A vehicle is going at 21 m/s when the driver abruptly slams on the brakes locking the wheels. The tires and the road's kinetic friction coefficients are both 0.72. It takes the car 2.76 seconds to come to a stop.
When a car is moving and the driver slams on the brakes, the kinetic friction between the tires and the road will cause the car to decelerate. The force of friction can be calculated using the equation:
f_k = μ_k × N
where f_k is the force of kinetic friction, μ_k is the coefficient of kinetic friction, and N is the normal force (equal to the weight of the car) acting on the car.
The force of friction is equal and opposite to the force applied by the brakes, so we can write:
f_k = ma
where m is the mass of the car and a is its acceleration.
Combining these equations and solving for a, we get:
a = -μ_k × g
where g is the acceleration due to gravity (9.81 m/s^2) and the negative sign indicates that the car is decelerating.
The time it takes for the car to come to a stop can be found using the equation:
v = u + at
where v is the final velocity (zero in this case), u is the initial velocity (21 m/s), a is the acceleration (-μ_k × g), and t is the time.
Substituting the given values, we get:
0 = 21 m/s + (-μ_k × g) × t
Solving for t, we get:
t = -21 m/s / (-μ_k × g)
= 2.76 s
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Select the correct term to complete the sentences. fluorescence translucent object
RGB color model
visible light index of refraction nanometer white light rod cell
transparent
pixel
color
cone cell
converging lens
prism
specular reflection electromagnetic spectrum
CMYK incandescence photon diffuse reflection electromagnetic wave diverging lens photoreceptor lens mirror
Section 25.1
1. contains an equal mix of all colors.
2. You can use light produced by to heat food.
3. Atoms produce light by
4. A(n) travels at the speed of light.
5. A light wave at 500 THz is the orange.
6. You see all the colors of when you see a rainbow.
7. Light wavelengths are measured in _(s).
8. Ultraviolet light and microwaves are part of the
9. A(n) is the smallest possible amount of light.
Section 25.2
10. A(n) specializes in detecting color.
11. A(n) specializes in detecting light intensity.
12. The human eye has about 137 million _
13. An HDTV screen has more_than an ordinary TV screen.
14. Magenta is a pigment used in the color model.
15. The is used by video cameras to achieve a range
of colors.
Section 25.3
16. A surface with
produces a single beam of reflected light rays.
17. occurs when light enters a material and bends.
18. Three examples of optical devices are…. And….
19. Glass is a(n) material because light passes through it without scattering.
20. materials allow light to pass but scatter it in all directions.
21. The of water is 1.33.
22. Surfaces that scatter light when it reflects have
23. A(n) … bends light rays inward toward the focal point.
24. A(n) ….bends light rays outward away from the
focal point.
Section 25.1: 1.) white light, 2.)incandescence, 3.) emitting photons , 4.) photon, 5.) orange, 6.) visible light, 7.) nanometers, 8.) electromagnetic spectrum, 9.) photon
What is rod cells?Rods are the type of photoreceptor cell in retina and are sensitive to light levels and help give us good vision in low light.
Section 25.2
10. Cone cell specializes in detecting color.
11. Rod cell specializes in detecting light intensity
12. Human eye has 137 million : photoreceptors.
13. An HDTV screen has more than an ordinary TV screen : pixels
14. Magenta is a pigment used in the color model : CMYK
15. The is used by video cameras to achieve a range of colors : RGB color model
Section 25.3
16. A surface with produces a single beam of reflected light rays : specular reflection
17. occurs when light enters a material and bends : Refraction
18. Three examples of optical devices are converging lens, diverging lens and prism.
19. Glass is transparent material because light passes through it without scattering.
20. Materials that allow light to pass but scatter it in all directions : translucent
21. The index of refraction of water is 1.33
22. Surfaces that scatter light when it reflects have : rough surfaces
23. Converging lens bends light rays inward toward the focal point
24. Diverging lens bends light rays outward away from the focal point.
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a mass on a 500 n/m spring is submersed in a liquid. it is pulled down 4 cm from the equilibrium position and released. after ten seconds, the amplitude has been dampened to 3 cm. how much energy did the liquid gain during those ten seconds, in j?
The liquid gained 0.175 J of energy during the ten-second period.
The initial potential energy of the spring-mass system is:
U = [tex](1/2)kx^2 = (1/2)(500 N/m)(0.04 m)^2 = 0.4 J[/tex]
The amplitude of the oscillation decreases from 4 cm to 3 cm over 10 seconds, so the damping constant is:
b = ln(4/3)/(10 s) ≈ 0.0337 s^-1
The general equation for the motion of a damped harmonic oscillator is:
x(t) = A exp(-bt/2m) cos(ωt + φ)
The angular frequency is related to the spring constant and mass by:
ω = [tex]\sqrt{(k/m)[/tex]
A(t) = A exp(-bt/2m)
After 10 seconds, the amplitude has decreased from 4 cm to 3 cm, so:
3 cm = A exp(-b(10 s)/(2m))
Dividing by the initial amplitude, we get:
0.75 = exp(-b(10 s)/(2m))
Taking the log of each aspects, we get:
ln(0.75) = -b(10 s)/(2m)
Solving for the mass, we get:
m = -b(10 s)/(2 ln(0.75)) ≈ 0.25 kg
The very last capability strength of the machine is:
U' = [tex](1/2)kx'^2 = (1/2)(500 N/m)(0.03 m)^2 = 0.225 J[/tex]
The energy lost due to damping is:
ΔE = U - U' = 0.4 J - 0.225 J = 0.175 J
Energy is essential for all forms of life and for many human activities, such as transportation, heating and cooling buildings, and producing electricity. However, the use of energy also has environmental and social impacts, including greenhouse gas emissions and resource depletion. The development and use of renewable energy sources, such as solar and wind power, is increasingly important for reducing these impacts and ensuring a sustainable energy future.
Thermal energy is the energy that comes from heat, while kinetic energy is the energy of motion. Potential energy is stored energy that can be converted into kinetic energy, such as a ball held up high before being dropped. Chemical energy is the energy stored in the bonds between atoms and molecules, while electromagnetic energy is energy that travels in waves, such as light or radio waves.
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you are working as an electrician installing fluorescent lights. you notice that the lights were made in europe and that the ballasts are rated for operation on a 50-hz system. will these ballasts be harmed by overcurrent if they are connected to 60 hz? if there is a problem with these lights, what will be the most likely cause of the trouble?
The solution would be to either replace the ballasts with ones designed for a 60-hz system or to use lights that are designed to operate on a 60-hz system.
When answering questions on Brainly, it is important to always be factually accurate, professional, and friendly. Answers should be concise and relevant to the question being asked. Typos and irrelevant parts of the question should be ignored.
Here is the answer to the student question:If you are an electrician installing fluorescent lights and notice that the lights were made in Europe and the ballasts are rated for operation on a 50-hz system, they will not be harmed by overcurrent if they are connected to a 60 hz system.
However, there may be a problem with these lights because they are designed to operate on a 50-hz system and not a 60-hz system. This could cause the lights to flicker, not turn on, or burn out prematurely.The most likely cause of the problem is that the ballasts are not designed to operate on a 60-hz system.
The solution would be to either use lights made to work on a 60 hz system or replace the ballasts with ones made for a 60 hz system.
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Which of the following is the formula for Electric Charge?
The formula for Electric Charge is (Q = I ∙ t) I is the electric current and t is time
What is Electric Charge?Electric charge is a fundamental property of matter that describes the amount of electric force that a particle can exert on other charged particles. It is a property of particles, such as electrons and protons, that gives rise to the electromagnetic force, which is one of the four fundamental forces in nature.
Electric charge can be positive or negative, and particles with the same charge repel each other, while particles with opposite charges attract each other. The unit of electric charge is the Coulomb (C), and it is measured using an instrument called an electrometer.
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characteristic best describes the inner planets? responses made of gases such as hydrogen and helium made of gases such as hydrogen and helium fast rotations fast rotations made of rocks and metals made of rocks and metals lots of moons lots of moons
In terms of the characteristics that best describe the inner planets, it is important to note that the inner planets (Mercury, Venus, Earth, and Mars) are those that orbit closest to the Sun.
As a result, these planets are generally characterized by several shared features, including that they are made of rocks and metals rather than gases such as hydrogen and helium, and they also have relatively fast rotations compared to other planets in the solar system.
The inner planets are also generally smaller and less massive than the outer planets, and they have fewer moons (or, in the case of Mercury, no moons). Additionally, the inner planets are much hotter than the outer planets due to their proximity to the Sun, which results in high temperatures that make it difficult for life to survive on these planets.
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a cart with mass 390 g moving on a frictionless linear air track at an initial speed of 1.6 m/s undergoes an elastic collision with an initially stationary cart of unknown mass. after the collision, the first cart continues in its original direction at 1.0 m/s. (a) what is the mass of the second cart? (b) what is its speed after impact? (c) what is the speed of the two-cart center of mass?
Let m1 = 390 g be the mass of the first cart and m2 be the mass of the second cart. Since the collision is elastic, linear momentum is conserved.
Using the equation:m1v1i + m2v2i = m1v1f + m2v2fwhere v1i = 1.6 m/s, v1f = 1.0 m/s, and v2f = 0 (since the second cart is initially stationary), we get:m2 = (m1v1i - m1v1f) / v2i m2 = 390 × (1.6 - 1.0) / 0 m2 = 624 g The mass of the second cart is 624 g.(b) Using the same equation as in (a), we can solve for v2i:v2i = (m1v1i - m1v1f) / m2 v2i = (390 × 1.6 - 390 × 1.0) / 624 v2i = 0.429 m/sThe speed of the second cart after impact is 0.429 m/s.(c) The total momentum of the system is conserved in an elastic collision, so the velocity of the centre of mass (CM) of the two carts does not change. Therefore, the speed of the two-cart centre of mass is the same before and after the collision. We can use the formula:vCM = (m1v1 + m2v2) / (m1 + m2)where v1 = 1.6 m/s, v2 = 0.429 m/s, m1 = 390 g, and m2 = 624 g. The speed of the two-cart center of mass is:vCM = (390 × 1.6 + 624 × 0.429) / (390 + 624) vCM = 1.17 m/sThe speed of the two-cart center of mass is 1.17 m/s.
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a 60 g g ball of clay traveling at speed 6.5 m/s m / s hits and sticks to a 1.0 kg k g block sitting at rest on a frictionless surface. what is the speed of the block after the collision?
A 60 g ball of clay traveling at speed 6.5 m/s m / s hits and sticks to a 1.0 kg k g block sitting at rest on a frictionless surface. The speed of the block after the collision is approximately 0.368 m/s.
After the collision, the speed of the block can be found using the conservation of momentum principle.
The initial momentum of the system is equal to the final momentum of the system.
Initial momentum = (mass of clay * velocity of clay) + (mass of block * velocity of block)
Final momentum = (mass of clay + mass of block) * final velocity
60 g = 0.06 kg (convert to kg)
1.0 kg block is at rest, so its initial velocity = 0 m/s.
Initial momentum = (0.06 kg * 6.5 m/s) + (1.0 kg * 0 m/s) = 0.39 kg m/s
Final momentum = (0.06 kg + 1.0 kg) * final velocity
Since, Initial momentum = Final momentum, we have
0.39 kg m/s = (1.06 kg) * final velocity
Final velocity = 0.39 kg m/s / 1.06 kg
Final velocity ≈ 0.368 m/s
The speed of the block after the collision is approximately 0.368 m/s.
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which of the following statements concerning this collision are correct? a. both vehicles are acted upon by the same average force during the collision. b. the small car is acted upon by a greater average force than the suv. c. the small car undergoes a greater change in momentum than the suv. d. both vehicles undergo the same change in momentum. which of the following statements concerning this collision are correct? a. both vehicles are acted upon by the same average force during the collision. b. the small car is acted upon by a greater average force than the suv. c. the small car undergoes a greater change in momentum than the suv. d. both vehicles undergo the same change in momentum. a a, d b, c b, d
The correct statements concerning this collision are:
Both vehicles are acted upon by the same average force during the collision.The small car undergoes a greater change in momentum than the SUV. Options A and C are correctIn a collision between two objects, the total momentum of the system is conserved. This means that the total momentum before the collision is equal to the total momentum after the collision. However, the kinetic energy of the system may not be conserved, as some of it may be lost to other forms of energy, such as heat, sound, or deformation of the objects involved.
When two vehicles collide, the total momentum of the system is conserved, but the kinetic energy of the system is not necessarily conserved. During the collision, both vehicles experience an equal and opposite average force, as required by Newton's Third Law of Motion. However, the change in momentum experienced by each vehicle depends on its mass and velocity before and after the collision. The small car will experience a greater change in momentum than the SUV because it has a smaller mass. Options A and C are correct
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A container holds a gas consisting of 9.75 moles of oxygen molecules. One in a million of these molecules has lost a single electron. NA=6.022×10^23mol−1, e=1.60×10^−19C
The oxygen molecules have lost a total of 0.94 coulombs in charge of their electrons.
How did Avogadro's number, 6.022 x 1023, come to be?AVOGADO'S CALL SIGN-
Amadeo Avogadro (1776–1856), an Italian chemist, stated the principle in 1811 that equivalent volumes of gases under the same temperature and stress contain an equal range of molecules regardless of the molecules' chemical make-up and physical characteristics. It is 6.023 x 1023, or Avogadro's number.
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9. Which of the following is true about insulators?
A) Insulators have very tightly bound valance electrons.
B) Insulators do not allow electricity to flow through it easily.
C) ceramic and glass are examples of good insulators.
D) All of the above
how often should a fire detection and alarm system backup electrical generator be run under load? answer
When it comes to the frequency with which a fire detection and alarm system backup electrical generator should be run under load, it is recommended that it be run under load at least once a month.
A fire detection and alarm system is a collection of systems that work together to detect and alert occupants to the presence of fire through audio and visual signals.
In addition to being a component of a building's life safety system, fire detection and alarm systems are also utilized to activate fire suppression systems, elevators, and other safety features. Intended to notify emergency services in the event of an alarm, allowing for prompt evacuation and the implementation of any necessary emergency response procedures.When it comes to the detection of fire, fire detection, and alarm systems utilize a variety of technologies, including photoelectric detectors, ionization detectors, and thermal detectors, to detect the presence of fire. Furthermore, once the alarm has been triggered, the system is designed to notify emergency services so that they can respond as quickly as possible to the scene of the fire.Therefore, it is advisable to operate the backup electrical generator of a fire detection and alarm system under load at least once per month.
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a scientist on earth drops a hammer and a feather at the same time an astronaut on the moon drops a hammer and a feather. which result is expected?
The answer depends if air resistance is ignored. If ignored, the feather and hammer on moon and earth will reach the ground at the same time with respect to their gravitational force (earth > moon)
If air resistance is not ignored, the hammer will reach the ground first on both earth and moon
When a scientist on Earth drops a hammer and a feather at the same time, the expected result is that the hammer would hit the ground first.
When an astronaut on the moon drops a hammer and a feather at the same time, they would hit the ground at the same time. This is because the gravitational pull on the moon is weaker than that on Earth, so objects fall at the same rate regardless of their mass.
What is gravity?Gravity is the force that exists between any two masses, any two bodies, any two particles. It is an attraction force that always exists between objects, and the magnitude of the force depends on the masses of the objects and the distance between them. On the surface of the earth, gravity acts to pull all objects towards the center of the earth, resulting in weight of objects on the surface of the earth.
What is free fall?Free fall refers to the motion of an object falling under the influence of gravity. When an object is dropped from a certain height, it will fall at an accelerating rate towards the ground, until it hits the ground. Objects fall at the same rate regardless of their mass.
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6. a 60 kw pump is used to pump up water from a mine that is 40 m deep. find the mass of water that can be lifted by the pump in 1.2 min.
We can substitute all the values in the formula for mass of water lifted:mass of water lifted = power x time / work done against gravity x efficiency= 60 x 72 / (1232.56r²) x 0.8= 26.25/r² kgAnswer: mass of water lifted = 26.25/r² kg.
To find the mass of water that can be lifted by a 60 kW pump in 1.2 minutes from a mine that is 40 m deep, we use the following formula:mass of water lifted = power x time / work done against gravity x efficiencyWe know that the power of the pump is 60 kW, the depth of the mine is 40 m, and the time taken is 1.2 minutes or 72 seconds. The efficiency of the pump is not given, so we assume it to be 80%.Now, we need to find the work done against gravity. The work done against gravity is equal to the weight of the water lifted. The weight of water is given by the formula:weight of water = mass x gravitywhere gravity is 9.8 m/s²Substituting the values, we get:weight of water = volume of water x density x gravitySince we are not given the density of water, we assume it to be 1000 kg/m³.Substituting the values, we get:work done against gravity = weight of water x depth of mine= volume of water x density x gravity x depth of mine= πr² x h x 1000 x 9.8 x 40= 1232.56r²Now, we can substitute all the values in the formula for mass of water lifted:mass of water lifted = power x time / work done against gravity x efficiency= 60 x 72 / (1232.56r²) x 0.8= 26.25/r² kg.
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car is travelling on a straight level section of a highway through a small town at a constant speed of 108 km/h. the absented-minded driver misses the posted speed limit sign. a police car that is stopped next to the sign accelerates 7.5 m/s 2 from rest 5.0 s after the speeding car has passed (c) [4 marks] what is the speed of the police car when it catches up to the speeder?
The speed of the police car when it catches up to the speeder is 37.5 m/s.
How to determine speed?
To solve the problem, we can use the following kinematic equation:
v = u + at
where:
v = final velocity (unknown)
u = initial velocity of the police car (0 m/s)
a = acceleration of the police car (7.5 m/s²)
t = time elapsed after the police car starts accelerating (5.0 s)
We can also convert the speed of the car from km/h to m/s:
108 km/h = (108 km/h) x (1000 m/km) x (1 h/3600 s) = 30 m/s
Now we can substitute the values into the equation:
v = 0 + (7.5 m/s²) x (5.0 s)
v = 37.5 m/s
Therefore, the speed of the police car when it catches up to the speeder is 37.5 m/s.
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an air-filled parallel-plate capacitor has a capacitance of 4.0 pf. the separation of the plates is doubled and wax is inserted between them. the new capacitance is 8.0 pf. find the dielectric constant of the wax.
The capacitance of an air-filled parallel-plate capacitor is 4.0 pf. Wax is placed between the pieces as they are double separated. The dielectric constant of the wax is approximately 0.903.
The capacitance of an air-filled parallel-plate capacitor is given by:
C = ε0 × A / d
where C is the capacitance, ε0 is the permittivity of free space, A is the area of the plates, and d is the distance between the plates.
Given that the initial capacitance of the capacitor is 4.0 pF, we can rearrange the equation to solve for the initial plate separation:
d = ε0 × A / C1
where C1 is the initial capacitance. Substituting the given values, we have:
d = (8.85 x 10^-12 F/m) × A / 4.0 pF
= 2A × 10^-3 m
Next, we are told that the plate separation is doubled and wax is inserted between the plates, resulting in a new capacitance of 8.0 pF. We can use the same equation to find the new plate separation:
d' = ε0 × A / C2
where C2 is the new capacitance. Substituting the given values, we have:
d' = (8.85 × 10^-12 F/m) × A / 8.0 pF
= A × 10^-3 m
To find the dielectric constant of the wax, we can use the formula:
C2 = εr × ε0 × A / d'
where εr is the relative permittivity (dielectric constant) of the wax. Substituting the values we have calculated, we get:
8.0 pF = εr × (8.85 × 10^-12 F/m) × A / (A × 10^-3 m)
Simplifying, we get:
εr = 8.0 / 8.85 = 0.903
It's worth noting that this calculation assumes that the area of the plates remains constant when the wax is inserted. In practice, the insertion of the wax may affect the plate geometry, which could affect the capacitance. Additionally, the dielectric constant of the wax may depend on factors such as temperature and frequency.
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To create artificial gravity, the space station shown in the drawing is rotating at a rate of 1.5 rpm. The radii of the cylindrically shaped chambers have the ratio rA/rB = 5.05. Each chamber A simulates an acceleration due to gravity of 6.7 m/s2.
(a) Find rA.
(b) Find rB.
(c) Find the acceleration due to gravity that is simulated in chamber B.
rA is equal to 23.15 metres, rB is equal to 4.58 metres, and the gravity simulation acceleration in chamber B is 0.11 m/s².
One approach to make a space station feel like it has artificial gravity is to spin it?Applying a force to an astronaut that results in an acceleration of 9.8 metres per second, or 32 feet per second, is the only known way to create artificial gravity. Bungee cords, body restraints, or a fast enough spin of the spaceship to generate sufficient centrifugal acceleration can all be used to accomplish this.
6.7 = rA(0.1571)²
Solving for rA, we get:
rA = 23.15 meters
23.15/rB = 5.05
Solving for rB, we get:
rB = 4.58 meters
a = rBω²
Substituting the values we just found, we get:
a = (4.58)(0.1571)²
Solving for a, we get:
a = 0.11 m/s²
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a 0.800-kg copper rod rests on two horizontal rails 0.500 m apart and carries a current of 53.0 a from one rail to the other. the coefficient of static friction between rod and rails is 0.330. what is the magnitude and direction of the smallest magnetic field that puts the rod on the verge of sliding? give the direction relative to the vertical. magnitude: direction:
The magnitude of the smallest magnetic field that puts the rod on the verge of sliding is 0.0559 T.
The force required to overcome the static friction between the copper rod and the rails is given by:
fs = μs * N
where μs is the coefficient of static friction, N is the normal force, and fs is the force required to overcome static friction.
In this case, the normal force is equal to the weight of the rod, which is given by:
N = mg
where m is the mass of the rod and g is the acceleration due to gravity.
The magnetic force on the rod is given by:
Fm = BIL
where B is the magnetic field strength, I is the current in the rod, and L is the length of the rod.
For the rod to be on the verge of sliding, the magnetic force must be equal to the force required to overcome static friction:
Fm = fs
Substituting the given values and solving for B, we get:
B = fs / IL
B = μs × N / IL
B = μs × mg / IL
B = (0.330) × (0.800 kg) × (9.81 m/s^2) / (0.500 m × 53.0 A)
B = 0.0559 T
The direction of the magnetic field relative to the vertical is perpendicular to the plane of the rails and into the page, because the direction of the magnetic force is perpendicular to both the direction of the magnetic field and the direction of the current, as determined by the right-hand rule.
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if two objects each carrying a charge of 1 coulomb were placed 1 meter apart, how much force would they exert on each other? group of answer choices 106 n 9 n zero 1 n 9 x 109 n
Answer:
F = 9×10⁹ N
Explanation:
Coulomb's Law, k = 8.98755×10⁹Nm²/C² , q₁ = 1C , q₂ = 1C, r = 1m[tex]F=k\frac{q_1q_2}{r^2} \\\\F=(8.98755*10^9 Nm^2/C^2)*\frac{(1C)(1C)}{(1m)^2} \\\F = 9*10^9 N[/tex]
The force between the two objects is approximately [tex]9 * 10^9[/tex] N. So, the last option is accurate
Coulomb's law is an important principle in physics. It states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
To find the force between two charged objects, we can use Coulomb's Law, which states:
[tex]F =k *\frac{ (q1 * q2)}{r^2}[/tex]
Where F is the force, k is Coulomb's constant ([tex]8.99 * 10^9 N m^2/C^2[/tex]), q₁ and q₂ are the charges of the objects, and r is the distance between them. In this case, q₁ = q₂ = 1 C (coulomb) and r = 1 m (meter). Plugging these values into the equation:
[tex]F = \frac{(8.99 * 10^9) * (1 * 1) }{ (1)^2}[/tex]
[tex]F = 8.99 * 10^9 N[/tex].
The force is attractive when the charges are opposite (one negative and one positive), and the force is repulsive when the charges are the same (both negative or both positive).
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moment of inertia of an object does not depend on a. angular velocity b. mass distribution
Answer:
Explanation:
The moment of inertia of an object is a property that describes its resistance to rotational motion.
It is determined solely by the mass distribution of the object and the geometry of its shape, and it does not depend on the angular velocity of the object.
This can be seen from the formula for the moment of inertia, which is given by:I = ∫ r^2 dmwhere I is the moment of inertia, r is the distance from the axis of rotation to the mass element dm, and the integral is taken over the entire mass distribution of the object.
The moment of inertia depends only on the mass distribution of the object and how that mass is distributed around the axis of rotation.
This means that even if the object is rotating at different speeds or in different directions, its moment of inertia will remain the same, as long as the mass distribution is unchanged.
doubling only the spring constant of a vibrating mass-and-spring system produces what effect on the system's mechanical energy? increases the energy by a factor of two increases the energy by a factor of square root of two increases the energy by a factor of three increases he energy by a factor of four produces no change\
When doubling only the spring constant of a vibrating mass-and-spring system, the effect on the system's mechanical energy is to increase the energy by a factor of four. A mass and spring system is a simple harmonic oscillator that can move back and forth when displaced from equilibrium.
When a spring is extended or compressed, it exerts a force in the opposite direction, which causes the mass to accelerate. When the mass reaches equilibrium, the spring force balances the force of gravity acting on the mass.
The force of a spring can be expressed as F = -kx, where k is the spring constant and x is the displacement from equilibrium. The amount of energy stored in the spring can be calculated by the following formula: E = 1/2 kx²When the spring constant k is doubled, the potential energy stored in the spring is doubled.
This means that if the displacement from equilibrium remains constant, the mechanical energy will double. Thus, doubling only the spring constant of a vibrating mass-and-spring system produces an effect on the system's mechanical energy that increases the energy by a factor of four.
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a horizontally directed force of 25-n is used to pull a box through a distance of 2.6 m across a tabletop. how much work is done by the 25-n force?
A horizontally directed force of 25-n is used to pull a box through a distance of 2.6 m across a tabletop. The work done by the 25-N force is 65 Joules.
The work done by the 25-N force is calculated using the formula:
Work = Force × Distance × cos(θ), where θ is the angle between the force and displacement vectors.
In this case, the force is horizontal, and the displacement is also horizontal, so the angle (θ) is 0 degrees.
Therefore, cos(θ) = 1.
Work = 25 N × 2.6 m × 1 = 65 J (Joules)
So, the work done by the 25-N force to pull a box through a distance of 2.6 m across a tabletop is 65 Joules.
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Why did new and existing aquatic organisms thrive during the Mesozoic?
The new and existing aquatic organisms thrive during the Mesozoic era for oceanic expansion, warm climate, abundant food and Evolutionary innovations
What is the Mesozoic?
The Mesozoic era, which lasted from about 252 million years ago to 66 million years ago, was a time of great change in the Earth's climate and geography. During this period, new and existing aquatic organisms thrived due to several factors:
Oceanic Expansion: During the Mesozoic era, the Earth's continents began to separate, leading to the expansion of ocean basins. This created more habitat for aquatic organisms to colonize and diversify.Warm Climate: The Mesozoic era was characterized by a warm and stable climate, which allowed marine organisms to thrive in the shallow, sunlit waters near the coasts.Abundant Food: The oceans of the Mesozoic were rich in nutrients, which supported the growth of plankton and other primary producers. This, in turn, provided a food source for a wide variety of marine organisms, including fish, marine reptiles, and invertebrates.Evolutionary innovations: During the Mesozoic era, many new types of aquatic organisms evolved, including dinosaurs, marine reptiles such as ichthyosaurs and plesiosaurs, and various types of fish. These evolutionary innovations allowed aquatic organisms to exploit new niches and diversify their lifestyles.Learn about Mesozoic era here https://brainly.com/question/4824228
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you must build the cantilever shown in the figure. the maximum length of cable you have available is 5 m and the maximum tension the cable can support is 245 n. the material used for the cantilever has a density of 40 kg per meter length of the cantilever. what is the maximum length (in m) of the cantilever that you can build?
The maximum length of the cantilever that can be built is approximately 0.63 m.
When answering questions on Brainly, it is important to always be factually accurate, professional, and friendly. It is also important to be concise and not provide extraneous amounts of detail. It is recommended to use the following terms in your answer if they are relevant to the question being asked.
For example, in the question "you must build the cantilever shown in the figure. the maximum length of cable you have available is 5 m and the maximum tension the cable can support is 245 n.
the material used for the cantilever has a density of 40 kg per meter length of the cantilever. what is the maximum length (in m) of the cantilever that you can build?",
one would need to use terms such as cantilever, cable, tension, and density in their response.In order to calculate the maximum length of the cantilever that can be built, the following formula can be used:
L = T / (d * g)Where L is the maximum length of the cantilever,
T is the maximum tension the cable can support, d is the density of the cantilever material, and g is the acceleration due to gravity (9.8 m/s^2).Plugging in the given values, we get:
L = 245 / (40 * 9.8) ≈ 0.63 m
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im not sure what to write in the blanks.
Explanation:
meters per second
meters per second
seconds
a rigid, circular metal loop begins at rest in a uniform magnetic field directed away from you as shown. the loop is then pulled through the field toward the right, but does not exit the field. what is the direction of any induced current within the loop?
The induced current in the loop will flow in a counterclockwise direction, as it opposes the change in magnetic flux and follows the right-hand rule.
To determine the direction of the induced current within the loop, we can use Lenz's Law and the right-hand rule.
Step 1: Lenz's Law states that the induced current will flow in a direction that opposes the change in magnetic flux through the loop. In this case, since the loop is being pulled to the right, the magnetic flux is decreasing.
Step 2: Using the right-hand rule, point your right thumb in the direction of the magnetic field (away from you). Then, curl your fingers in the direction of the loop's motion (to the right). The direction of your fingers curling indicates the direction of the induced current.
Based on these steps, the induced current in the loop will flow in a counterclockwise direction, as it opposes the change in magnetic flux and follows the right-hand rule.
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a camera lens has a focal length of 50.0 mm and an aperture setting of f/4.00. what is the aperture diameter of this lens? question 3 options: 12.5 mm 10.1 mm 13.6 mm 14.2 mm 15.0 mm
The aperture diameter of this lens is 12.5 mm. The correct option is 12.5 mm.
Aperture refers to the opening of a lens's diaphragm through which light passes. In cameras, it is a hole through which light travels. The larger the hole, the more light passes through. Aperture is measured in f-stops, with a low number indicating a larger aperture (more light passing through) and a high number indicating a smaller aperture (less light passing through).
A camera lens has a focal length of 50.0 mm and an aperture setting of f/4.00, as given in the question. To find the aperture diameter of this lens, we can use the formula:
Aperture diameter = Focal length / f-number
Given that the focal length is 50.0 mm and the aperture setting is f/4.00, we have:
f-number = 4.00focal length = 50.0 mm
Substituting these values in the formula, we get:
Aperture diameter = Focal length / f-number= 50.0 mm / 4.00= 12.5 mm
Therefore, the aperture diameter of this lens is 12.5 mm. The correct option is 12.5 mm.
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A light bounces off the surface of a metal cup and shines in Harold’s eyes. Which best describes what is happening to the light waves in this scenario
When a light bounces off the surface of a metal cup and shines in Harold's eyes, the light waves undergo reflection. Reflection occurs when a wave encounters a boundary between two media and bounces back into the original medium.
When a light wave strikes the surface of the metal cup, some of the energy from the light is absorbed by the metal, causing electrons in the metal to become excited and move to higher energy levels. These excited electrons then release the energy they have absorbed by emitting new light waves, in a process called reflection. The reflected light waves bounce off the surface of the metal cup in many different directions, including towards Harold's eyes. When these waves enter Harold's eyes, they stimulate the cells in his retina, which sends electrical signals to his brain. His brain then processes these signals as visual information, allowing him to see the cup and the reflected light.
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in aviation a standard rate turn proceeds at an angular speed of per minute. what is the radius of a standard rate turn for a plane moving at 240 m/s?
The radius of a standard rate turn for a plane moving at 240 m/s is approximately 933 meters.
A standard rate turn in aviation refers to a turn in which an aircraft completes a full 360-degree rotation in 2 minutes, resulting in an angular speed of 3 degrees per second (180 degrees per minute). To calculate the radius of a standard rate turn for a plane moving at 240 m/s, we can use the formula:
Radius = V / (G × Tan(Bank Angle))
where:
- V is the velocity of the plane (240 m/s)
- G is the gravitational constant (approximately 9.81 m/s²)
- Bank Angle is the angle at which the aircraft is tilted during the turn.
First, we need to find the bank angle. Since we know that the angular speed is 3 degrees per second, we can use the following formula to find the bank angle:
Bank Angle = Arc Tan((V² × Angular Speed) / (G × 180))
Bank Angle = Arc Tan((240² × 3) / (9.81 × 180))
Bank Angle ≈ 14.7 degrees
Now that we have the bank angle, we can calculate the radius of the turn:
Radius = 240 / (9.81 × Tan(14.7))
Radius ≈ 933 meters
So, the radius of a standard rate turn for a plane moving at 240 m/s is approximately 933 meters.
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a 10-volt power supply is placed in series with two 5-ohm resistors. what is the current in the circuit after it passes through each of the two resistors?(1 point)
The current in the circuit after passing through each 5-ohm resistor is 1 Ampere, using Ohm's Law.
To compute the ongoing in the circuit, we can utilize Ohm's Regulation, which expresses that the ongoing moving through a circuit is straightforwardly corresponding to the voltage and contrarily relative to the opposition.The all out opposition of the circuit is equivalent to the amount of the singular protections in series, which is 5 ohms + 5 ohms = 10 ohms.Utilizing Ohm's Regulation, we can compute the ongoing in the circuit as follows:
I = V/R
Where I is the current, V is the voltage, and R is the opposition.Subbing the qualities, we get:
I = 10 V/10 ohms = 1 Ampere
Subsequently, the ongoing in the circuit after it goes through every one of the two 5-ohm resistors is 1 Ampere.
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A horse pulls a tree trunk there is a force of 1500N. and moves a distance of 10m in 15s find the work and the power.
Answer:
Work=15000
Power=1000
Explanation:
Foce=1500N
Distance=10m
Time=15s
Work=Force*Distance
Work=1500*10=15000Nm
Power=Work/Time=15000/15=1000nm/s