the canister relative to the other ship must be 0.999c + v.
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an electrician is running wire from the electric box on a house to a utility pole 75 feet away, the angle of elevation to the connection on the pole is . how much wire does the electrician need?
Answer: The electrician need78 feet of wire are required by the electrician as a result.
Reason:
The elevated angle between the horizontal plane and line of sight to the connection on the pole.
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In thinking about the uniform distribution of a gravitational field over a sphere, why does gravitational force have an inverse-square relationship with the distance between objects?.
In the first case it is increased by a factor of 9.
Explain in detail.
In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body.
This model is used to explain gravitational phenomena, and is measured in newtons per kilogram. The formula for determining the gravitational field strength is weight divided by mass. On Earth, the gravitational field strength is 10 N/kg, and other planets have different gravitational field strengths. For example, the Moon has a gravitational field strength of 1.6 N/kg.
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Nuclear decay occurs according to first-order kinetics. How long will it take for a sample of titanium-45 to decay from 65. 0 grams to 25. 0 grams? the half-life of titanium-45 is 3. 08 hours.
The mass of Ti-51 remaining after 1 hour will be 0.0977 g
Is radioactive decay first order kinetics?Since radioactive decay is a first-order process, we can also use this equation for the rate constant, which comes from first-order kinetics, which says that the rate constant k is equal to 0.693 divided by the half-life.Nuclear decay is an excellent example of a first order process. The rate of decay is simply proportional to the amount of the radioactive isotope. This is due to the fact that any isotope has the same chance of decaying at any given time.Because nuclear decay reactions follow first-order kinetics and have a rate constant that is independent of temperature and the chemical or physical environment, we can perform similar calculations using the half-lives of isotopes to estimate the ages of geological and archaeological artifacts.The first-order radioactive decay law states that the rate of decay (number of disintegrations per second) is proportional to the number of radioactive atoms (N) present at that time t. N = No e-λt.#a. ⁵¹₂₂ Ti + ⁰₋₁e → ⁵¹₂₃V
#b. 0.0977 g
#a.
Titanium-51 is the radioisotope that undergoes Beta emission to emit a daughter isotope Vanadium-51 (Mass number-51 and atomic number -23).
Titanium-51 has a mass number of 51 and atomic number of 22.
A beta particle is equivalent to ⁻¹₀e
Beta emission does not affect the mass number of an isotope but increases the atomic number by 1.
Therefore;
The reaction will be;
⁵¹₂₂Ti + ⁻¹₀e → ⁵²₂₂V
#b.
The half life of Ti-51 is 6 minutes
We can calculate the mass remaining after 1 hour (60 min)
Original mass of the sample = 10.0 g
But; using the formula;
Remaining mass = Original mass × (1/2)^n , where n is the number of half lives.
in this case, n = time/half life
= 60 min ÷ 6 min
= 10
Therefore;
Remaining mass = 100 g × (1/2)^10
= 0.0977 g
Therefore, the mass of Ti-51 remaining after 1 hour will be 0.0977 g
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which of the following statement(s) is/are correct? i) the energy change, , when ( 15.99491461956 amu) is formed from 8 protons and 8 neutrons is less than zero.ii) nuclear fission is used to produce electric power in nuclear reactorsiii) the first example of nuclear fission involved bombarding with nuclei.
The statement that is true is that; nuclear fission is used to produce electric power in nuclear reactors.
What is a fission reaction?We know that a fission reaction has to do with a kind of reaction in which a radioactive nucleus is bombarded by the use of a particle and then there is the disintegration of the atomic nucleus in order to produce energy.
This has been one of the ways by which we can be able to generate electricity in several power plants across the world. The loss in the mass of the reactants is the equivalent of the energy produced.
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