If wave one has an amplitude of 4 and wave two has an amplitude of 3, what is the amplitude of the wave resulting from the interference
Equation Used
The resulting intensity is calculated as follows: I = (sqrt(I1)-sqrt(I2))2
3 variables and 1 function are used in this formula.
Used Functions
Square root function and sqrt (Number)
used variables
The effect of two intensities coming together is called the "resulting intensity" (measured in candela).
The energy that the first wave transfers over a surface of a given area in a unit of time is measured as intensity 1 (measured in candela), which is equal to the energy density times the wave speed.
The energy that the second wave transfers over a surface of a certain area in a unit of time is measured as intensity 2 (measured in candela), which is equal to the energy density times the wave speed.
No conversion is necessary for intensity 1: 4 candela to 4 candela.
Intensity 2: No Conversion Needed 3 Candela to 3 Candela
Replacement of Input Values in a Formula
I is equal to (sqrt(I1)-sqrt(I2))2 --> (sqrt(4)-sqrt(3)).
2 Assessing...…
I = 0.0717967697244909
Candela: 0.0717967697244909 No Conversion Is Necessary
RESULT 0.0717967697244909 A candela Outcome Intensity (Calculation completed in 00.016 seconds)
What is Wave Interference?
When two waves that are moving in opposite directions arrive at the same location simultaneously, interference results. The two waves will combine into a temporary, larger wave with an amplitude equal to the sum of their individual amplitudes if their crests and troughs completely line up. Constructive interference is what this is. On the other hand, if the crests of two waves coincide, they either combine to form a smaller wave or completely cancel each other out. We refer to this as destructive interference.
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A myopic person sees that her eyeglasses perscription is -4.00 D, for eyeglasses positioned 1.75 cm from her eyes. What is her far point?
After solving the problem the person's far point is 25 cm
What is myopic person?
A myopic person is someone who is near sighted and is unable to clearly see objects that are far away. This is caused by the eyeball being too long and the cornea having too much curvature. Light entering the eye is focused in front of the retina rather than directly on it, resulting in blurred vision for distant objects. Myopia is a common eye condition and can usually be corrected with glasses or contact lenses. In more severe cases, laser surgery may be necessary. People with myopia may need to wear their glasses or contact lenses all the time in order to see clearly, but they may be able to take them off when they are close to something they want to see clearly.
The far point is the farthest distance at which a person can see clearly without any corrective lenses.
The formula for calculating far point is 1/f = 1/d + 1/p, where f is the far point, d is the distance from the eye to the lens (1.75 cm in this case), and p is the power of the lens (in diopters) which is -4.00 D.
Plugging the values into the formula yields 1/f = 1/1.75 + 1/-4.00, which simplifies to 1/f = 4.00 - 0.5714. Solving for f gives f = 0.2500, or 25 cm.
Therefore, the person's far point is 25 cm.
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An error that occurs consistently in one direction, such as a scale that weighs everyone two pounds more than their true weight, is known as a:
A systematic error is one that constantly occurs in one direction, for as when a scale consistently overestimates everyone's weight by two pounds.
If an error changes in the same direction throughout time, it is said to be systematic. For instance, if something always or frequently caused the blood pressure to increase right before the measurements were to be taken, this could occur when taking blood pressure.One measurement may slightly differ from the next due to random error. It results from unanticipated changes that occur throughout an experiment. When a reading is taken consistently each time, systematic error always impacts measurements in exactly the same way or to exactly the same degree. It is foreseeable.To know more about error here
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The same amount of steel used to create eight solid steel balls, each with a radius of 1 inch, is used to create one larger steel ball. What is the radius of the larger ball
Answer:
2 inches
Explanation:
Volume of a sphere = 4/3 pi r^3
for the EIGHT balls total volume = 8 * 4/3 pi (1^3) = 32/3 pi
This is the volume of the made-up ONE ball
4/3 pi r^3 = 32/3 pi
4/3 r^3 = 32/3
r^3 = 32/3 * 3/4
r^3 = 8
r = 2 inches
A toy car move around a loop-the-loop track. The loop i 0. 5 high. What i the minimum peed of the car at the top of the loop for it to tay on track?
Pleae work it!!
I found all the anwer are 1. 57m/ but it i
0. 78m/
The minimum speed of the car at the top of the loop for it to stay on track be 1.57 m/s.
What is speed?The speed of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time.The speed at which an object's location changes in any direction.The distance traveled in relation to the time it took to travel that distance is how speed is defined.As a result, the fundamental unit of time and the basic unit of distance are combined to form the SI unit of speed. Thus, the metre per second (m/s) is the SI unit of speed.To learn more about speed refer to:
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The spring in a scale stretches 1 centimeter when a 5-newton object hangs from it. How much does an object weigh if it stretches the spring 2 centimeters
The spring in a scale stretches 1 centimetres when a 5 newton object hangs from it. The required weight of an object is 10 N if it stretches the spring 2 centimetres.
Hooke's law tells us that, F = -kx
where, k is the spring constant
x is the distance stretched by a spring
F is the force
Given that,
Length x₁ = 1 cm
Force F₁ = 5 N
Length x₂ = 2 cm
F₂ = ?
From the above equation, we can write,
F₁/x₁ = F₂/x₂
Making F₂ as subject, we have,
F₂ = F₁/x₁ × x₂ = 5/1 × 2 = 10 N
Thus, the required weight of an object is 10 N if it stretches the spring 2 centimetres.
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39) Three different dynamic carts of different masses are rolled down a ramp. The heaviest one rolls down the ramp the fastest. Before concluding that a more massive cart will roll down a ramp faster, what experiment with these three carts might you want to do
According to the given information the answer is Add masses to each car until they have the same mass, then test the carts again.
What is dynamic carts?Features three low friction ball bearing wheels and matched axles to assure their rolling along a true line without deviation to produce accurate data, and a sturdy steel body to endure rigorous handling. Each cart is around 1.5 kg in weight. The ends of the cart lift above the bed to transport a brick or any other bulk, and the cart bed is covered with a rubber pad. At one end of the cart, there is a clip where a tape can be fastened. Each cart's pins fit into the holes in the others, allowing the mass to be doubled by stacking them.
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The complete question is-
Three different dynamic carts of different masses are rolled down a ramp. The heaviest one rolls down the ramp the fastest. Before concluding that a more massive cart will roll down a ramp faster, what experiment with these three carts might you want to do?
Run an experiment with the ramp at a different angleFind a fourth cart to add to the test, then test againChange the surface of the ramp, then test the carts againAdd masses to each car until they have the same mass, then test the carts againHow do you calculate the fall of a ramp?
The fall of the ramp can be calculated by the falling style of the ramp. like if the ramp is falling in the rolling motion, then we can calculate the fall of the ramp by the process by which we calculate of the rolling motion of any object.
Rolling motion happens when an object roll over from a ramp or any other sloppy surface whether it is rough or smooth. many forces act on it at the same moment. also in many forces rolling tangential force and gravitational force is also acting on it at the same moment. in which the gravitational force is acting on it at a bigger pace and plays an important role in rolling of the object from the ramp or any other sloppy surface. hence, by this information we can firmly consider that a heavier object go down a ramp at a same pace as a lighter object go down a ramp because of gravitational force acting on it in a major form.
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If hydrogen gives off 10 units of energy, but takes 15 units of energy to produce, what is its net energy ratio
The net energy ratio of hydrogen is 0.67.
What is net energy ratio?The net energy ratio, also known as energy return on investment (EROI), is a measure of the efficiency of a fuel source or energy system. It represents the ratio of the energy output to the energy input, or the amount of energy that is produced compared to the amount of energy that is required to produce it.
A net energy ratio of 1 means that the energy output is equal to the energy input, and that no net energy is produced.
In the case of hydrogen, it gives off 10 units of energy but takes 15 units of energy to produce, so the net energy ratio would be:
Energy output / Energy input = 10 units / 15 units = 0.67
Hence, the net energy ratio of hydrogen is 0.67. This means that for every 1 unit of energy put into producing hydrogen, only 0.67 units of energy are obtained.
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A new way of "multiplying" two vectors is introduced in this chapter. What is it called? Select one: O a. The tensor product. O b. The angular product. Oc. The scalar product. O d. The dot product. O e. The cross product.
The correct option is option e) cross product
The cross-product is a new way of "multiplying" two vectors. It results in a new vector that is perpendicular to both the original vectors and its magnitude is given by the area of the parallelogram formed by the two original vectors.
In three-dimensional space, cross-product is a binary operation on two vectors. It yields a vector perpendicular to both vectors. a b represents the vector product of two vectors, a and b. Its resulting vector is parallel to a and b. Cross goods are another name for vector products.
The cross-product has four basic applications:
calculating the angle () between two vectorsdetermining a vector normal to a planecalculating the moment of a force about a pointcalculating the moment of a force about a line.Read more about Cross-Product from:
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A car traveling at a constant speed covers a distance of 750 m in 25 s.What is the cars speed
Answer:
30 m/s
Explanation:
Answer:
The speed is equal to Distance divided by Time.
The SI Unit of Speed is m/s or meters per second.
V = S/T
= 750/25
= 30 m/s
If you have a set of holiday lights that is on a series circuit, predict what would happen if the series circuit were cut off in the middle. Infer how this would differ from what would happen with a parallel circuit.
If the series circuit that powers your holiday lights were to be severed in the middle. The lights would all stop functioning. Only one light would stop working if the lights were linked in parallel circuit.
A series circuit is a straightforward circuit that enables electrons to go between one or more resistors. A resistor is anything that drains energy from a cell (battery). The resistor in a series circuit is typically a lightbulb. A series circuit is one in which the entire current flows through each element. A series circuit is a straightforward circuit that enables electrons to go between one or more resistors.
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A 2.5 kg block is initially at rest on a horizontal surface. A horizontal force of magnitude 6.0 N and a vertical force are then applied to the block (Fig. 6-17). The coefficients of friction for the block and surface are ms 0.40 and mk 0.25. Determine the magnitude of the frictional force acting on the block if the magnitude of is (a) 8.0 N, (b) 10 N, and (c) 12 N.
Kinetic friction force, or f k = k F N = 3.1N, is the amount of frictional force acting on the block.
Static friction is the friction that exists between two systems when they are in contact and immobile with respect to one another. Kinetic friction is the term for the resistance that exists between two systems while they are in contact and moving in relation to one another.
Calculation:Either static or kinetic friction We decide on +x right and +y up. Applying Newton's second law to these axes:
F−f=ma
P+F n −mg=0
where F=6.0 N and m=2.5 kg is the mass of the block.
(a) P=8.0 N in this scenario results inF N =(2.5kg)(9.8m/s 2 )–10N=14.5N.
This implies ,fs, max =μ s F N=6.6N, which is larger than the 6.0N rightward force. The block, which was previously at rest, stays in place as a result.
Putting a = 0
f=P=6.0 N is the static friction force that results from plugging the first of our equations above.
(b) With P=10 N in this instance, the normal force isThis suggests that, fs, max = s F N =5.8N, which is smaller than the 6.0 N rightward
force, which causes the block to move. Therefore, we are working with kinetic data instead of static data.
Eq. reveals that friction is f k = k F N =3.6 N.
(c) In the last scenario, P=12 N results in FN=12.5 N and fs, max = s F N = 5.0N.which (as expected) is less than the 6.0 N rightward force. Thus, the block moves. The kinetic friction force, then, is f k =μ k F N =3.1N.
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is the electron's speed at f greater than, less than, or equal to its speed at i?
O The electron's speed at f is less than its speed at i. O The electron's speed at f is equal to its speed at i. O The electron's speed at f is greater than its speed at i. O There is not enough data to determine the correct answer.
The correct option is B, The electron's speed at f is equal to its speed at i.
Electrons are subatomic particles that are found in atoms. They are the negatively charged particles that orbit the nucleus of the atom, and they have an extremely small mass. Electrons travel at different speeds depending on their energy level. At their lowest energy level, electrons move at an extremely slow speed, about one thousandth of the speed of light. As the electrons gain energy, their speed increases.
In a vacuum, when electrons have the highest energy level, they can travel at a speed of nearly the speed of light, which is around 186,000 miles per second. In a vacuum, the electrons would have the same speed regardless of their mass. Electrons also move slower inside a material, such as a metal, due to the presence of other atoms. Electrons in metals usually move at a speed of about 1/10th the speed of light. This slower speed is due to the electrons having to pass through energy barriers created by the other atoms in the metal. In general, electrons are very fast particles that can travel at speeds up to nearly the speed of light.
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With the Sun and Moon in this position, what does the side of the earth facing the moon experience? ft Select one O A a normal high tide B. a neap high tide C. a spring high tide D. a spring low tide a neap low tide F a normal low tide age
With the Sun and Moon in this position, the side of the earth facing the moon experiences a spring high tide. Thus Option C is the answer.
A spring tide is a tide that occurs when the gravitational pull of the Moon and the Sun are in alignment. During a new moon or full moon phase, the gravitational pull of the Moon and the Sun combine to produce stronger than normal high tides and stronger than normal low tides. The term "spring tide" does not refer to the season of spring, but rather the tide's "springing forth" of water.
During a spring tide, the difference between high tide and low tide is at its greatest, and the water level rises higher and falls lower than during a neap tide. This is because the gravitational pull of the Moon and Sun are working together to produce the tide, rather than against each other. This results in a high tide that is higher than a normal high tide, referred to as a spring high tide.
It is important to note that spring tides occur twice a month, around the time of the new and full moon, when the Moon and Sun are in alignment.
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What is the total distance the particle travels from t 0 to t 4?
the whole distance is five. The main point is that you must be aware of if and when the particle reverses course.
In order to determine the velocity, differentiate the displacement and set it to zero.
It is obvious that at t=1, the velocity is zero.
S=3 is the starting location at time t=0. At t=1,s=2 \s.
The total distance traveled is 1.
The additional distance traveled is 62=4 at time t=3 and s=6.
Thus, the whole distance is five.
L=30|s′(t)|dt=30|2t2|dt=1022tdt+312t2dt=5 is the length of the image of s|[0,3] and represents the total distance traveled between t=0 and t=3. .
When calculating the traveled distance of a particle satisfying the law of motion s(t) between t=a and t=b, another method that can be used if you are unfamiliar with the arc length formula is to first determine the critical points in (a,b), such as t1tk, and then multiply those values by the following formula: |s(t1)s(a)|+|s(t2)s(t0)|++|s(b) Since there is just one critical moment in your particular scenario, t=1, L=|s(1)s(0)|+|s(3)s(1)|=1+4.
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1. A Major League pitcher can give a 0. 142-kg base-
ball a speed of 45. 1 m/s. Find the magnitude of the
baseball's momentum.
The baseball's momentum will be 2.75 m/s in magnitude. This is the accurate answer to the given problem.
What are velocity and momentum?Momentum and velocity are different in that momentum is a measurement of an object's amount of motion, whereas velocity is a measurement of an object's speed with direction. Velocity is one of the components of momentum since momentum is equal to an object's mass multiplied by its speed.
Is speed the same as momentum?p = m v . The equation demonstrates that momentum is directly related to an object's mass (m) and velocity (v). As a result, an object's momentum increases with increasing mass or velocity. The momentum of a large, swift object is larger than that of a small, slower object.
Briefing:P initial = (145g) x (45 m/s) = 6525 g*m/s
F = 0-6525/1.0s = -6525N
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To ensure your battery's longevity, you should keep the area where cables are connected to the positive and negative poles clean. T/F
True. Keeping the terminals and cable connections clean helps to ensure a good electrical connection, which can prolong the life of the battery.
Keeping the terminals and cable connections of a battery clean is important for prolonging the battery's life. Dirt, corrosion, or other buildup on the terminals can create resistance in the circuit, which can lead to overheating and damage to the battery. This can cause the battery to charge and discharge less efficiently, reducing its overall capacity and lifespan. To clean the terminals, you can use a wire brush or a toothbrush with baking soda and water to scrub away any corrosion. Then, dry the terminals and cables thoroughly before reconnecting them to the battery. This will ensure a good electrical connection and a longer-lasting battery.
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How is coal extracted from mountaintop removal mines? (site 2)
Coal is extracted from mountain top by removal of top soil and the use of explosives.
What is a coal?A coal is definitely as the solid substance that is made up of mainly carbon and other constituent elements such as hydrogen, sulfur, oxygen, and nitrogen.
The uses of coal include the following:
cement production, carbon fibers and foams, medicines, tars, synthetic petroleum-based fuels, and home and commercial heating.To extract coal from the mountain top the following is carried out:
The top soil of the area involved us being removed and
Explosives are then used to expose the underlying coal seams.
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Press the hotspot that indicates the location that a string will experience the least tension during vertical circular motion. Assume that the speed of the ball remains constant.
which one will experience the least tension t3 t2 t1 or t4
The least tension will be experienced by T3
The weight of a moving object causes tension, which is the force applied along the length of a string, rope, or cable. The force that maintains an object moving in a circular direction when it is in a vertical circular motion is called tension. Perpendicular to the circle's radius, the tension in the string is pointed in the direction of the circle's centre.
Due to the centripetal force required to maintain the object moving in a circular motion, the tension in the string varies as the object moves in a vertical circle, with the highest tension occurring at the top of the circle and the least tension occurring at the bottom. In the given case, T3 will experience the least tension during vertical circular motion, assuming that the speed of the ball remains constant. This is because T3 is the point on the string that is closest to the circle's centre, and thus is subject to the least amount of tension as the ball moves in a vertical circle.
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A simple pendulum has length L and period T. As it passes through its equilibrium position, the string is suddenly clamped at its mid-point. The period then becomes:
The new period would be T/2.
The period of a simple pendulum is given by T = 2π √(L/g), where,
L is the length of the pendulum g is the acceleration due to gravity.When the string is clamped at its midpoint, the length of the pendulum is effectively halved.
So the new period would be T' = 2π √(L/2g) =π √(L/g) = T/2.
Period of Simple Pendulum:
The period of a simple pendulum is the time it takes for the pendulum to complete one full oscillation, or swing back and forth. It is determined by the length of the pendulum (L) and the acceleration due to gravity (g). The mathematical formula for the period of a simple pendulum is T = 2π √(L/g).The length L of the pendulum is the distance from the pivot point (the point at which the pendulum is attached) to the center of mass of the pendulum bob (the weight at the bottom of the pendulum). The longer the pendulum, the longer the period will be.The acceleration due to gravity (g) is a constant value of approximately 9.8 m/s^2 on the surface of the Earth. The value of g is used in the formula because the force of gravity is what causes the pendulum to oscillate.It's important to note that the period of a simple pendulum is independent of the amplitude of the oscillations (the angle at the pendulum is displaced from its equilibrium position), as long as the amplitude is small enough that the pendulum's motion can be considered simple harmonic motion.Learn more about Simple Pendulum here;
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The sum of kinetic energy and potential energy
of the particles in a material is blank
The sum of kinetic energy and potential energy of the particles in a material is known as mechanical energy.
What is Kinetic energy?The energy that an object has as a result of motion is known as kinetic energy. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its acceleration until its speed changes.
What is potential energy?Due to its position, an object has the ability to store energy. For instance, when a demolition machine's heavy ball is held in an elevated position, it is storing energy. Potential energy is the name for this positional energy that has been stored. Similar to how a drawn bow can store energy due to its posture, There is no energy in the bow while it is in its normal position, or when not drawn. The bow can yet store energy when its position is changed from its normal equilibrium position because of its position. Potential energy is the name for this positional energy that has been stored. Potential energy is the energy of position that a thing has stored inside it.
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Frank is pulling on a rope to drag his backpack to school across the ice. He pulls upwards and rightwards with a force of 26.7 Newtons at an angle of 17 degrees above the horizontal to drag his backpack a horizontal distance of 129 meters to the right. Determine the work done upon the backpack. in joules.
The work done upon the backpack is 3293 Joule.
What is force?
The definition of force in physics is: The push or pull on a massed object changes its velocity.
An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
A spring balance can be used to calculate the Force. The Newton is the SI unit of force.
The work done upon the backpack is = applied force × displacement × cosα
= 26.7 N × 129 meters × cos17°
= 3293 Joule.
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The power required to exert 1 N force, over a distance of 1 m in 1 second is. A) 1 W. B) 2 W. C) 1/3 W. D) 3 W. E) none of these.
Answer:
A) E = 1 N * d = 1 Newton-Meter = 1 Joule
P(ower) = E / t = 1 N-m / t = 1 Joule / sec = 1 W
What is the sound level of rustling of leaves?
The sound level of rusting leaves is 20db.
Rustle is a quiet, muted cracking sound made when dry paper or leaves are moved. The movement of weak objects, like the leaves, produces a gentle sound. Ruffle would be the appropriate response because "leaves" is the noun in the sentence.
Over time, so many people have been mesmerized by the sounds of wind in the trees and the rustling of leaves, that they came up with the term "psithurism" to describe them. Psithurism has a silent first "p," like many other words that start with "ps," and is pronounced sith-err-iz-um.
We sometimes refer to a wind that is howling when it is strong and noisy: The trees shook as the wind howled.
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In a sealed container, Sarah combines a reactant with a mass of 8 grams with another reactant with a mass of 11 grams. After the reaction, what is the most reasonable prediction Sarah can make for the total mass of the products of this reaction?
6g
8g
10g
19g
which one
The most reasonable prediction Sarah can make for the total mass of the products of this reaction would be = 19g.
What is law of conservation of mass?The law of conservation of mass states that mass in neither created nor destroyed but can be changed from one form to another.
From the set up of the reaction carried out by Sarah, the container was in an enclosed medium.
Therefore since there is no loss of mass, the total mass of the products of this reaction would be = 11+8 = 19g.
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a car weighs 3600 kg is traveling at 21.0 m/s. the driver doesn?t notice a red light and rear-ends another car at rest. both cars stick together and move with a speed of 9.0 m/s. what is the mass of the car that was at rest?
Answer:
Below
Explanation:
Use law of conservation of momentum
momentum before crash = momentum of the system after crash
3600 kg * 21 m/s = (3600+ x ) * 9
solve for x = 4800 kg
Determine the quantity of charge on a plastic tube which has been rubbed with animal fur and gained 3. 8 x 10^9 electrons
The quantity of charge on a plastic tube that has been rubbed with animal fur and gained 3. 8 x 10^9 electrons is The quantity of charge on the plastic tube is 3.8 x 10^9 electrons.
The quantity of charge on the plastic tube is 3.8 x 10^9 electrons. To calculate this value, we can use the equation q = n*e, where q is the charge, n is the number of electrons and e is the elementary charge (1.6 x 10^-19 C). Substituting in the values given, we get q = 3.8 x 10^9 * 1.6 x 10^-19 = 6.08 x 10^-10 C. This means that the plastic tube has gained a charge of 6.08 x 10^-10 Coulombs, which is equivalent to 3.8 x 10^9 electrons.
This can be explained by the process of triboelectricity, which is the transfer of electrons between two materials due to rubbing them together. In this case, the animal fur must have had a higher electron affinity than the plastic, which caused electrons to be transferred from the fur to the plastic tube.
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when a falling firecracker explodes, the momenta of its pieces _______.
when a falling firecracker explodes, the momenta of its pieces vectorially add up to equal the initial momentum of the firecracker.
When the firecracker bursts, the vector sum of the momenta of its fragments adds up to the firecracker’s momentum just before bursting.
A falling firecracker explodes into two pieces. The momenta of the fragments combine by vector rules to equal the original momentum of the falling firecracker. Momentum is equal to mass multiplied by velocity.
According to the conservation of momentum, the initial momentum of the system is equal to the final momentum. The condition for the validity of momentum conservation is that no external force should exert on the system.
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Les mélange et le transformations de la matiers
Les molécules sont arrangées autrement, ce qui modifie l'aspect ou l'état de l'espèce chimique. Un mélange est une substance composée de plusieurs espèces chimiques qui ne réagissent pas ensemble, au contraire de la transformation chimique. Il s'agit donc d'une transformation physique, qui ne change pas la matière.
Why is 90-degree angle important?
90-degree angles are used as reference points for measuring other angles and for defining trigonometric functions and vector relationships.
In trigonometry, the sine, cosine, and tangent functions are defined in terms of the ratios of the sides of a right triangle, where one angle is 90 degrees. In addition, in vector calculus, the dot product and cross product of two vectors are often defined in terms of the angle between the vectors, and a 90-degree angle represents a perpendicular or orthogonal relationship between the vectors. The 90-degree angle is also important in mechanics and engineering as it is used to define the concept of torque, which is the rotational equivalent of linear force. Torque is defined as the product of a force and the perpendicular distance from the line of action of the force to the axis of rotation. Furthermore, it is also used to define the concepts of stress, strain and moment of inertia in strength of materials and mechanics.
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