Two kids of different masses take part in a tug of war with no friction. The distance of their center of mass can be calculated, and if child B pulls on the rope towards child A, the distance he will move before colliding with child A can also be calculated.
A. To find the center of mass (CM) of the system, we need to take into account both the masses and their distances from each other. The formula for the position of the CM is:
CM = (m1x1 + m2x2) / (m1 + m2)
where m1 and m2 are the masses, x1 and x2 are their distances from a chosen reference point.
In this case, let's take child A as the reference point, so x1 = 0 (since child A is at the origin), and x2 = 11 m. Then we have:
CM = (m1x1 + m2x2) / (m1 + m2)
= (26 kg * 0 + 49 kg * 11 m) / (26 kg + 49 kg)
= 7.6 m
Therefore, the center of mass of the system is located 7.6 m from child A.
B. As child B pulls on the rope, he will move towards child A, and their separation distance will decrease. At the same time, the center of mass of the system will move towards child B. Since there is no external force acting on the system, the position of the center of mass will not change.
Let's assume that child B moves a distance of x towards child A before they collide. Then the distance between child A and the CM of the system will be (11 - x), and the distance between child B and the CM will be x. Using the formula for the position of the CM, we can set up an equation:
CM = (m1x1 + m2x2) / (m1 + m2)
= ((26 kg) * 0 + (49 kg) * (11 - x)) / (26 kg + 49 kg)
= (539 - 49x) / 75
Since the CM does not move, this must be equal to the initial position of the CM, which we found to be 7.6 m from child A:
(539 - 49x) / 75 = 7.6
Solving for x, we get:
x = 6.4 m
Therefore, child B will have moved a distance of 6.4 m towards child A before they collide.
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What voltage is produced by a 27 μh inductor if the current through the inductor is increasing at a rate of 63 ma/s?
The voltage produced by the 27 µH inductor, if the current through the inductor is increasing at a rate of 63 mA/s, is 1.701 mV.
The voltage produced by an inductor is given by the formula:
V = L*(di/dt)
where V is the voltage, L is the inductance, and di/dt is the rate of change of current.
Substituting the given values:
L = 27 µH = 27 x [tex]10^{-6}[/tex] H
di/dt = 63 mA/s = 63 x [tex]10^{-3}[/tex] A/s
V = (27 x [tex]10^{-6}[/tex] H) * (63 x [tex]10^{-3}[/tex] A/s) = 1.701 mV
Therefore, the voltage produced by the 27 µH inductor if the current through the inductor is increasing at a rate of 63 mA/s is 1.701 mV.
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Which of the following is one of the main functions of a transistor in a circuit?
Answer:
To act as a switch to control the flow of charge in a circuit
Explanation:
A transistor acts like a gate, this we can say it closes and opens , this is what we call control
a sphere completely submerged in water is tethered to the bottom with a string. the tension in the string is one-half the weight of the sphere.
The tension in the string is equal to the weight of the water displaced by the submerged sphere.
Based on the information given, we can make several observations about the situation.
The sphere is completely submerged in water, which means it is experiencing buoyancy force equal to the weight of the water displaced by the sphere. The tension in the string is one-half the weight of the sphere.
Let's analyze these observations further:
Buoyancy Force: When an object is submerged in a fluid, it experiences an upward force called buoyancy. According to Archimedes' principle, the buoyant force acting on an object is equal to the weight of the fluid it displaces.
In this case, the sphere is submerged in water, so the buoyant force acting on it is equal to the weight of the water displaced by the sphere. This buoyant force acts in the upward direction.
Tension in the String: The tension in the string is one-half the weight of the sphere. The weight of an object is the force exerted on it due to gravity.
In this case, the weight of the sphere is acting downward, and the tension in the string is acting upward. According to the given information, the tension in the string is one-half the weight of the sphere.
From these observations, we can conclude that the buoyant force acting on the sphere is equal to the tension in the string. Mathematically, we can express this as:
Buoyant force = Tension in the string
Weight of the water displaced by the sphere = Tension in the string
In summary, the tension in the string is equal to the weight of the water displaced by the submerged sphere.
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(a) Calculate the focal length of the mirror formed by the shiny back of a spoon that has a 2.30 cm radius of curvature. (b) What is its power in diopters?
(a) The focal length of the mirror formed by the shiny back of a spoon that has a 2.30 cm radius of curvature is 1.15 cm and (b) The power is 86.96 diopters.
(a) The focal length of a spherical mirror is half of its radius of curvature, so the focal length of the mirror formed by the shiny back of a spoon with a 2.30 cm radius of curvature is:
focal length = radius of curvature / 2
focal length = 2.30 cm / 2
focal length = 1.15 cm
Therefore, the focal length of the mirror is 1.15 cm.
(b) The power of a spherical mirror in diopters is given by the formula:
power = 1 / focal length (in meters)
Since the focal length is in centimeters, we need to convert it to meters first:
focal length in meters = 1.15 cm / 100
focal length in meters = 0.0115 m
Now we can calculate the power in diopters:
power = 1 / focal length
power = 1 / 0.0115
power = 86.96 diopters
Therefore, the power of the mirror formed by the shiny back of a spoon with a 2.30 cm radius of curvature is 86.96 diopters.
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when the sun oscillates, a region of gas alternates between moving toward earth and moving away from earth by about 10 km. when the gas is moving toward earth its light is
When the gas is moving toward earth, its light is shifted to shorter wavelengths due to the Doppler effect. This means that the light appears bluer than when the gas is moving away from earth.
When the sun oscillates, a region of gas alternates between moving toward Earth and moving away from Earth by about 10 km. When the gas is moving toward Earth, its light is blueshifted. This is because the wavelengths of light emitted by the gas are compressed as the gas moves toward us, causing the light to shift toward the shorter (blue) end of the spectrum.
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Part A Rank, from largest to smallest, the following four collisions according to the magnitude of the change in the momentum of cart B, which has twice the inertia of cart A Rank from largest to smallest. To rank items as equivalent, overlap them O A initially moving right at 1.0 m/s, B initially stationary; stick together on impact.O A initially stationary, B initially moving on left at 1.0 m/s; stick together on impact.O A initially moving right at 1.0 m/s, B initially moving left at 1.0 m/s; stick together on impact.O A initially moving right at 1.0 m/s after impact, A moving left at 0.33 m/s, B moving right at 0.67 m/s. Largest > Smallest
Largest to smallest change in momentum of cart B: 1>2>3>4.
Rank collisions by momentum change in cart B ?Ranking of collisions based on the magnitude of change in momentum of cart B, which has twice the inertia of cart A, from largest to smallest:
O A initially moving right at 1.0 m/s, B initially moving left at 1.0 m/s; stick together on impact.O A initially stationary, B initially moving on left at 1.0 m/s; stick together on impact.O A initially moving right at 1.0 m/s after impact, A moving left at 0.33 m/s, B moving right at 0.67 m/s.O A initially moving right at 1.0 m/s, B initially stationary; stick together on impact.In this collision, both carts stick together after the impact. Since cart B has twice the inertia of cart A, it will experience a larger change in momentum than cart A. The change in momentum of cart B will be equal in magnitude but opposite in direction to the change in momentum of cart A, making this collision the one with the largest change in momentum for cart B.In this collision, cart B initially has a velocity to the left, while cart A is stationary. After the collision, both carts stick together, and move to the left with the same velocity. Cart B experiences a larger change in momentum than cart A due to its greater inertia.In this collision, both carts have initial velocities in opposite directions. After the impact, cart A moves in the opposite direction with a smaller velocity, while cart B moves in the same direction with a larger velocity. Cart B experiences a smaller change in momentum than in the previous two collisions due to the transfer of momentum to cart A.In this collision, cart A has a velocity to the right, while cart B is initially stationary. After the collision, both carts stick together, and move to the right with the same velocity. Since cart A experiences the same change in momentum as cart B, this collision has the smallest change in momentum for cart B.Learn more about momentum
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suppose a current of flows through a copper wire for minutes. calculate how many moles of electrons travel through the wire. be sure your answer has the correct unit symbol and round your answer to significant digits.
To calculate the number of moles of electrons that travel through the wire, we need to know the current in amperes, the time in seconds, and Faraday's constant.
Once we have these values, we can use the formula n = (I x t) / (F x e-) to calculate the number of moles of electrons. The unit symbol for moles is mol, and we should round our answer to the appropriate number of significant digits.
To solve this problem, we need to use the formula relating current, time, and the number of electrons:
n = (I * t) / (F * e)
where:
n is the number of moles of electrons
I is the current in amperes
t is the time in seconds
F is Faraday's constant (96,485 coulombs/mole)
e is the charge on an electron (1.602 x 10⁻¹⁹ coulombs)
First, we need to convert the time from minutes to seconds:
t = 1 minute * 60 seconds/minute = 60 seconds
Then, we can plug in the values and solve for n:
n = (I * t) / (F * e)
n = (I * 60 s) / (96,485 C/mol * 1.602 x 10⁺¹⁹ C/e)
n = 3.725 * 10⁺⁴ * I mol
Therefore, the number of moles of electrons that travel through the wire is 3.725 * 10⁻⁴ times the current, in moles. We don't know the current, so we can't give an exact answer, but we can write it in general form:
n = 3.725 x 10⁻⁴ I mol
Note that the unit of current is amperes (A), and the unit of moles is mol, so the final answer should have units of mol.
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Which type of fault has NO vertical motion of rocks associated with it?
A)shear fault
B)strike-slip fault
C)reverse fault
D)normal fault
The correct answer is B) strike-slip fault. It is the type of fault that has no vertical motion of rocks associated with it. Instead, the rocks move horizontally past each other, resulting in a side-to-side motion.
This type of fault does not involve any vertical motion of the rocks, and therefore has no associated vertical motion of rocks associated with it. Like shear faults, strike-slip faults also have no vertical motion of rocks associated with them. In a strike-slip fault, the rocks on either side of the fault move horizontally in opposite directions. This type of fault is also known as a 'lateral fault' since there is only horizontal movement along the fault plane.
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Two point charges with charges 3 micro coulombs and 4 micro coulombs are separated by 2 cm.The value of the force between them? A. 400 B. 600 C. 540N D. 270 E. 300
The value of the force between two point charges will be 540 N. The correct option is C.
The value of the force between two point charges can be determined using Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be represented as [tex]F = k * (q1 * q2) / r^2[/tex], where F is the force, k is the Coulomb's constant [tex](9 * 10^9 N*m^2/C^2)[/tex], q1 and q2 are the magnitudes of the charges, and r is the distance between them.
In this case, the two point charges have magnitudes of 3 micro coulombs and 4 micro coulombs, respectively, and they are separated by a distance of 2 cm (or 0.02 m). Therefore, using Coulomb's Law, the force between them can be calculated as F =[tex](9 * 10^9 N*m^2/C^2) * [(3 * 10^{-6} C) * (4 * 10^{-6} C)] / (0.02 m)^2[/tex], which simplifies to F = 540 N. Therefore, the answer is option C.
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part a what is the magnitude of the charge on the half of the rod farther from the sphere? activate to select the appropriates template from the following choices. operate up and down arrow for selection and press enter to choose the input value typeactivate to select the appropriates symbol from the following choices. operate up and down arrow for selection and press enter to choose the input value type |q|
To determine the magnitude of the charge on the half of the rod farther from the sphere, we need to consider the principle of conservation of charge.
Since the rod and the sphere are initially neutral, any charge transferred from one to the other must be equal in magnitude but opposite in sign.
Assuming that the sphere acquires a positive charge, an equal amount of negative charge must accumulate on the half of the rod closer to the sphere. By the principle of conservation of charge, an equal amount of positive charge must accumulate on the half of the rod farther from the sphere.
Therefore, the magnitude of the charge on the half of the rod farther from the sphere would be |q|, where |q| represents the magnitude of the charge transferred from the sphere. However, the sign of this charge would be positive to ensure that the net charge on the rod remains neutral.
In summary, the magnitude of the charge on the half of the rod farther from the sphere would be |q|, with a positive sign to conserve the net charge.
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you have been hired to design a family-friendly see-saw. your design will feature a uniform board of mass m and length l that can be moved so that the fulcrum (pivot) is a distance d from the center of the board. this will allow riders to achieve static equilibrium even if they are of different masses, which is typical. you have decided that each rider will be positioned so that his/her center of mass will be a distance xoffset from the end of the board when seated, as shown. a child, seated on the right, has mass m , and an adult, seated on the left, has a mass that is a multiple n of the mass of the child. calculate all torques relative to the position of the fulcrum, and treat counterclockwise toques as positive.
The torque due to the child's weight is nmgx_offset, and the torque due to the adult's weight is -mnmg(x_offset + d), where n is the multiple of the child's mass for the adult rider, m is the mass of the child, g is the acceleration due to gravity, x_offset is the distance of the child's center of mass from the end of the board, and d is the distance of the fulcrum from the center of the board. The total torque is the sum of these two torques.
Mass of the child (m)
Mass of the adult (n * m, where n is the multiple of the child's mass)
Acceleration due to gravity (g)
Distance of the child's center of mass from the end of the board (x_offset)
Distance of the fulcrum from the center of the board (d)
To achieve static equilibrium, the total torque acting on the see-saw must be equal to zero. The torque due to the child's weight is given by nmgx_offset, where n is the multiple of the child's mass for the adult rider, m is the mass of the child, and x_offset is the distance of the child's center of mass from the end of the board.
The negative sign in front of mnmg(x_offset + d) is because the adult is seated on the left side of the fulcrum, causing a clockwise torque. The total torque is the sum of these two torques, which must be equal to zero for static equilibrium.
Mathematically, the torque equation can be written as:
nmgx_offset - mnmg(x_offset + d) = 0
Simplifying, we get:
nmgx_offset - mnmgx_offset - mnmgd = 0
Combining like terms, we obtain:
mnmgd = nmgx_offset
Finally, solving for d, we get:
d = x_offset/n
Therefore, the distance of the fulcrum from the center of the board (d) is equal to the distance of the child's center of mass from the end of the board (x_offset) divided by the multiple of the child's mass for the adult rider (n).
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The first spacecraft which did not merely fly bya jovian (or giant) planet, but actually went into orbit around it for an extended period of time was
a. Galileo
b. Einstein
c. Voyager
d. the Hubble Space Telescope
e. Cassini
Answer:The first spacecraft which did not merely fly by a jovian (or giant) planet, but actually went into orbit around it for an extended period of time was option a, Galileo. The Galileo spacecraft was launched in 1989 and orbited Jupiter for almost eight years, from 1995 to 2003.
Explanation:
Calculate the escape velocity from a white dwarf and a neutron star. Assume that each is 1 solar mass. Let the white dwarf's radius be 10^4 kilometers and the neutron star
The escape velocity from the white dwarf is approximately 4.12 × [tex]10^5[/tex] m/s, and the escape velocity from the neutron star is approximately 2.12 × [tex]10^8[/tex] m/s.
To calculate the escape velocity from a white dwarf and a neutron star, we can use the escape velocity formula:
[tex]v_{escape[/tex] = √(2 * G * M / R)
where [tex]v_{escape[/tex] is the escape velocity,
G is the gravitational constant (approximately 6.674 × [tex]10^{-11} m^3 kg^{-1} s^{-2}[/tex]),
M is the mass of the celestial body (in this case, 1 solar mass, which is approximately 1.989 × [tex]10^{30[/tex] kg), and
R is the radius of the celestial body.
For the white dwarf with a radius of [tex]10^4[/tex] kilometers (or 1 × [tex]10^7[/tex] meters):
[tex]v_{escape[/tex] = √(2 * (6.674 × [tex]10^{-11} m^3 kg^{-1} s^{-2}[/tex]) * (1.989 × [tex]10^{30[/tex] kg) / (1 × [tex]10^7[/tex] m))
[tex]v_{escape[/tex] ≈ 4.12 × [tex]10^5[/tex] m/s
For the neutron star, we need its radius. However, since the radius is not provided in the question, I'll assume a typical value for a neutron star's radius, which is about 10 kilometers (or 1 × [tex]10^4[/tex] meters):
[tex]v_{escape[/tex] = √(2 * (6.674 × [tex]10^{-11} m^3 kg^{-1} s^{-2}[/tex]) * (1.989 × [tex]10^{30[/tex] kg) / (1 × [tex]10^4[/tex] m))
[tex]v_{escape[/tex] ≈ 2.12 × [tex]10^8[/tex] m/s
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While stirring, solid table salt is added to a beaker of water until no more salt will
dissolve and salt crystals are visible at the bottom of the beaker. When the beaker is
heated, the crystals dissolve. The effect of heat in this situation -
A increased the polarity of the salt water
B melted the salt crystals into a liquid
C reacted with salt so it became water
D increased the solubility of the salt crystals
While stirring, solid table salt is added to a beaker of water until no more salt will dissolve and salt crystals are visible at the bottom of the beaker. When the beaker is heated, the crystals dissolve effect of heat in this situation D increased the solubility of the salt crystals
What is solubility?Solubility can be described as the term that is been used in chemistry which express the ability of a substance, known as the solute, to form a solution .
The substance that this solute form a substance with an be regarded as the solvent howevr the solubility of different compound is differnt from each other.
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If the current is 4 Amps and the Wattage produced is 200, how many volts are present?
Answer:
50 volts
Explanation:
Wattage (W) = Current (I) x Voltage (V)
We know the current is 4 Amps and the wattage produced is 200, so we can plug these values into the formula and solve for voltage:
200 = 4 x V
Dividing both sides by 4 gives:
V = 50
Therefore, the voltage present is 50 volts.
wire 1 carries 1.80 a of current north, wire 2 carries 3.80 a of current south, and the two wires are separated by 1.40 m. 1) calculate the magnitude of the force acting on a 1.00-cm section of wire 1 due to wire 2. (express your answer to three significant figures.)
To calculate the force acting on a section of wire 1 due to wire 2, we can use the formula for the magnetic force between two parallel wires: [tex]F = μ₀I₁I₂L/(2πd)[/tex]
where μ₀ is the permeability of free space, [tex]I₁ and I₂[/tex] are the currents in wires 1 and 2, L is the length of the wires, and d is the distance between them.
Plugging in the given values, we get
[tex]F = (4π×10⁻⁷ T·m/A) × (1.80 A) × (3.80 A) × (0.01 m) / (2π×1.40 m) ≈ 3.69×10⁻⁵ N.[/tex]
This means that there is a force of about [tex]3.69×10⁻⁵ N[/tex] acting on a 1.00-cm section of wire 1 due to wire 2.
This force is attractive, since the currents in the two wires are in opposite directions.
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an 8 lb weight attached to a spring exhibits simple harmonic motion. determine the equation of motion if the spring constant is 1 lb/ft and if the weight is released 6 in. below the equilibrium position with a downward velocity of 3 2 ft/s.
Therefore, the equation of motion for the system is: x(t) = 0.5 cos(2.0147 t + 2.103)
The equation of motion for a simple harmonic oscillator is:
x(t) = A * cos(ωt + φ)
x is the displacement from equilibrium at time t, A is the amplitude of the motion, ω is the angular frequency, and φ is the initial phase angle.
The equation of motion for the given system, we need to determine the values of A, ω, and φ.
The amplitude of the motion is the maximum displacement from equilibrium, which occurs when the weight is released. Since the weight is released 6 inches below the equilibrium position, the amplitude is 6 inches, or 0.5 feet.
The angular frequency of the motion is given by:
ω = (k/m)
where k is the spring constant and m is the mass of the weight. Converting the mass from pounds to slugs (since the unit of force in the English system is pounds), we have:
m = 8 lb / 32.174 ft/s = 0.2483 slugs
Therefore, the angular frequency is:
ω = sqrt(1 lb/ft / 0.2483 slugs) = 2.0147 rad/s
To find the initial phase angle, we need to know both the initial displacement and the initial velocity. Since the weight is released 6 inches below the equilibrium position with a downward velocity of 3 2 ft/s, the initial displacement is -0.5 feet and the initial velocity is -3.2 ft/s (since it is downward).
The phase angle can be found using the equation:
φ = arctan(-v0/(ωx0))
where v0 is the initial velocity, x0 is the initial displacement, and arctan is the inverse tangent function. Plugging in the values, we get:
φ = arctan(-(-3.2 ft/s) / (2.0147 rad/s * 0.5 ft)) = 2.103 radians
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What evidence is there that some meteorites originated inside larger objects?
There are several pieces of evidence that suggest that some meteorites originated inside larger objects. First, the chemical composition of certain meteorites is very similar to that of rocks found on the Moon and Mars, indicating that they may have come from these planets.
Additionally, some meteorites contain tiny mineral grains that are only formed under high pressures, suggesting that they were once part of larger bodies such as asteroids. Finally, the presence of gas bubbles in some meteorites indicates that they were once part of a larger body with an atmosphere. All of this evidence supports the idea that some meteorites are fragments of larger objects that have broken apart and fallen to Earth. Evidence suggests that some meteorites originated inside larger objects, such as asteroids or planets, based on their composition and structure.
1. Mineral composition: Meteorites often contain minerals that can only form under high pressure and temperature conditions. These minerals indicate that the meteorites originated within larger objects, where such conditions exist.
2. Isotopic ratios: The isotopic ratios of certain elements in meteorites can be used to trace their origins. Some meteorites have isotopic ratios similar to those found on Earth and other solar system bodies, suggesting they originated from larger objects.
3. Chondrules: Many meteorites contain small, spherical particles called chondrules. These chondrules are thought to have formed during the early stages of the solar system when larger objects were forming from the surrounding dust and gas.
4. Differentiated meteorites: Some meteorites are classified as differentiated, meaning they have distinct layers resulting from a melting and cooling process. This suggests that they originated from larger objects that had enough heat and pressure to cause differentiation.
These pieces of evidence collectively point to the conclusion that some meteorites originated inside larger objects in our solar system.
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A 0.150-kg rubber stopper is attached to the end of a 1.00-m string and is swung in a circle. If the rubber stopper is swung 2.3 m above the ground and released, how far will the stopper travel horizontally before hitting the ground?
The stopper travels approximately 4.5 meters horizontally before hitting the ground.
We can use conservation of energy to solve this problem. At the highest point of the stopper's motion, all of its energy is in the form of potential energy, and at the lowest point (when it hits the ground), all of its energy is in the form of kinetic energy.
The potential energy of the stopper at the highest point is:
Ep = mgh
where m is the mass of the stopper, g is the acceleration due to gravity, and h is the height above the ground. Plugging in the values given in the problem, we get:
Ep = (0.150 kg) * (9.81 m/s²) * (2.3 m) ≈ 3.2 J
At the lowest point, all of the potential energy has been converted to kinetic energy:
Ek = (1/2) * mv²
where v is the speed of the stopper just before it hits the ground. Since the stopper is released from rest, we can use conservation of energy to equate the potential energy at the highest point to the kinetic energy just before hitting the ground:
Ep = Ek
mgh = (1/2) * mv²
Solving for v, we get:
v = √(2gh)
where h is the height from which the stopper was released. Plugging in the values given in the problem, we get:
v = √(2 * 9.81 m/s² * 2.3 m) ≈ 6.6 m/s
Now we can use the time it takes for the stopper to fall to the ground to calculate the horizontal distance it travels. The time is given by:
t = √(2h/g)
Plugging in the values given in the problem, we get:
t = √(2 * 2.3 m / 9.81 m/s²) ≈ 0.68 s
During this time, the stopper travels a horizontal distance given by:
d = vt
Plugging in the values we just calculated, we get:
d = (6.6 m/s) * (0.68 s) ≈ 4.5 m
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A car is travelling at a speed of 31 m/s
the car travels 46m between the driver seeing an emergency and starting to brake
calculate the driver's reaction time
The driver's reaction time is approximately 1.48 seconds.
The distance travelled by the car during the driver's reaction time can be calculated using the formula:
[tex]d=v*t[/tex]
where:
d is the distance travelled
v is the initial velocity
t is the time taken
In this case, the car travels a distance of 46 m before the driver starts to brake. Let's assume that the car maintains its initial speed of 31 m/s during this distance, and the driver's reaction time is denoted by t. Then, the distance travelled by the car during the driver's reaction time is also 46 m. Therefore, we have:
[tex]46m = 31m/s*t[/tex]
Solving for t, we get:
[tex]t=46m/31m/s = 1.48s[/tex]
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1. What is the energy change (in J) associated with an electron in a hydrogen atom moving from energy leveln=3 to n=6?Type answer:2. If a photon has a wavelength of 449.8 nm, what is the energy of the photon (in J)?
1. The energy change associated with the electron moving from n=3 to n=6 is approximately: -6.05 x [tex]10^{-20[/tex] Joules.
2. The energy of the photon with a wavelength of 449.8 nm is approximately: 4.42 x [tex]10^{-19[/tex] Joules.
1. To calculate the energy change (in J) associated with an electron in a hydrogen atom moving from energy level n=3 to n=6, we can use the following formula:
ΔE = -13.6 * ([tex]1/nf^2 - 1/ni^2[/tex]) eV
where ΔE is the energy change,
nf is the final energy level (6), and
ni is the initial energy level (3).
Convert eV to Joules by multiplying by 1.6 x [tex]10^{-19[/tex] J/eV.
ΔE = -13.6 * ([tex]1/6^2 - 1/3^2[/tex]) eV
ΔE = -13.6 * (1/36 - 1/9) eV
ΔE = -13.6 * (0.0278) eV
ΔE = -0.378 eV
ΔE = -0.378 * (1.6 x [tex]10^{-19[/tex]) J
ΔE ≈ -6.05 x [tex]10^{-20[/tex] J
2. To find the energy of a photon with a wavelength of 449.8 nm, we can use the equation:
E = (hc) / λ
where E is the energy of the photon,
h is Planck's constant (6.63 x [tex]10^{-34[/tex] Js),
c is the speed of light (3 x [tex]10^8[/tex] m/s), and
λ is the wavelength (449.8 nm, converted to meters: 449.8 x [tex]10^{-9[/tex] m).
E = (6.63 x [tex]10^{-34[/tex] Js)(3 x [tex]10^8[/tex] m/s) / (449.8 x [tex]10^{-9[/tex] m)
E ≈ 4.42 x [tex]10^{-19[/tex] J
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What feature of molecular orbital theory is responsible for bond formation?
Molecular Orbital Theory (MOT) is a key concept in understanding chemical bonding, and it explains the formation of bonds through the interaction of atomic orbitals. The essential feature of MOT responsible for bond formation is the concept of constructive and destructive interference between the overlapping atomic orbitals.
When two atoms approach each other, their atomic orbitals overlap and combine to form molecular orbitals. These molecular orbitals can be bonding or antibonding, depending on the nature of their interaction. Constructive interference occurs when the wave functions of the atomic orbitals combine in-phase, resulting in a lower energy molecular orbital with electron density concentrated between the nuclei. This increased electron density strengthens the electrostatic attraction between the positively charged nuclei and the negatively charged electrons, forming a stable chemical bond.
On the other hand, destructive interference occurs when the wave functions of the atomic orbitals combine out-of-phase, leading to the formation of a higher energy antibonding molecular orbital. In this case, electron density is reduced between the nuclei, creating a node that weakens the electrostatic attraction and destabilizes the bond. Electrons in antibonding orbitals can counteract the bonding effect of electrons in bonding orbitals.
Bond order, a measure of bond strength, is determined by the difference between the number of electrons in bonding and antibonding orbitals. A positive bond order signifies a stable bond, while a zero or negative bond order indicates that the bond is not formed or is weak.
In summary, the formation of molecular orbitals through constructive and destructive interference between atomic orbitals is the key feature of MOT responsible for bond formation. Bonding orbitals result in stable chemical bonds, while antibonding orbitals can weaken or prevent bonds from forming.
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use the impulse-momentum theorem to find how long a stone falling straight down takes to increase its speed from 5.8 m/s m / s to 9.70 m/s m / s .
It takes the stone roughly 0.397 seconds to get from moving at 5.8 m/s to 9.70 m/s.
What is impulse?In physics, the term "impulse" is used to characterise or measure the impact of force operating gradually to alter an object's motion. It is commonly stated in Newton seconds or kg m/s and is denoted by the sign J.
The impulse-momentum theorem relates the impulse of a force to the change in momentum of an object. It can be written as:
impulse = change in momentum
In this problem, a stone is falling straight down under the influence of gravity. The force of gravity is the only force acting on the stone, so the impulse it experiences is equal to the change in its momentum. We can write this as:
J = Δp
where J is the impulse, and Δp is the change in momentum.
The momentum of an object can be expressed as:
p = m * v
where p is momentum, m is the mass of the object, and v is its velocity.
Therefore, the change in momentum of the stone as it falls from a velocity of 5.8 m/s to 9.70 m/s can be written as:
Δp = m * (9.70 m/s) - m * (5.8 m/s) = m * (9.70 m/s - 5.8 m/s) = 3.9 * m * kg/s
The impulse experienced by the stone is equal to this change in momentum. The impulse can also be expressed as the product of force and time:
J = F * Δt
where F is the force acting on the stone (in this case, the force of gravity), and Δt is the time for which the force acts.
We can rearrange this equation to solve for the time:
Δt = J / F
Substituting the values we have calculated, we get:
Δt = Δp / F = (3.9 * m * kg/s) / (m * g) = 3.9 s/g
where g is the acceleration due to gravity (approximately 9.81 m/s^2).
Therefore, the time for the stone to increase its speed from 5.8 m/s to 9.70 m/s is approximately 0.397 seconds.
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A uniform rod BC of mass 4 kg is connected to a collar A by a 250-mm cord AB. Neglecting the mass of the collar and cord, determine (a) the smallest constant acceleration aA for which the cord and the rod lie in a straight line, (b) the corresponding tension in the cord.
(a) The smallest constant acceleration aA for which the cord and the rod lie in a straight line is -2.4275 [tex]m/s^2[/tex].
(b) The corresponding tension in the cord is 19.65 N.
To solve this problem, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration.
(a) Let's start by considering the motion of the collar A. The tension in the cord pulls the collar towards the right, and the weight of the rod pulls it downwards. The acceleration of the collar, aA, is also the acceleration of the rod, since they are connected by the cord.
Using Newton's second law, we can write the equation:
maA = T - mg
where m is the mass of the rod, g is the acceleration due to gravity, T is the tension in the cord, and we have taken upwards as positive.
Since we want the cord and the rod to lie in a straight line, we can assume that the angle between the cord and the vertical is very small, and thus we can approximate sin(theta) = theta. This allows us to relate the tension T to the distance AB:
T = kAB
where k is a constant that depends on the angle between the cord and the vertical, but we can approximate it as 1.
Substituting this into the equation above, we get:
maA = AB - mg
Solving for aA, we get:
aA = (AB - mg)/m
Substituting the given values, we get:
aA = (0.25 - 4*9.81)/4 = -2.4275 [tex]m/s^2[/tex]
Note that the negative sign means that the collar and rod will move to the left.
(b) To find the tension in the cord, we can use the equation T = maA + mg. Substituting the values we get:
T = 4*(-2.4275) + 4*9.81 = 19.65 N
Therefore, the corresponding tension in the cord is 19.65 N.
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If the resitance of 0.17 Ohms was measured across the given length of a conductive material, what is the resistivity?
Diameter is 10cm
Lenght is 1 meter
A) 0.25Ohm cm
B) 2.25Ohm cm
C) 0.13345 Ohm cm
D) 0.29 Ohm cm
E) 0.54 Ohm cm
The resistivity of the conductive material can be calculated using the formula: Resistivity = Resistance x (pi x diameter^2)/4 x Length. The resistivity of the conductive material is C) 0.13345 Ohm cm.
Resistance (R) = 0.17 Ohms
Diameter (d) = 10 cm = 0.1 m
Length (l) = 1 m
Using the formula,
Resistivity (p) = R x (pi x d^2)/4 x l
Substituting the values,
p = 0.17 x (pi x 0.1^2)/4 x 1
p = 0.13345 Ohm cm
Therefore, the resistivity of the given conductive material is 0.13345 Ohm cm.
Note: The resistivity of a material is a measure of its ability to resist the flow of electric current through it. It is an intrinsic property of the material and depends on factors such as the type of material, temperature, and impurities present in the material.
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A 2.0 kg object is moving to the right in the positive x direction with a speed of 1.4 m/s.
Object experiences the force shown in (Figure 1). What is the object's speed after the force ends?
Figure 1
The plot shows the horizontal component of the force applied to the object in newtons as a function of time in seconds. The magnitude stays at value 0 newtons from 0 seconds for a while, then jumps to 2 newtons and stays at this value for one half of asecond. At the end of this time, it drops back to 0 newtons and stays at this value.
The object's speed after the force ends is 1.5 m/s.
Velocity is a vector quantity that describes the rate and direction of an object's motion. It is defined as the displacement of an object per unit of time and in a specific direction.
To find the object's speed after the force ends, we need to use the force to calculate the object's acceleration, and then use the acceleration to calculate the object's final velocity.
The force-time plot in Figure 1 can be broken down into three parts:
1. The force is 0 N from 0 to 1 s.
2. The force is 2 N from 1 to 1.5 s.
3. The force is 0 N from 1.5 s onwards.
Using Newton's second law (F=ma), we can calculate the object's acceleration during each of these time intervals:
1. For the first time interval (0 to 1 s), the force is 0 N, so the acceleration is also 0 m/s^2.
2. For the second time interval (1 to 1.5 s), the force is 2 N and the mass of the object is 2.0 kg, so the acceleration is:
a = F/m = 2 N / 2.0 kg = 1 m/s^2
3. For the third time interval (1.5 s onwards), the force is 0 N, so the acceleration is also 0 m/s^2.
To find the object's speed after the force ends, we can use the following kinematic equation:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
We can assume that the displacement of the object during the time intervals in Figure 1 is negligible, since the force is applied horizontally and the object is already moving horizontally. Therefore, we can ignore the displacement term in the equation.
For the first time interval (0 to 1 s), the object's initial velocity is 1.4 m/s, so we can calculate the final velocity after 1 second as:
v^2 = u^2 + 2as = (1.4 m/s)^2 + 2(0 m/s^2)(1 s) = 1.96 m^2/s^2
v = sqrt(1.96 m^2/s^2) = 1.4 m/s
For the second time interval (1 to 1.5 s), the object's initial velocity is 1.4 m/s, and the acceleration is 1 m/s^2. We can calculate the final velocity after 0.5 seconds as:
v^2 = u^2 + 2as = (1.4 m/s)^2 + 2(1 m/s^2)(0.5 s) = 2.2 m^2/s^2
v = sqrt(2.2 m^2/s^2) = 1.5 m/s
For the third time interval (1.5 s onwards), the object's final velocity is the same as its velocity at the end of the second time interval (1.5 m/s), since there is no further acceleration.
Therefore, the object's speed after the force ends is 1.5 m/s.
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You want your mulitmeter to have high or low resistance?
A) high
B) low
Answer:the answer is A) high.
Explanation:If you want to measure voltage or current without affecting the circuit or device being tested, you should use a multimeter with high input impedance or high resistance.
A two-dimensional, conservative force is zero on the x– and y-axes, and satisfies the condition (dFx/dy) = (dFy/dx) = (4N/m3
)xy. What is the magnitude of the force at the point x = y = 1m?
The magnitude of the force at (1,1) is F = sqrt[tex]((2N/m)^2 + (2N/m)^2)[/tex] = 2.828N/m. To find the magnitude of the force at the point x=y=1m, we can use the formula for the magnitude of a 2D force: F = sqrt([tex]Fx^2 + Fy^2[/tex]).
Since the force is conservative, we can find its potential energy function by integrating: U(x,y) = ∫Fx dx + ∫Fy dy.
From the given condition, we know that (dFx/dy) = (dFy/dx) = (4N/m3)xy.
Integrating this gives us Fx = 2N/m *[tex]x^2 * y^2[/tex] and Fy = 2N/m * [tex]x^2 * y^2.[/tex] Substituting x=y=1m, we get Fx = Fy = 2N/m.
This means that the force is pulling with a strength of 2.828N/m at a 45-degree angle from both the x and y axes.
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the critical angle for a ray incident in material x at the boundary of material x and material y is found to be 59.0 degrees. if the index of refraction for material y is 1.07, what is the index of refraction of material x, given that light is going from material y to x and x has a higher refractive index?
The index of refraction for material x is approximately 1.205, given the critical angle and[tex]n_y[/tex] = 1.07.
The critical angle, θ_c, is the angle of incidence at which the refracted ray in material y is at the boundary with material x. It is related to the refractive indices of the two materials by the equation:
sin(θ_c) = [tex]n_y[/tex] / [tex]n_x[/tex]
where [tex]n_y[/tex] and [tex]n_x[/tex] are the refractive indices of materials y and x, respectively. We are given that the critical angle is 59.0 degrees and the index of refraction for material y is 1.07. Rearranging the equation, we can solve for [tex]n_x[/tex]:
[tex]n_x[/tex] = [tex]n_y[/tex] / sin(θ_c)
Plugging in the given values, we have:
[tex]n_x[/tex] = 1.07 / sin(59.0°)
Using a calculator, we find:
[tex]n_x[/tex] ≈ 1.205
Therefore, the index of refraction for material x is approximately 1.205, given that light is going from material y to x, and x has a higher refractive index.
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PART OF WRITTEN EXAMINATION:
are naturally-occurring dynamic stray currents that
are caused by disturbances in the earth's magnetic field by sun spot activity.
A) telluric currents
B) dynmaic stray currents
C) steady state stray currents
The answer to your question is A) telluric currents. Telluric currents are naturally-occurring electric currents that flow within the Earth's crust and upper mantle.
These currents are caused by the interaction between the Earth's magnetic field and the ionosphere, which is the layer of the Earth's atmosphere that is ionized by the sun's radiation. Sun spot activity can cause disturbances in the Earth's magnetic field, which can in turn affect the strength and direction of telluric currents.It is important to note that while telluric currents are caused by the interaction between the Earth's magnetic field and the sun's radiation, they are not the same thing as magnetic fields or magnetic currents. Magnetic fields are a fundamental force in nature that are generated by the motion of charged particles, while magnetic currents refer to the flow of electric charge within a magnetic field.Overall, the study of telluric currents is an important field of research that has many practical applications, such as in the exploration for mineral resources and the detection of underground structures. By understanding the complex interplay between the Earth's magnetic field and the sun's radiation, scientists can gain valuable insights into the inner workings of our planet and the forces that shape it.
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