acceleration depends on the change in velocity
Is acceleration affected by speed or velocity?Acceleration is a vector quantity because it is affected by changes in velocity. This indicates that acceleration has a magnitude as well as a direction. Meters per second squared, or m/s2, are the conventional units of acceleration. These units are derived from velocity units, meters per second, and time units, seconds.
Without zero velocity, a bode can have acceleration. For example, when an object is hurled upwards, the velocity at the body is zero at that point, yet it experiences acceleration owing to gravity. It is feasible that when an item is hurled upward, its velocity is zero at the highest point and it has a finite acceleration owing to gravity.
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Why do you wet the lighter and dry it to best of your ability prior to taking its mass?
Although it appears that the soil particles are touching, there are gaps between them. Pores are the name for these voids.
Dry soil can be observed to include a variety of particles of various mass when it is crushed in the hand. These are known as mineral particles, and the majority of them come from the breakdown of rocks. Some are known as organic particles, and some come from leftovers of plants or animals (rotting leaves, bones, etc). (or organic matter). Although it appears that the soil particles are touching, there are gaps between them. Pores are the name for these voids. The pores in "dry" soil are primarily air-filled. The pores mostly contain water after rain or irrigation. In the soil is living material. Live roots, beetles, worms, larvae, and other organisms are all possible. By aerating the soil, they aid to improve the plant roots' growing environment.
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two point charges, q1=-15.0mc and q2= 75.0 mc are separated at distance of 8.0 cm. what is the distance (in cm) from charge q2 to the point at which net electric field is equal 0?
The distance from charge q2 to the point at which net electric field is 4 cm. The electric field is a vector field that describes the force experienced by a charged particle due to an electric charge distribution.
Using Coulomb's law:
E1 = k x q1 / r^2
E2 = k x q2 / (d-r)^2
where k is Coulomb's constant, d is the separation between the charges (8 cm), and r is the distance from charge q2 to the point at which the net electric field is equal to zero.
Setting E1
= E2:k x q1 / r^2
= k x q2 / (d-r)^2
Solving for r:r
= d x sqrt(q1/q2)
= 8 cm x sqrt(-15.0 mc / 75.0 mc)
= 4 cm
So, the distance from charge q2 to the point at which the net electric field is equal to zero is 4 cm.
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most duct insulation is made of ___________?
Most duct insulation is made of fiberglass as it is one of the most ubiquitous insulation materials.
For loose-fill insulation, cellulose, fibreglass, and mineral (rock ) wool are the most frequently utilised material types. These materials were all created utilising recycled waste. Recycled newsprint is mostly used to make cellulose. 40% to 60% of fibreglass goods recycle glass.
A fibreglass is a type of fiber-reinforced plastic in which the reinforced plastic is made of glass fibre. This may be the cause of fibreglass' other names, glass reinforced plastic and glass fibre reinforced plastic. Typically, the glass fibre is weaved into a fabric, randomly distributed, or flattened into a sheet. The most popular version of fiber-reinforced plastic that uses glass fibre is fibreglass. The fibres can be woven into glass fabric, flattened into a sheet known as a chopped strand mat, or randomly distributed.
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consider the differential equation with initial condition . a. use euler's method with two steps to estimate when : 2 (be sure not to round your calculations at each step!) now use four steps: 3.25 (be sure not to round your calculations at each step!) b. what is the solution to this differential equation (with the given initial condition)? 4.5 c. what is the magnitude of the error in the two euler approximations you found? magnitude of error in euler with 2 steps
To find an approximate solution to the given differential equation with the given initial condition, you can use Euler's method with two steps.
The approximate solution at t = 2 is 3.25 and with four steps is 4.5. The magnitude of the error in the two Euler approximations you found would be the difference between the two approximate solutions, which is 1.25.
To further explore Euler's method, it is important to understand the concept of numerical errors. In the numerical solution of a differential equation, numerical errors occur when the approximate solution is not close enough to the true solution. These errors can be caused by a variety of factors, including the choice of numerical method, the step size used in the method, the number of steps taken, and the accuracy of the initial conditions.
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Calculate the wavelength of Radio 4 which broadcasts on a frequency of 198 kHz?
Answer:
The wavelength of Radio 4, which broadcasts on a frequency of 198 kHz, is approximately 15.152 meters.
Explanation:
The wavelength of a radio wave is calculated by dividing the speed of light (approximately 3 x 10^8 meters per second) by the frequency of the wave.
To calculate the wavelength of Radio 4, which broadcasts on a frequency of 198 kHz, we can use the following equation:
wavelength = (speed of light) / (frequency)
wavelength = (3 x 10^8 m/s) / (198 x 10^3 Hz)
wavelength = 15.152 meters
So the wavelength of Radio 4, which broadcasts on a frequency of 198 kHz, is approximately 15.152 meters.
It takes the planet Jupiter 12 years to orbit the sun once in a nearly circular orbit. Assuming that Jupiter's orbit is truly circular, what is the distance from Jupiter to the Sun, given that the distance from the earth to the sun is 1.5 × 10 11 m ?
Jupiter is about 5.2 astronomical units away from the Sun.
Jupiter's distance from the Sun, also known as its astronomical unit (AU), can be calculated using Kepler's third law of planetary motion.
Kepler's third law states that the square of the orbital period of a planet (in years) is proportional to the cube of its average distance from the Sun (in astronomical units).
Using the fact that Jupiter takes 12 years to orbit the Sun and the average distance from the Earth to the Sun is 1.5 x 10^11 meters (which is approximately equal to 1 astronomical unit), we can solve for Jupiter's distance from the Sun.
The formula for Kepler's third law can be written as:
(Period of Jupiter)^2 = (Distance of Jupiter from the Sun)^3 / (Distance of Earth from the Sun)^3
Plugging in the values, we get:
(12^2) = (x^3) / (1^3)
where x is Jupiter's distance from the Sun in astronomical units.
Solving for x, we get:
x = (12^2)^(1/3) = 5.2 astronomical units
So, Jupiter is about 5.2 astronomical units away from the Sun.
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determine the ultimate load of a rectangular footing with dimensions of 6x4 wiht eccentric load
Without additional information, the ultimate load of a rectangular foundation with 6 x 4 dimensions that is being subjected to an eccentric load cannot be computed.
The ultimate load capacity of the footing is influenced by a number of variables, including the material properties, the soil characteristics, and the size and placement of the eccentric load.
It would be necessary to conduct a structural study taking into account the footing's geometry, material qualities, and load circumstances in order to calculate the ultimate load. For the analysis to establish the maximum load that the footing can support, calculations for soil bearing capacity, shear strength, and bending moments are commonly used. It is significant to highlight that a competent engineer who is knowledgeable should carry out the computations.
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an object moves according to the function x = t7/2 where x is the distance traveled and t is the time. its kinetic energy is proportional to:
The kinetic energy of the object which moves according to the function x = t7/2 is proportional to t^5.
The kinetic energy (KE) of an object is proportional to its mass (m) and the square of its velocity (v). If x = t^(7/2) is the equation for the distance traveled by the object, then its velocity (v) can be obtained by taking the derivative of x with respect to time (t).
v = dx/dt = (7/2)t^(5/2)
So the kinetic energy can be calculated as:
KE = 1/2 * m * v^2 = 1/2 * m * [(7/2)t^(5/2)]^2 = (49/8) * m * t^5
Therefore, the kinetic energy of the object is proportional to t^5.
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2.2.1. collapse depth (or crush depth) is the submerged depth that a submarine cannot exceed without collapsing because of the surrounding water pressure. the collapse depth of modern submarines is not quite a kilometer . assuming seawater to be incompressible , what is the crush depth pressure in and ? is the pressure you computed absolute or gauge pressure?
The collapse depth of a submarine is the depth at which the surrounding water pressure becomes great enough to cause the submarine's hull to collapse. At this depth, the pressure is sufficient to cause the submarine's material to reach its crush strength.
Given that the collapse depth of modern submarines is around a kilometer, and assuming seawater to be incompressible, the crush depth pressure can be calculated as follows:
Pressure = density of seawater * depth * gravitational acceleration
Density of seawater = 1025 kg/m^3
Gravitational acceleration = 9.8 m/s^2
Crush depth = 1000 m
So the pressure at crush depth would be:
Pressure = 1025 kg/m^3 * 1000 m * 9.8 m/s^2 = 10,250,000 N/m^2 = 10.25 MPa
The pressure you computed is an absolute pressure. It is the force per unit area exerted by the water on the submarine's hull. It is measured relative to a perfect vacuum and it is independent of any other external pressure.
a car moving with a constant velocity travels 100 meters in 2 seconds. what was the average velocity of the car in m/
The average velocity of the car in m/s is: 50 m/s
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this problem is:
v= x/t
Where:
x = distancet = timev = velocityInformation about the problem:
x = 100 mt = 2 sv=?Applying the velocity formula we get:
v = 100 m / 2 s
v = 50 m/s
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Match the graph to the speed description
Graph 1 shows the increasing speed.
Graph 2 shows the sitting still.
Graph 3 shows the constant speed.
What is Speed-time graph?The speed-time graph is described in such a way that speed is always plotted on the vertical axis and time is always plotted on the horizontal which gives the speed of a particle accelerating at time 0, u at time t represents the speed up to v.
For uniformly varying speed the speed-time graph will be a straight line while the acceleration in the graph is given by the slope of the graph. The distance covered by a moving body in a given time can be calculated from the speed time graph.
Like in above given example, graph 1 shows the increasing as it is increasing with time, graph 2 shows the sitting still position as time is increasing but distance is constant and graph 3 shows the constant speed as with time equal distance increases.
Thus, Graph 1 shows the increasing speed.
Graph 2 shows the sitting still.
Graph 3 shows the constant speed.
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What is the relation between wavelength and period of a wave?
The primary distinction between wavelength and period is that the former measures the shortest path between consecutive locations on a wave that are in phase, while the latter measures the amount of time needed for an oscillation to complete at a particular position.
What is the formula for a wave's period?T = 1 / f, where "T" stands for the period, or the length of time it takes for one cycle to complete, and "f" stands for frequency, which is the formula for the period. Convert frequency from Hertz to 1/s to obtain period from frequency. Multiply 1 by the frequency now. Time (period) given in seconds will be the outcome.
What are SI units and wavelengths?A meter, commonly abbreviated as m, is the SI unit of wavelength. The multiples or fractions of a meter are also used to measure wavelength. Notably, when wavelengths are a significant feature, exponential powers of 10 are used. Shorter wavelengths are described as having a negative exponential.
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two 2.0-cm-diameter insulating spheres have a 5.30 cm space between them. one sphere is charged to 79.0 nc , the other to - 84.0 nc . part a what is the electric field strength at the midpoint between the two spheres?
The electric field strength at the midpoint between the two sphere is 110.63 × 10⁴ N/C, if the distance between them is 5.30 cm.
Diameter of each sphere, D = 2 cm = 0.02 m
Radius of each sphere, r = 0.02/2 = 0.01 m
Charge on first sphere, q₁ = 79 × 10⁻⁹ C
Charge on second sphere, q₂ = -84 × 10⁻⁹ C
Permittivity constant, ε₀ = 8.8 × 10⁻¹² Farad/meter
Distance of the center of first sphere from the mid-point, d = 0.01 + 0.053/2
d = 0.0365 m
Electric field strength at the midpoint due to the first sphere, E₁ = q₁/(4πε₀d²)
E₁ = 79 × 10⁻⁹/(4π × 8.8 × 10⁻¹² × 0.0365²)
E₁ = 53.62 × 10⁴ N /C
Similarly, electric field strength at the midpoint due to the second sphere, E₂ = q₂/(4πε₀d²)
E₁ = -84 × 10⁻⁹/(4π × 8.8 × 10⁻¹² × 0.0365²)
E₁ = -57.02 × 10⁴ N /C
So the strength at the mid point will be E = E₁ - E₂
E = 53.62 × 10⁴ - (-57.02 × 10⁴)
E = 110.63 × 10⁴ N/C
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Speed= 11.8m/ S +9%
what's s? how do I find it??
Answer:
Explanation:
Not sure what you're asking here, but I'll take a guess. If the question is what is the final speed if there is a 9% increase in speed from a starting speed of 11.8 m/s, then the answer is:
(11.8 m/s) + (11.8 m/s)(0.09) = 12.86 m/s
suppose that fred’s velocity is vf (t) = 20t cos(πt) meters/minute and marie’s velocity is vm(t) = 30t sin(πt) meters/minute at time t minutes after the start of a race.
The time at which Fred and Marie have the same velocity is t = 0.
Determine the velocity difference between Fred and Marie.
Difference in velocity = vf(t) - vm(t)
= 20t cos(πt) - 30t sin(πt)
= 10t[cos(πt) - sin(πt)] meters/minute
The velocity difference's magnitude should be determined.
Magnitude of the difference in velocity = |10t[cos(πt) - sin(πt)]|
= |10t| |cos(πt) - sin(πt)|
Determine the moment when Fred and Marie move at the same speed.
Make the velocity difference equal to 0.
0 = 10t[cos(πt) - sin(πt)]
To convert the equation into terms of t 0 = 10t2, multiply both sides by t.
0 = 10t²[cos(πt) - sin(πt)]
To get an equation in terms of cos(πt) and sin(πt), divide both sides by 10t².
0 = [cos(πt) - sin(πt)]
Solve for t by setting cos(πt) = sin(πt)
cos(πt) = sin(πt)
πt = arcsin(sin(πt))
πt = arcsin(cos(πt))
πt = arccos(cos(πt))
Fred and Marie's velocities are equal at time t = 0, or at that instant.
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a 10-cm -long thin glass rod uniformly charged to 13.0 nc and a 10-cm -long thin plastic rod uniformly charged to -13.0 nc are placed side by side, 4.50 cm apart. what are the electric field strengths e1 to e3 at distances 1.0 cm , 2.0 cm , and 3.0 cm , from the glass rod along the line connecting the midpoints of the two rods?
A. At a point 1cm from the glass rod, E = 1.36 × 10⁶ N/C
B. At a point 2cm from the glass rod, E = 5.17 × 10⁵ N/C
C. At a point 3cm from the glass rod, E = 6.993 × 10⁵ N/C
How to calculate electric filed strength?Parameters given:
Charge of glass rod, Q = 14nC = 14 × 10⁻⁹ C
Charge of plastic rod, q = 14nC = 14 × 10⁻⁹ C
Distance between both rods = 4.5cm = 0.045
A. Electric field strength at a point 1.0cm (0.01m) from the glass rod is the sum of electric field strength due to both rods i.e.
E = E₁ + E₂
Where
E₁ = electric field strength due to glass rod
E₂ = electric field strength due to plastic rod
E₁ = kQ/0.01²
E₂ = kq/(0.045 - 0.01)² = kq/(0.035)²
E = kQ/0.01² + kq/(0.035)² = k(Q/0001 + q/0.001225)
E = 9 * 10⁹ [(14 * 10⁻⁹ / 0.001) + (14 * 10⁻⁹)/0.001225]
E = 9 * 10⁹[(14 * 10⁻⁵) + (1.143 * 10⁻⁵)]
E = 9 * 10⁹ * 15.143* 10⁻⁵
E = 1.36 × 10⁶N/C
B. Electric field strength at a point 2.0cm (0.02m) from the glass rod is the sum of electric field strength due to both rods i.e.
E = E₁ + E₂
E₁ = kQ/0.02²
E₂ = kq/(0.045 - 0.02)² = kq/(0.025)²
E = kQ/0.02² + kq/(0.025)² = k(Q/0.0004 + q/0.000625)
E = 9 * 10⁹ [(14 * 10⁻⁹ / 0.0004) + (14 * 10⁻⁹)/0.000625]
E = 9 * 10⁹[(3.5 * 10⁻⁵) + (2.24 * 10⁻⁵)]
E = 9 * 10⁹ * 5.74 * 10⁻⁵
E = 5.17 × 10⁵ N/C
C. Electric field strength at a point 3.0cm (0.03m) from the glass rod is the sum of electric field strength due to both rods i.e.
E = E₁ + E₂
E₁ = kQ/0.03²
E₂ = kq/(0.045 - 0.03)² = kq/(0.015)²
E = kQ/0.03² + kq/(0.015)² = k(Q/0009 + q/0.000225)
E = 9 * 10⁹ [(14 * 10⁻⁹ / 0.009) + (14 * 10⁻⁹)/0.000225]
E = 9 * 10⁹[( 1.55 * 10⁻⁵) + (6.22 * 10⁻⁵)]
E = 9 * 10⁹ * 7.77 * 10⁻⁵
E = 6.993 × 10⁵ N/C
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When freshly cut sodium metal is exposed to all the mass of the substance increases. Which of the following is the best explanation for this apparent violation of the Law of Conservation of Mass? a. The air "pushes down on the metal, causing the balance to display a falsely high mass b. The sodium atoms move closer to one another, causing the sample to gain mass c. The sodium reacts with a component of the air, and the total mass of the reactants is equal to the total of the producte d. Thermal energy of the air is converted into the additional mass e. The Law of Conservation of Moss does not apply to metals
The best explanation for the statement "when freshly cut sodium metal is exposed to all the mass of the substance increases" is that the sodium reacts with a component of the air, and the total mass of the reactants is equal to the total mass of the products.
Hence, the Correct Option is c. i.e. sodium reacts with a component of the air, and the total mass of the reactants is equal to the total mass of the products.
Due to the oscillations of free electrons, freshly cut sodium metal has a brilliant, sparkling surface that rapidly turns dull grey when it interacts with oxygen in the air surrounding it. The metal eventually develops a white crust of sodium oxide that inhibits the metal and oxygen from reacting further.
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can someone please help me with this
The acceleration of Argus in the first 25 s is approximately 0.8 m/s2.
Calculate the distance of the mother from the father?The distance of the mother from the father can be calculated by using the equation v = u + at, where v is the velocity of Argus, u is the initial velocity of Argus, a is the acceleration of Argus and t is the time taken for Argus to run from the father to the mother. Using the values from Graph 1, we can calculate the distance to be approximately 12.5 m.Graph 1 shows the velocity of Argus as a function of time. The graph shows that Argus has a negative acceleration in the first 25 s of its motion, meaning that it is slowing down. This is consistent with the family playing with their dog, as Argus is initially running towards the girl and then reversing his direction of movement to run towards the mother. The acceleration of Argus in the first 25 s can be calculated by taking the derivative of the velocity graph. This gives a result of -0.16 m/s2.The distance of the mother from the father can also be calculated from Graph 1. By taking the area under the graph from 0 to 150 seconds, we get a result of 150 m. This indicates that the mother is 150 m away from the father.In conclusion, Graph 1 shows the velocity of Argus as a function of time. By taking the derivative of the graph, we can calculate the acceleration of Argus in the first 25 seconds and by taking the area under the graph, we can calculate the distance of the mother from the father.To learn more about The acceleration refer to:
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which moment corresponds to the maximum kinetic energy of the system? view available hint(s)for part d which moment corresponds to the maximum kinetic energy of the system? a b c d consider the block in the process of oscillating. if the kinetic energy of the block is increasing, the block must be consider the block in the process of oscillating.if the kinetic energy of the block is increasing, the block must be at the equilibrium position. at the amplitude displacement. moving to the right. moving to the left. moving away from equilibrium. moving toward equilibrium. to learn to apply the law of conservation of energy to the analysis of harmonic oscillators. systems in simple harmonic motion, or harmonic oscillators, obey the law of conservation of energy just like all other systems do. using energy considerations, one can analyze many aspects of motion of the oscillator. such an analysis can be simplified if one assumes that mechanical energy is not dissipated. in other words, e
The answers for Part A = A, Part B = A, Part C = moving toward equilibrium, Part D = C, Part E = C, Part F = D, and Part G = 3/8kA².
For part A: The maximum PE is when the spring is fully compressed. D might look like the correct answer, but actually, A is when the spring is at amplitude. Even though it’s stretched, that still counts as compression: A
For part B: When PE is maximized, KE is minimized, so the correct answer is the same as from Part A: A
For part C: KE is maximized when PE is minimized. PE is most prominent at amplitude, and KE is most prominent at equilibrium. So choice F is correct: F. moving toward equilibrium.
For part D: KE is greatest at equilibrium: C
For part E: Minimum PE is when KE is greatest, i.e. at equilibrium: C
For part F: When U = KE, U = 1/2Umax (this is just a fact, which we won’t bother solving for here). So:
U = 1/2(U)
1/2kx² = 1/2(1/2kA²)
x² = 1/2A²
x = √(1/2A²)
x = A√(2)/2
Note- if it isn’t obvious where the √(2)/2 came from, use 2/4 for the fraction above instead of 1/2:
x = √((2/4)A²)
x = A√(2)/2
The diagram doesn’t give this as an answer, but it does give -A√(2)/2, which is equivalent: D
For part G: Since total energy = KE + PE and we only have enough information to find PE, we can work backwards by first finding the maximum PE and then subtracting the PE at point B.
Maximum PE:
PE(max) = 1/2kA²
PE at Point B:
PE(B) = 1/2k(A/2)²
PE(B) = 1/2k(A²/4)
PE(B) = 1/8k(A²)
Now find the difference between the Potential energies, and that difference must be kinetic energy since there is no friction:
KE(B) = PE(max) – PE(B)
KE(B) = 1/2kA² – 1/8k(A²)
KE(B) = 3/8kA²
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--The given question is incomplete; the complete question is
" Consider a harmonic oscillator at four different moments, labelled A, B, C, and D, as shown in the figure. Assume that the force constant k, the mass of the block, m, and the amplitude of vibrations, A, are given. Answer the following questions:
Part A
Which moment corresponds to the maximum potential energy of the system?
A
B
C
D
Part B
Which moment corresponds to the minimum kinetic energy of the system?
A
B
C
D
Part C
Consider the block in the process of oscillating. If the kinetic energy of the block is increasing, the block must be:
A. at the equilibrium position.
B. at the amplitude displacement.
C. moving to the right.
D. moving to the left.
E. moving away from equilibrium.
F. moving toward equilibrium.
Part D
Which moment corresponds to the maximum kinetic energy of the system?
A
B
C
D
Part E
Which moment corresponds to the minimum potential energy of the system?
A
B
C
D
Part F
At which moment is K = U?
A
B
C
D
Part G
Find the kinetic energy K of the block at the moment labelled B.
Express your answer in terms of k and A."--
the half-life of sodium-24 is 14.96 hours. if a sample contains 320 mg, how many mg will remain after 150 hours?
The half-life of a radioactive isotope is the time it takes for half of the initial amount to decay. So 0.31 mg will remain after 150 hours.
For sodium-24, the half-life is 14.96 hours. To determine the amount of sodium-24 that remains after 150 hours, we need to calculate the number of half-lives that have occurred during that time. We can do this by dividing the total elapsed time by the half-life of the isotope:
150 hours / 14.96 hours = 10.07 half-lives
Since each half-life reduces the amount of the isotope by half, after 10 half-lives, we would expect the amount to be reduced by a factor of [tex]2^{10}[/tex] = 1024. So, the amount of sodium-24 that remains after 150 hours would be:
320 mg × (1/1024) = 0.31 mg
This is the theoretical minimum amount of sodium-24 that would remain after 150 hours. In practice, other factors such as environmental conditions and decay products can affect the actual amount remaining.
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Two
Imagine an alternate universe where the value of the Planck constant is 6.62607 x 108 J.S.
In that universe, which of the following objects would require quantum mechanics to describe, that is, wou
objects would act like everyday objects, and be adequately described by classical mechanics?
object
A grain of sand with a mass of 170 mg, 670. um wide,
moving at 4.00 mm/s.
An eyelash mite with a mass of 13.5 µg, 270 um wide,
moving at 31. um/s..
An airplane with a mass of 1.88 x 10 kg, 14.0 m long,
moving at 1500. km/h.
A turtle with a mass of 480. g, 28. cm long, moving at 1.6
cm/s.
quantum or classical?
A grain of sand with a mass of 170 mg, 670. um wide, moving at 4.00 mm/s - Classical.
What is mass?Mass is the measure of an object’s inertia, or its resistance to changes in motion. It is a fundamental property of matter and is typically measured in kilograms. It is different from weight, which is a measure of the force of gravity acting on an object.
An eyelash mite with a mass of 13.5 µg, 270 um wide, moving at 31. um/s. - Quantum
An airplane with a mass of 1.88 x 10 kg, 14.0 m long, moving at 1500. km/h - Classical
A turtle with a mass of 480. g, 28. cm long, moving at 1.6 cm/s. - Classical
All of the objects in question are macroscopic, meaning that their behavior can be accurately described with classical mechanics. However, because the Planck constant is larger than its value in our universe, the eyelash mite is at the limit of being small enough to require quantum mechanics to describe its behavior. Therefore, it would be the only object that would require quantum mechanics in this alternate universe.
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The thrust of a certain boat’s engine generates a power of 10kW as the boat moves at constant speed 10ms through the water of a lake. The magnitude of the drag force that is exerted on the boat’s hull as it is moving through the water is directly proportional to the boat's speed and is given by the equation F=kv. The increase in power needed for the boat to move through the lake at a constant speed of 12ms is
The increase in power needed for the boat to move through the lake at a constant speed of 12ms is 4.4 kW.
What is power?Power can be defined as the amount of work completed in a given amount of time. Watt (W), which is derived from joules per second (J/s), is the SI unit of power.
We know that:
Power = force × speed
For 1st case:
10000 = k × 10 × 10
k = 100
Hence, the increase in power needed for the boat to move through the lake at a constant speed of 12ms is = 100 ( 12² - 10²) watt
= 4400 watt
= 4.4 kW
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what is the mechanical advantage of a first class lever that has an input force of 200 N and produces and output force of 1300 N
at a certain altitude above the earth's surface, the electric field has a magnitude of 108 v/m. how much energy is stored in 1.00 m3 of air due to this field?
108kg energy is stored in 1.00 m3 of air due to this field.
How is energy density calculated?
To = [M0 L3 T0]-1 [M1 L-1 T-2] [M1 L2 T-2] [M0 L2 T-2] As a result, the energy density is represented in dimensions as [M1 L-1 T-2].
The quantity of energy held between the plates of a parallel-plate capacitor is given by the formula UC=uE(Ad)=120E2Ad=120V2d2Ad=12V20Ad=12V2C, which is the energy density times the volume between the plates.
We will use small u to represent the quantity known as energy density, which is straightforward to define. It is described as the amount of energy per volume that the capacitor's electric fields can hold. It is equal to the volume of the area between the capacitor's plates divided by u sub E.
In this case-
108 * 1.00 = 108.
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An object moves such that its velocity is defined as v(t) = −t³ + 4t² + 2t for 0 ≤ t ≤ 8 seconds. When does the object reach its maximum acceleration?Group of answer choices1.333 s2.897 s4.449 s12.270 s
The object reaches its maximum acceleration at the time which is calculated to be 1.333 s.
The given equation of velocity is v(t) = −t³ + 4t² + 2t.
On differentiation of the equation of velocity, we get acceleration.
a(t) = d/dt v(t) = d/dt [−t³ + 4t² + 2t] = -3t² + 8t +2
a(t) = -3t² + 8t +2
The maximum value of acceleration can be obtained when t = -b/2a
where, b is the coefficient of t
a is the coefficient of t²
So, t = -b/2a = -8/(-3×2) = 1.333 s
Thus, acceleration function is maximum at t = 1.333 s.
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To practice Problem-Solving Strategy 8.1 Static equilibrium problems.When you lift an object by moving only your forearm, the main lifting muscle in your arm is the biceps. Suppose the mass of a forearm is 1.50kg . If the biceps is connected to the forearm a distance dbiceps = 2.50cmfrom the elbow, how much force Fbiceps must the biceps exert to hold a 700g ball at the end of the forearm at distance dball = 30.0cm from the elbow, with the forearm parallel to the floor? How much force Felbow must the elbow exert? (Figure 1)
The biceps force (F biceps) and the elbow force (F elbow) is mathematically calculated to be F biceps = 188.352 N towards the upward direction, F elbow = 165.295 N towards the downwards direction.
Generally, the equation for the Weight of the forearm is mathematically given as
W = mass × gravity
W = 1.50 kg × 9.81 m/s²
W = 14.715 N
The moment about the elbow is, since the sum of moments about the elbow is equated to 0.
[0.85 × 9.81 = 8.3385 N]
8.3385 N× 30 cm + 14.715 N× 15 cm - F biceps × 2.5 cm = 0
250.155 + 220.725 - F biceps × 2.5 cm = 0
F biceps × 2.5 cm = 470.88 N cm
F biceps = (470.88 N cm)/(2.5 cm)
F biceps= 188.352 N towards the upward direction
The sum of moments about the point b/w biceps and forearm is
F elbow × 2.5 cm = 8.3385 N × 27.5 cm + 14.715 N× 12.5 cm
F elbow × 2.5 cm = 229.30 + 183.9375
F elbow = 165.295 N towards the downwards direction
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chloe, a russian cosmonaut, goes outside her ship for a spacewalk, but when she is floating 15 m from the ship, her tether catches on a sharp piece of metal and is severed. chloe tosses her 2.0 kg camera away from the ship with a speed of 12 m/s. a) how fast will chloe , whose mass is now 68 kg, travel toward the spaceship? b) assuming the spaceship remains at rest with respect to chloe, how long will it take her to reach the ship? (0.352941 / 42.5)
Answers to part A and B are as follows:
A: At 0.352941 m/s Chloe travels toward the spaceship.
B: The time it takes Chloe to reach the ship is 42.5 s.
A) After Chloe tosses the camera, the momentum of the system (Chloe + Camera) must be conserved. The momentum of Chloe before she tosses the camera is:
p_before = m_chloe * v_before = 68 kg * 0 m/s = 0 kg m/s
The momentum of Chloe and the camera after she tosses the camera is:
p_after = m_chloe * v_after + m_camera * v_camera = 68 kg * v_after + 2.0 kg * 12 m/s
Since momentum must be conserved, we have:
p_before = p_after
0 = 68 kg * v_after + 2.0 kg * 12 m/s
Solving for v_after:
v_after = -2.0 kg * 12 m/s / 68 kg = -0.352941 m/s
B) To find the time it takes Chloe to reach the ship, we can use the kinematic equation:
d = v_0 * t + 0.5 * a * t^2
where d is the distance from Chloe to the ship, v_0 is her initial velocity, t is time, and a is acceleration due to gravity.
We know that the distance from Chloe to the ship is 15 m, her initial velocity is -0.352941 m/s, and acceleration due to gravity is 9.8 m/s^2.
Substituting these values into the kinematic equation:
15 = -0.352941 * t + 0.5 * 9.8 * t^2
Solving for t using the quadratic formula:
t = (-0.352941 +/- sqrt(0.352941^2 - 4 * 0.5 * 9.8 * 15)) / (2 * 0.5 * 9.8)
The time it takes Chloe to reach the ship is the positive value of t:
t = (0.352941 + sqrt(0.352941^2 + 4 * 0.5 * 9.8 * 15)) / (2 * 0.5 * 9.8)
t = 42.5 s
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according to newton's law of inertia, a railroad train in motion should continue going forever even if its engine is turned off. we never observe this because railroad trains are much too heavy. move too slowly. always have forces that oppose the motion. must go up and down hills.
According to Newton's law of inertia, a railroad train in motion should continue going forever even if its engine is turned off.
We never observe this because railroad trains are much too heavy and therefore require a great deal of energy to keep them moving.
Additionally, railroad trains move too slowly for the effects of inertia to be easily visible, and they are also subject to opposing forces such as air resistance, friction and gravity which slow them down and eventually bring them to a stop. Finally, railroad trains must go up and down hills, and this requires additional energy which is not available after the engine is turned off.
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what is the linear charge density of a thin wire bent into a circle (or ring) of radius 7.48 cm if the total charge on the wire is 3.76 µc?
The required value of linear charge density of a thin wire bent into a circle is 0.08 × 10⁻⁴ c/m.
The wire is curved into a circular form.
The radius of the circle is given as R = 7.48 cm = 7.48 × 10⁻² m
The total charge on the wire Q = 3.76 µc = 3.76 × 10⁻⁶ c
The relation between total charge, radius and linear charge density is known as,
Q = 2 π R α
where, Q is the total charge
R is the radius of the wire bent into a circle
α is linear charge density
Making α as subject, we have,
α = Q /(2 π R) = (3.76 × 10⁻⁶)/(2 π ×7.48 × 10⁻²) = (3.76 × 10⁻⁶)/(46.97 × 10⁻²) = 0.08 × 10⁻⁴ c/m
Thus, the value of linear charge density of a thin wire is calculated to be 0.08 × 10⁻⁴ c/m.
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circuit b has battery voltage = 9.0 volts and three identical bulbs. with the switch open, lamps 1 and 2 are in series, and the ammeter reads an initial current of 0.60 a.
To calculate the total current of the circuit, we must first determine the equivalent resistance of the series connection of lights 1 and 2, which can be accomplished using Ohm's law.
I = V/R. Because we know the current (0.60 A) and the voltage (9.0 V), we can calculate the equivalent resistance: R = V/I = 9.0 / 0.60 = 15. We can use the same approach to determine the current through each light now that we know the equivalent resistance of lamps 1 and 2. I = V/R = 9.0 / 15 = 0.6 A. Finally, in order to compute the current through lamp 3, we must first calculate the total resistance of the complete circuit with the switch closed, which can be calculated as the sum of the equivalent resistances of lights 1 and 2. and 2, as well as the lamp's resistance 3. If the lights are similar, they will have the same resistance, and we can compute the total resistance using the current calculated in the previous step (0.6 A). The current flowing through bulb 3 may therefore be calculated using Ohm's law: I = V/R.
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