Answer:
22 Watts
Explanation:
From the question given above, the following data were obtained:
Current (I) = 2 A
Voltage (V) = 11 V
Power (P) =?
The power of the generator can be obtained as follow:
P = IV
P = 2 × 11
P = 22 Watts
Therefore, the output power of the generator is 22 Watts
List three ways regular physical activity contributes to wellness.
Answer:
Explanation:
Exercise controls weight. Exercise can help prevent excess weight gain or help maintain weight loss. ...
Exercise combats health conditions and diseases. ...
Exercise improves mood. ...
Exercise boosts energy. ...
Exercise promotes better sleep. ...
Exercise puts the spark back into your sex life. ...
Exercise can be fun … and social!
Which two foods are most like homogeneous mixtures?
A. Tossed Salad
B. Trail mix
C. Mayonnaise
D. Mustard
Answer: It’s most likely Mayonnaise and mustard.
Explanation: It’s definitely mayonnaise because it’s not possible to see the different substances and for mustard it depends on what type. Hope this helps. Good luck :)
Answer:
Mayonnaise and mustard.
Explanation:
A proton is to orbit Earth at the equator using Earth's magnetic field to supply part of the necessary centripetal force. In what direction should the proton move
identify the balanced nuclear equation for the beta decay of europium-157.
The balanced nuclear equation for the beta decay of europium-157 is:
157/63Eu -> 157/64Gd + 0/-1e
In this equation, europium-157 (157/63Eu) undergoes beta decay, emitting a beta particle (0/-1e) and transforming into gadolinium-157 (157/64Gd). The beta particle represents an electron (e-) that is emitted from the nucleus during the decay process. The atomic numbers and mass numbers are conserved in the equation, indicating that the total number of protons and neutrons on both sides remains the same. The decay of europium-157 through beta decay results in the formation of gadolinium-157.
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In an action-reaction pair
a. action force is exerted first
b. action force and the reaction force are equal in magnitude and act in the same direction.
c. action force and the reaction force are contact forces only.
d. action force and the reaction force act on two different objects.
Answer:
d. action force and the reaction force act on two different objects.
Hope you could understand.
If you have any query, feel free to ask.
In an action-reaction pair, action force and the reaction force act on two different objects.
What is Newton's Third Law of Motion?Newton's Third Law of Motion states that "For every action, there is an equal and opposite reaction, action and reaction act on two different bodies."
It means that equal force are act on reaction force that is it is also known as reciprocal law of motion.
When considering the options,
The first option is incorrect because action and reaction forces act simultaneously.The second option is also false because they act in opposite direction.The third option is wrong because for action-reaction force, physical contact is not necessary.So, In an action-reaction pair, action force and the reaction force act on two different objects. Thus, Option B is the correct answer.
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Calculate the repulsion force between the two Arkon nuclei when the distance between them is 1x10-3μm (note that the Arkon nucleus contains 18 protons) (The electric charge of one electron is 1.6x10-19C) a. 7.4x10-8N
b. 2.7X10-30N c. 7.4X10-20N d. 7.4x10-14N
The repulsion force between the two Arkon nuclei when the distance between them is 1x10⁻³μm is approximately 7.4x10⁻¹⁴N. The correct option is d. 7.4x10⁻¹⁴N.
The formula for repulsion force between two Arkon nuclei when the distance between them is given by Coulomb's law. Coulomb's law states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, the law can be expressed as F=kq1q2/r²,
Where F is the force, q1 and q2 are the charges, r is the distance between the charges, and k is the Coulomb's constant.The electric charge of one electron is 1.6x10⁻¹⁹C.
Therefore, the charge of the Arkon nucleus with 18 protons = 18(1.6x10⁻¹⁹) C = 2.88x10⁻₈⁸ CThe force between the two Arkon nuclei can be calculated using the formula above.
F=kq1q2/r²
Substituting the values we have;F = (9x10⁹)(2.88x10⁻¹⁸ C)2/(1x10⁻³ m)2F ≈ 7.4x10⁻¹⁴ N. Therefore, the repulsion force between the two Arkon nuclei when the distance between them is 1x10-3μm is approximately 7.4x10⁻¹⁴N. The correct option is d. 7.4x10⁻¹⁴N.
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Question 7 (2 points)
Which statement accurately describes the charge of the nucleus of an atom? (2 points)
O a The nucleus can be either positively charged or neutral.
Ob
The nucleus never has an electrical charge.
O c
The nucleus always has a positive charge.
Od
The charge of a nucleus can change from positive to negative.
The nucleus of an atom will have a positive charge due to the existence of protons, which are positively charged subatomic particles.
Protons and neutrons are present in an atom's nucleus. We are aware that a proton has a charge of + 1 and a neutron has a charge of 0 (or no charge). As a result, the atom's nucleus will always be positively charged. A nucleus is a name for the dense area in the middle of an atom. Because there are positively charged subatomic particles present, the nucleus usually has a positive charge. The subatomic particles, which are present in atoms but far smaller than atoms, are there. Protons, neutrons, and electrons are the three primary subatomic particles found in matter. An atom's nucleus contains protons and neutrons, while its outermost nucleus contains electrons. Neutrons are subatomic particles with a charge of zero, whereas protons are positively charged.
Therefore, the nucleus of an atom will always have a positive charge. Consequently, an atom's nucleus has a positive charge because of the presence of protons.
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4. These bikes have narrow tires, an aerodynamic riding position, and generally higher gearing. They are mainly for riding on pavement.
road
race
touring
sport
Narrow tires bikes are used in racing competitions.
Bikes that have narrow tires are used in race because narrow tires have an advantage over wider tires due to their higher speed as they provide less air resistance. Less air resistance on the bike having narrow tires allows the bike to move faster as compared to those bikes having wider tires due to more air resistance so we can conclude that bikes with narrow tires are used in racing competitions.
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Road bikes are meant for optimum performance
The option that gives the type of bikes that have the given specifications is the option;
roadReason:
A road bike is a bike usually for competitive driving, meant for roads and that are paved roads, and not for racing tracks or rough terrains.
The specifications of a road bike are;
The frames are very lightweight, including the wheels and other parts
The handlebar is curled
The wheels of the tires are narrow
A front fork made of carbon fiber composite
It does not have have front or rear suspension
Includes variety for male and female riders
Therefore, the correct option is; road
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Part D What is the rest mass m of a particle traveling with the speed of light in the laboratory frame. Express your answer in MeV/c? to one decimal place. ► View Available Hint(s) Vo C ΑΣΦ ? т 6 1.7. 106 M Submit Previous Answers X Incorrect; Try Again; 4 attempts remaining = CODSpring2021 Phys3C Course Home
It is not possible for a particle with rest mass to travel at the speed of light in the laboratory frame. According to the theory of relativity, the speed of light is the maximum speed that any particle with mass can reach, and particles without mass (such as photons) always travel at the speed of light. Therefore, the question is not well-defined and cannot be answered.
According to the laws of physics, a particle with a non-zero rest mass cannot reach the speed of light. As a particle approaches the speed of light, its relativistic mass increases, and it would require infinite energy to accelerate it to the speed of light. Therefore, if a particle is observed to be traveling at the speed of light in the laboratory frame, it must be a massless particle like a photon. In this case, the rest mass (m) of the particle would be 0 MeV/c².
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Example 2
Linus and Edrick walked together from their work in Starbucks Metrowalk Pasig down to The 30th
Mall (also in Pasig). If the mall is 800 m south of Metrowalk, and both men were walking at a
velocity of 1.33 m/s in the same direction, how long did they walk?
Answer:
They walked for 10.025 minutes or 601.5 seconds
Explanation:
\({ \rm{velocity = \frac{ \triangle displacement}{time} }} \\ \\ { \rm{time = \frac{displacemet}{velocity} }} \\ \\ { \rm{time = \frac{800}{1.33} }} \\ \\ { \rm{time = 601.5 \: seconds}}\)
DUE in 10 MINS 20 points will mark BRAINLIEST what happens to a substance when it reaches a point above it's boiling point?
Answer:
When a liquid is heated, it eventually reaches a temperature at which the vapor pressure is large enough that bubbles form inside the body of the liquid. This temperature is called the boiling point. Once the liquid starts to boil, the temperature remains constant until all of the liquid has been converted to a gas.
Explanation:
Categorize each description below under the principle that describes that particular behavior of fluids.
Descriptions:
Describes hydraulic lifts
Describes airplane flight
Describes floating objects
Buoyant force equals weight of fluid displaced
Pressure decreases as a fluid moves faster
Pressure is the same throughout an enclosed fluid
Principles:
Archimedes' principle
Bernoulli's principle
Pascal's principle
each description below under the principle that describes that particular behavior of fluids:
Buoyant force equals weight of fluid displaced - Archimedes' principle
Pressure decreases as a fluid moves faster - Bernoulli's principle
Pressure is the same throughout an enclosed fluid - Pascal's principle
Describes hydraulic lifts - Pascal's principle
Describes airplane flight - Bernoulli's principle
Describes floating objects - Archimedes' principle
What is fluid?Fluids are defined as any material that flows in response to an applied force; hence, liquids and gases are fluids. Fluids are non-fixed-shape substances that flow readily due to enlarged intermolecular gaps. Fluids include both liquids and gases. When exposed to such a stress, a fluid, any liquid or gas, or any substance in general cannot maintain a tangential, or shearing, force and suffers a constant change in form.
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Which must be included when drawing ray diagrams? Check all that apply.
focal point
lens
three easy rays
axis
When drawing ray diagrams, several essential elements must be included to ensure an accurate representation of the optical system. These elements are the focal point, lens, three easy rays, and axis.
The focal point is a crucial aspect of ray diagrams, as it is the point where parallel light rays converge or diverge after passing through the lens. It is important to accurately identify and mark the focal point to understand the behavior of light within the system.
The lens is another vital component of ray diagrams, as it is the medium through which light rays pass and change direction. Lenses can be converging or diverging, and their type and shape directly influence the behavior of light rays in the system.
Three easy rays are essential for constructing ray diagrams, as they simplify the process and allow for a clear understanding of the image formation. These rays include the parallel ray, which runs parallel to the axis and passes through the focal point; the focal ray, which passes through the focal point and then runs parallel to the axis; and the central ray, which passes through the center of the lens and remains undeviated.
Finally, the axis is a critical reference line in ray diagrams. It is a straight line passing through the center of the lens and the focal points, serving as a guide for drawing the light rays and understanding their interactions with the lens and focal points.
By including these key elements in your ray diagrams, you can effectively analyze and predict the behavior of light in various optical systems.
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Find the distance traveled in 27 seconds by an object traveling at a constant velocity of 15 feet per second.
The distance d travelled by in object is 68.58 m
What is velocity ?
velocity is defined as rate of change of displacement d of the object with respect to rate of change in time t. In mathematics It is written as :
v = d/t
it should be noted that, velocity is nothing but speed in particular direction. That is velocity is vector quality having both magnitude and direction where as speed is just the magnitude of velocity.
1 feet = 0.3048 m
15 feet = 4.572 m
Now, calculating the distance d travelled by in object :
d = vt
d = 4.572 x 27
d = 68.58 m
Therefore, the distance d travelled by in object is 68.58 m
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Why Does Elasticity Matter?
Often, a lot of what is covered in courses has little application in the so-called "real world". In this discussion board, you need to post an entry to the discussion board stating why elasticity actually does matter in the everyday lives of businesses and consumers, using an example of a good or service as part of your explanation.
Part I
Using an example of a good or service, you will state why elasticity is applicable in the everyday lives of businesses and consumers. Please be clear in your explanation
Elasticity is of significant importance in the everyday lives of businesses and consumers as it helps them understand and respond to changes in prices and demand for goods or services. By considering elasticity, businesses can make informed decisions regarding pricing strategies, production levels, and resource allocation. Consumers, on the other hand, can assess the impact of price changes on their purchasing decisions and adjust their consumption patterns accordingly.
Elasticity, specifically price elasticity of demand, measures the responsiveness of consumer demand to changes in price. It indicates the percentage change in quantity demanded resulting from a one percent change in price. Understanding price elasticity allows businesses to determine how sensitive consumers are to changes in price and adjust their pricing strategies accordingly.
For example, let's consider the market for gasoline. Gasoline is a highly price-sensitive good, meaning that changes in its price have a significant impact on consumer demand. If the price of gasoline increases, consumers may reduce their consumption and seek alternatives such as carpooling or using public transportation. In this scenario, businesses need to consider the price elasticity of gasoline to predict and respond to changes in consumer behavior. They might lower prices to stimulate demand or introduce more fuel-efficient options to cater to price-conscious consumers.
In conclusion, elasticity matters because it provides valuable insights into the dynamics of supply and demand, enabling businesses and consumers to make informed decisions in response to price changes. By understanding elasticity, businesses can adapt their strategies to maintain competitiveness, while consumers can optimize their purchasing choices based on price sensitivity.
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Which force stops the car from moving?
The force of motion
The force of speed
The force of gravity
The force of Friction
Answer:
The force of friction.
Explanation:
Gravity keeps the car on the ground.
Motion Allows the car to move.
The force of speed doesnt make sense.
Friction would cause the car to stop moving.
Which statement about diffraction is correct?
O The amplitudes of two waves combine to appear as one big wave.
O Sound waves bend around the corners of various obstacles.
O The amplitudes of two waves combine to appear as a wave smaller than the individual waves.
O Sound waves can only travel in straight lines.
Answer:
Sound waves bend around the corners of various obstacles.
Explanation:
I took the test
chanice drives her scooter 7 kilometres north. she stops for lunch and then drives 5 kilometres east. what distance did she cover? what was her displacement?/8
By using vector
a. the distance traveled is 12 kilometres
b. the resultant displacement is (7 i + 5 j) kilometres
We need to know about vectors to solve this problem. Vector has magnitude and also direction. Displacement is included in vector. It can be written as
s = sx i + sy j + sz k
where s is displacement, sx is displacement on x-axis, sy is displacement on y-axis and sz us displacement on z-axis.
From the question above, we know that
east = positive x
south = negative y
west = negative x
north = positive y
s1 = 7 j
s2 = 5 j
The distance traveled is
s = s1 + s2
s = 7 + 5
s = 12 kilometres
The resultant displacement is
s = s1 + s2
s = 7 i + 5 j
s = (7 i + 5 j) kilometres
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If 29.5 ml of 0.150 m hcl neutralizes 25.0 ml of a basic solution, what was [oh] in the basic solution
The concentration of [OH] in the basic solution is 0.177 mol/L.
To find the concentration of [OH] in the basic solution, we first need to use the balanced chemical equation for the neutralization reaction between HCl and OH-:
HCl + OH- -> H2O
We can see from the equation that 1 mole of HCl reacts with 1 mole of OH-. Therefore, the number of moles of HCl used in the reaction is equal to the number of moles of OH- in the basic solution.
First, let's calculate the number of moles of HCl used:
n(HCl) = c(HCl) x V(HCl)
n(HCl) = 0.150 mol/L x 0.0295 L
n(HCl) = 0.004425 mol
Since 1 mole of HCl reacts with 1 mole of OH-, the number of moles of OH- in the basic solution is also 0.004425 mol.
Next, we can use the volume and number of moles of OH- to calculate its concentration:
c(OH-) = n(OH-) / V(OH-)
c(OH-) = 0.004425 mol / 0.0250 L
c(OH-) = 0.177 mol/L
Therefore, the concentration of [OH] in the basic solution is 0.177 mol/L.
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a bus velocity 20m/s towards the east and another bus has velocity 15m/s in west direction.if they start to move from a point simultaneously.what distance do they cover in 2 minutes. what will be their separation.
Answer:
Velocity towards east = 20m/s
Distance in 2 min(120 sec) = 20 x 120= 2400m = 2km
Velocity towards west = 15m/s
Distance in 2 min(120 sec) = 15 x 120 = 1800m = 1.8km
Separation= 2+1.8 = 3.8km
Explanation:
Hope it helps you:))))))
have a good day
a farsighted person has a near point of 50 cm . part a what strength lens, in diopters, is needed to bring his near point to 25 cm ?
A farsighted person has a near point of 50 cm, and to bring their near point to 25 cm, we will need a converging lens.
Let the required lens' focal length be f, and the near point be p1. We will now use the lens formula to determine the strength of the lens (in diopters).
Formula: 1/f = 1/p1 + 1/p2
Since the lens formula is expressed in meters, we must first convert the near point to meters: 50 cm = 0.5 mp1 = 0.5 m - 0.25 m (because we want the image to be formed 25 cm away from the eye) = 0.25 m
Putting in these values in the above formula, we get:1/f = 1/0.25 - 1/0.5 1/f = 4 - 2 f = 1/2 f = 0.5 m Diopters are defined as the reciprocal of the focal length in meters, and we get the strength of the lens as:
Strength of the lens = 1/f = 1/0.5 = 2 diopters. Therefore, a lens of 2 diopters strength will be required to bring the farsighted person's near point to 25 cm.
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Describe the four-step process that is required for an internal combustion engine to function. Use details to support your answer.
An internal combustion engine is an engine in which combustion takes place inside the engine and is used to generate mechanical power.
Step 1: Intake: During the intake stroke, the engine takes in air (if it is naturally aspirated) or a mixture of air and fuel (if it is fuel-injected) and compresses it. In the combustion chamber, this mixture is drawn in through the intake valve. The carburetor mixes the fuel and air, while the fuel injectors inject fuel directly into the combustion chamber.
Step 2: Compression: During the compression stroke, the piston moves back up to compress the mixture of air and fuel. The spark plug fires, igniting the compressed mixture of air and fuel, and generating a tremendous amount of heat.
Step 3: Combustion: When the spark plug ignites the fuel-air mixture, the mixture ignites and burns, causing a rapid expansion of the hot gases and the expulsion of the piston. This energy is used to generate power by pushing the piston down, which turns the crankshaft. This energy is then transmitted to the wheels via the transmission.
Step 4: Exhaust:During the exhaust stroke, the exhaust valve opens, and the piston moves up to push the hot gases out of the combustion chamber. The exhaust system then takes the hot gases away from the engine and discharges them into the atmosphere.
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If a rocket takes off from earth with a certain force what must be true about earth
If a rocket takes off from Earth with a certain force, there are several things that must be true about Earth to make this possible.
Firstly, Earth must have a gravitational field that attracts the rocket toward its center. This gravitational force pulls the rocket toward the ground, and the rocket must overcome it with a force greater than the force of gravity in order to take off.
Secondly, Earth's atmosphere must be present, as the rocket needs to push against the air molecules to create thrust and lift off the ground. Thirdly, Earth's surface must be firm enough to support the launch of the rocket, with a strong and stable launchpad to prevent any accidents.
Fourthly, Earth's rotational speed and position in its orbit around the Sun must also be taken into account, as this affects the required trajectory of the rocket for a successful launch. Overall, a combination of Earth's gravitational force, atmosphere, surface conditions, and position in its orbit all play a crucial role in enabling a rocket to take off from Earth.
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Jus need the answers <3
Answer:
blahhhhhh ummm
Explanation:
mark as brainlist pleaseeeee
A 6.0 kg box is at rest on a table. The static friction coefficient μ, between the box and table is 0.40, and
the kinetic friction coefficient is 0.20. Then, a 30 N horizontal force is applied to the box.
What is the best estimate of the magnitude of the box's acceleration?
Answer:
3.038 m/s^2
Explanation:
What we have
m = 6.0 kg
\(\mu_{k}\) = 0.20
\(\mu_{s}\) = 0.40
\(F_{applied}\) = 30 N
Since the situation is that the box has already been pushed, lets get the total net force of both components.
∑Fy = \(ma_{y}\) = 0 (bc the normal and weight cancel out each other)
∑Fx = \(F_{applied}\) - \(f_{k}\) = \(ma_{x}\) (We are going to use this equation to find acceleration)
To find the friction force
\(f_{k}\) = \(\mu_{k}\) * N
\(f_{k}\) = .20 * 6.0 kg * 9.81 m/s^2 = 11.772 N
Now we can use ∑Fx equation to actually find the acceleration of the box!
∑Fx = \(F_{applied}\) - \(f_{k}\) = \(ma_{x}\)
Plug it in
30 N - 11.772 N = 6 kg * a
Do the algebra...
a = \(\frac{30 N - 11.772 N}{6 kg}\) = 3.038 m/s^2
A. It Implies That M Is Finitely Generated. B. It Implies That M Has Nonzero Elements Of Nonzero Order. C. When Every Non-Null Element Has Null . D. In The Case That The Ring R Is A Body. E. None Of The Above Alternatives Gives A
Which of the following alternatives give a true statement. Justify your answer.
A modulus M over a ring R has a finite basis:
a. It implies that M is finitely generated.
b. It implies that M has nonzero elements of nonzero order.
C. When every non-null element has null .
d. in the case that the ring R is a body.
e. None of the above alternatives gives a true statement.
Which of the following statements are true?
a. If a subset of a module generates that whole module, then the subset cannot be
empty.
b. Every submodule S of a module M verifies the inequality C. Two different subsets of M have to generate two different submodules of M.
d. If S generates a submodule N of the module M, then contains S.
e. Neither statement is true.
The correct answer is e. None of the above alternatives gives a true statement. None of the statements in options a, b, c, and d are true when it comes to a modulus M over a ring R having a finite basis.
When a modulus M can be formed entirely from a finite set of elements, the modulus M is said to be finitely generated. M's finite basis does not, however, automatically imply that M is finitely generated. A basis is a set of linearly independent elements, and it might not be enough to produce all of the components of the modulus.
According to the assertion in option b, M must include nonzero items of nonzero order if it has a finite basis. This is untrue, though. The smallest positive number k, such that the element raised to the power of k equals the identity element, is referred to as the order of an element.
According to option c, every non-null element in a modulus with a finite basis has a null. Nevertheless, this claim is likewise untrue. It is possible for a modulus with a finite basis to have non-null elements without a null element.
According to option d, a ring R is a body, or a field, and only then can a modulus have a finite basis. However, this assertion is also untrue. Even though the ring R is not a field, a modulus can nonetheless have a finite basis. None of the given alternatives provides a true statement about a modulus M over a ring R having a finite basis.
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bill nye electricity notes
Answer:
the answer is c
Explanation:
Not
sure if I'm correct.
.bloow The fewer the number of substitutes for a good: (a.) the less elastic the demand. b. the more elastic the demand.easenoni vtitnsu c. the more elastic the supply. sesetoeb yliinau d. the less el
The fewer the number of substitutes for a good, the less elastic the demand.
The concept of elasticity measures the responsiveness of demand or supply to changes in price. When there are fewer substitutes available for a particular good, consumers have limited alternatives to switch to if the price of that good increases. As a result, the demand for the good becomes less elastic, meaning that the quantity demanded is less responsive to changes in price.
In this scenario, option (a.) is correct. When there are fewer substitutes for a good, consumers have a more limited range of choices, making them less likely to respond strongly to changes in price. On the other hand, if there are many substitutes available, consumers have more flexibility to switch to alternative goods if the price of one particular good increases, resulting in a more elastic demand.
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the complete question is
The fewer the number of substitutes for a good: (a.) the less elastic the demand. b. the more elastic the demand.easenoni vtitnsu c. the more elastic the supply. sesetoeb yliinau d. the less elastic the supply
How does the wavelength of infrared compared with the wavelength of?
According to the electromagnetic spectrum, ultraviolet light has wavelengths from 10 nm to 400 nm and infrared light from 750 nm to 1 mm.
This means that infrared light has a longer wavelength than ultraviolet light.
We know the relation between wavelength and frequency as λ = c / f
where, λ is the wavelength
c is the speed of light
f is the frequency
The above equation tells us that frequency is inversely proportional to the wavelength. In other words, if the wavelength increases, frequency decreases.
As infrared light has a longer wavelength than ultraviolet light, infrared has a lower frequency than ultraviolet rays.
The question is incomplete. The complete question is how do the wavelength and frequency of infrared light compare to the wavelength and frequency of ultraviolet light?
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A crate slides down a ramp that makes a 20∘ angle with the ground. To keep the crate from sliding too fast, Paige pushes back on it with a 69 N horizontal force.
A) How much work does Paige do on the crate as it slides 3.3 m down the ramp?
,Paige does 182.9 J of work on the crate as it slides 3.3 m down the ramp.
To determine the work done by Paige on the crate as it slides down the ramp, we need to calculate the component of Paige's force that is parallel to the direction of motion of the crate. This component will do work on the crate by exerting a force in the same direction as the crate's displacement.
We can first calculate the weight of the crate, which is given by
W = mg
where m is the mass of the crate and g is the acceleration due to gravity. We can assume that the crate is on a frictionless surface, so the force of friction is zero. Therefore, the weight of the crate is the only force acting on it parallel to the ramp. Using the angle of the ramp, we can calculate the component of the weight that is parallel to the ramp:
F_parallel = mg sin θ
where θ is the angle of the ramp, which is 20∘. We can also calculate th
m = W/g
where g is the acceleration due to gravity, which is 9.81 m/s^2.
Substituting the values, we get:
m = (F_parallel/sin θ)/g
m = (mg sin θ/sin θ)/g
m = g
Therefore, the mass of the crate is equal to g.
Next, we can calculate the force applied by Paige, which is given by:
F_applied = 69 N
Since Paige is pushing back on the crate, her force is in the opposite direction of the crate's motion, so we need to calculate the negative of F_parallel. Therefore, the net force acting on the crate is:
F_net = F_applied - F_parallel
F_net = 69 N - g sin θ
Finally, we can calculate the work done by Paige on the crate using the formula:
W = F_net d
where d is the distance traveled by the crate, which is 3.3 m. Substituting the values, we get:
W = (69 N - g sin θ) x 3.3 m
Using the value for g and θ, we get:
W = (69 N - 9.81\(m/s^2\)x sin 20∘) x 3.3 m
W = 182.9 J
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