For a group class project, students are building model roller coasters. Each roller coaster needs to begin at the top of the first hill, where a horizontal spring that is initially compressed 0.25 m will push a small car forward.

A hill with a compressed spring at the top. There is a car sitting against the compressed spring. The portion of the hill is vertically colored orange, the middle section is vertically colored yellow and the last section colored green.
Each group of students will choose a car and a spring to push the car and then build a track. The assignment is to make the car go 5.0 m/s when it reaches the bottom of the first hill. Four groups of students choose springs and build tracks as described in the table.

A 4 column table with 4 rows. The first column is labeled group with entries A, B, C, D. The second column is labeled car mass in kilograms with entries .75, .60, .55, .84. The third is labeled spring constant in newtons per meter with entries 65, 35, 40, 32. The last column is labeled hill height in meters with entries 1.2, .90, 1.1 , .95.
Which group’s roller coaster will most likely make the car travel closest to 5.0 m/s when it is at the bottom of the first hill?

A
B
C
D

When you squeeze marshmallow its volume decreases.

Mass remains constant

ρ = m/v ,So density increases as volume decreases.

The amount of three-dimensional space that is occupied is measured by volume. [1] It is frequently measured quantitatively using SI-derived units (such the cubic meter and litre) or by other imperial or US-standard units. Volume and length (cubed) are related concepts. The volume of a container is typically understood to be the capacity of the container, i.e., the amount of fluid (gas or liquid) that the container might store, rather than. the amount of space. the container. itself occupies.

Volume was first determined using naturally occurring vessels of a comparable shape and later with standardized containers. Arithmetic formulas make it simple to determine the volume of several straightforward three-dimensional shapes. Integral calculus can be used to determine the volumes of more complex shapes.

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The natural length of the spring is 4cm.

Solution:

15/9 = 19k - ka/13k - ka

15/9 = 19 - a/13 - a

195 - 15a = 171 - 9a

24 = 6a

a = 4cm

The term equilibrium length is sometimes used to describe stationary modal distributions. H. Length of multimode optical fiber required to achieve static mode distribution from given excitation conditions. Spring Balance The balance length of a spring is the length when no force is acting.

This is the natural state of spring. Spring constant A measure of elasticity. There is a point where the force and weight of the spring are equal and the directions are opposite. This point is called the equilibrium position. If the masses are in different positions, a net force called the restoring force is directed toward the equilibrium position.

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To find the apparent position of the fish to an observer outside the bowl, we can use the lens equation:

1/p + 1/q = 1/f

where p is the distance from the object (the fish) to the center of the lens (in this case, the center of the fishbowl), q is the distance from the image to the center of the lens, and f is the focal length of the lens.

The focal length of a lens is given by the formula:

f = (n-1)R/2(n-1)

where R is the radius of the lens (in this case, the radius of the fishbowl) and n is the refractive index of the lens material (in this case, water).

Since the diameter of the fishbowl is 28.0 cm, the radius is 14.0 cm. The refractive index of water is approximately 1.33, so the focal length is approximately 8.5 cm.

To find the apparent position of the fish, we need to find p and q. If we let q be the distance from the image to the center of the lens, then the distance from the fish to the center of the lens is p = R - q.

Substituting these values into the lens equation, we get:

1/p + 1/q = 1/f

1/(R-q) + 1/q = 1/f

Solving this equation for q, we find that q = R/2 = 14.0 cm/2 = 7.0 cm.

This means that the apparent position of the fish is 7.0 cm from the center of the fishbowl.

To find the magnification of the fish to an observer outside the bowl, we can use the formula:

m = -q/p

Substituting the values we found above, we get:

m = -7.0 cm / (14.0 cm - 7.0 cm) = -1/2 = -0.5

This means that the fish is magnified by a factor of -0.5, or half its size.

The car traveled at an average speed of 97 miles per hour and the truck traveled at an average speed of 78 miles per hour.

Average speed is a measure of the distance traveled over time, or the rate at which someone or something is moving. It is calculated by dividing the total distance traveled by the total amount of time it took to travel that distance. For example, if a person runs one mile in five minutes, their average speed is 12 miles per hour (mph).

To calculate this, we must use the equation:

Distance = Rate x Time

For the car: 1448 = (97 + 19) x 8

For the truck: 1448 = (78 - 19) x 8

Therefore, the car traveled at an average speed of 97 mph and the truck traveled at an average speed of 78 mph.

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The correct answer is option a. A red indicator light on a dashboard typically indicates a serious vehicle malfunction that needs to be addressed immediately.

This type of light is usually used to indicate a problem that could cause damage to the vehicle or affect its safety if not addressed promptly. It is important to pay attention to a red indicator light and to have the vehicle checked by a mechanic as soon as possible to diagnose and fix the problem.

A red indicator light on a dashboard typically indicates a serious or critical issue with the vehicle that requires immediate attention. Ignoring this light could lead to further damage or safety concerns. It is important to have the vehicle checked by a mechanic as soon as possible.

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It is moving with a speed of 3v.

The primary indication of an object's position and speed is its velocity. It is the distance that an item travels in one unit of time. The displacement of such item in one unit of time is the definition of velocity.

Given, initial velocity, u = 0

  velocity at distance d = v

by applying the concept of equation of motion,

v² = u² + 2as

v² = 0+2a×d

a = v²/2d

now, velocity at distance 8d, v°² = v² + 2a×8d

                                                v°² = v² + 2×v²/2d×8d

                                                v°² = v² + 8v²

                                                v° = √9v²² = 3v

It is moving with a speed of 3v.

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The kinetic energy of the horse and rider is equal to 1/2 (mass)(speed)2. 440 joules are equal to KE = 1/2 (55 kg) (4 m/s) at 4.0 m/s. KE = 1/2 (55 kg) (6 m/s) at a speed of 6.0 m/s. 2, or 990 joules. She added 550 joules to her own and her vehicle's kinetic energy.

The proportion of substances involved in any item and body serves as the most accurate definition of weight. We see mass in everything around us. Taking a table, chair, your bed, a football, and a glass as examples.

The quantity of matter or other constituents that make up an item is its mass. It is measured in kilograms, which can be shortened to kg. It's critical to keep in mind that mass and weight are two distinct concepts.

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Answer:

v = 3231.09887 m/s

Explanation:

The attached image includes the steps to get to the answer provided.

Through the equation of Continuity, The diameter of the pipe and the speed of the fluid are inversely proportional to each other.

According to the equation of Continuity,

Area multiplied by velocity results in a constant., A*v = Constant

Thus, the Area or diameter is inversely proportional to the speed or flow of the fluid.

The cross-sectional area of the pipe has an inverse relationship with flow velocity at any given flow rate.

Higher flow rates result from smaller pipes; slower speeds result from larger pipes. According to the continuity equation, we can increase the volume flow rate, or the velocity of the fluid passing through the pipe, by reducing the pipe's diameter. The fluid velocity is unaffected by the pipe's length, whether it is longer or shorter.

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The shear force V at A is 7.21 kN, between A and C is 4.01 kN, and the moment M at the support A is -7.22 kN.m

Consider forces acting along y direction:

∑Fy = 0

Ra + Rc = 1.4 + 1.8   .... equation (1)

Take a moment of A ie:

∑Ma = 0

1.4 x 3.1 + 1.8 x 1.6 + 1.8 + Rc = 0

Rc = 4.01kN (left direction)

From equation (1)

Ra + Rc = 1.4 + 1.8

Ra - 4.01kN = 1.4 + 1.8

Ra = 1.4 + 1.8 + 4.01

Ra = 7.21 kN

Consider free body diagram of portion BC: (see in the picture)

Shear force calculation:

Vb= 4.01kN

Consider free body diagram of portion AC:(see in the picture)

Taking a moment of A ie..

∑Ma = 0

Ma + 4.01 x 1.8 = 0

Ma + 7.22kN.m = 0

Ma = -7.22kN.m

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Maximum theoretical efficiency is 67.2%.

What is Maximum theoretical efficiency?
The utmost efficiency that a heat engine may achieve when working

between two temperatures is known as the Carnot Efficiency.
The degree of heat that the high temperature reservoir runs at ( T Hot ).
The degree of heat in the low temperature reservoir ( T Cold ).
The two temperatures in the case of a car are:

the temperature of the engine's combustion gases ( T Hot ).

The temperature at which the engine's gases are released ( T Cold ).

The maximum theoretical efficiency of this engine is the efficiency of a Carnot engine connected between the same two reservoirs, found from Equation
e C=1− T h

Substitute numerical values:
e C​ =1− 2143.15
703.15
=0.672
=67.2%
Maximum theoretical efficiency is 67.2%.

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An object must have a MOID of 0.05 AU or less in order to be considered a potentially hazardous object. This distance is equivalent to 4.65 million miles. Objects with a MOID between 0.05 and 0.25 AU are considered Near Earth Objects and could potentially become potentially hazardous object (PHOs) in the future.

A potentially hazardous object (PHO) is an asteroid or comet that has an orbital path that comes close enough to Earth to pose an impact hazard. The minimum distance that an object must be from Earth to be considered a PHO is defined by the International Astronomical Union (IAU). The IAU defines a PHO as an object whose Minimum Orbit Intersection Distance (MOID) with Earth's orbit is 0.05 AU or less.

In astronomical units (AU), the minimum distance for an object to be considered a PHO is 0.05 AU. An AU is equivalent to the average distance from Earth to the Sun, or about 93 million miles. Therefore, the minimum distance for an object to be considered a PHO is about 4.65 million miles.

The MOID is the closest approach an object can make to Earth’s orbit. The MOID of an asteroid or comet is calculated based on its orbital elements, such as its semi-major axis and eccentricity. An object with a MOID of 0.05 AU or less is considered to have a close enough approach to Earth’s orbit to pose an impact hazard.

The IAU also defines an object as a “Near Earth Object” (NEO) if its MOID is between 0.05 and 0.25 AU. NEOs are objects that could potentially come close enough to Earth to cause an impact hazard, but are not considered to be PHOs because the risk is not as high.

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Answer:

The coefficient of friction between all contact surfaces is 0.4. The force, necessary to move the block B with constant velocity, will be (g = 10 m/s)

The coefficient of friction between all contact surfaces is 0.4. The force, necessary to move the block B with constant velocity, will be (g = 10 m/s).

Two blocks A and B of masses 5 kg and 1 kg are connected with the help of massless strings and the system is just at the verge of slipping. The coefficient of static friction between the block A and surface below it is necessary to move the block B.

Static friction is the friction that exists between two surfaces that are not trying to move over each other and which must be overcome before one object starts moving the other.

Two blocks are static equilibrium indicates that the force acting on both blocks is equal.

The frictional force acting on block A is calculated as follows:

Frictional force =  coefficient of static friction * normal reaction

Normal reaction on Block A = 30 * 9.8

The coefficient of static friction between block A and the surface = 0.55

Frictional force = 30 * 9.8 * 0.55

Force on Block B = 161.7

Mass of Block B = 161.7 / 9.8

Mass of Block = 18 kg

Therefore, The coefficient of friction between all contact surfaces is 0.4. The force, necessary to move the block B with constant velocity, will be (g = 10 m/s).

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the oil drum traveled a distance of approximately 1.56 meters.

To find the distance that the oil drum traveled, we need to use the equation for average acceleration:

d = (vf^2 - vi^2) / 2a

where d is the distance traveled, vf is the final velocity, vi is the initial velocity, and a is the acceleration.

In this case, we are given that the final velocity is 3.0 m/s, the initial velocity is 0 m/s, and the acceleration is 520 N / 180 kg = 2.89 m/s^2. Substituting these values into the equation, we get:

d = (3.0^2 - 0^2) / 2 * 2.89

= 9 / 5.78

= 1.56 m

Therefore, the oil drum traveled a distance of approximately 1.56 meters.

If a photon's frequency is greater when it is absorbed by an electron, the electron will gain more energy.

Two fundamental quantum-mechanical particles, photons and electrons, have entirely distinct characteristics. The e is an elementary particle found in every atom, whereas the photon is a sort of subatomic particle that serves as an energy carrier.

The basic unit of light would be both commonplace and surprising. Others may just refer to what scientists refer to that as photons as light. Particles are the tiniest electro magnetism packets known as quanta of light.

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The acceleration of the center of mass of the ball is a =g*sin(β)/1.4 and  K=tanβ is the absolute minimum of the static friction coefficient.

A sort of opposition force known as frictional force attempts to counteract the motion of the body by acting on the surface of the body. Newton is its unit (N). It is described mathematically as the sum of the normal reaction and the coefficient of friction.

(a) A solid sphere rolling uphill has the equation of motion

M*g sinβ-(2/5)M*a = M*a, where an is the acceleration of the center of mass and mgcosβ = R.

We know that the static friction F=μR

By rearranging above formulas we get

2/5M*a + M*a = Mgsinβ

7/5a = gsinβ

Then a = gsinβ/1.4

(b) In the meantime, the normal force or maximum static friction force is equal to kmgcosβ, where k is the static friction's minimum coefficient. To prevent slippage, the frictional force must be less than the maximum static friction force.

Equating the two terms, we get: mgsinβ = kmgcosβ, k = (sinβ/cosβ) = tanβ.

As a result, k=tanβ is the lowest static friction coefficient.

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The force needed to break another wire of the same length and material but twice the diameter is 200N.

Because the wires are made of the same material, their modulus of elasticity must be the same.

As a result, the ratio of longitudinal stress to longitudinal strain (Young's Modulus of Elasticity) must be the same. Now, the strains in both wires must be the same before they break.

Therefore,

stress = Young's modulus × strain,

both wires must be the same.

Because the second wire has a diameter twice that of the first, its area of cross section is four times that of the first. As a result, in order to generate the same stress, the force applied to the second wire must be four times that applied to the first wire.(since stress = force/cross section area).

Thus, the force required to break the second wire is 4200=800N.

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Answer:

Approximately [tex]4.16 \times 10^{3}\; {\rm m}[/tex] (or equivalently, [tex]4.16\; {\rm km}[/tex]) assuming this planet is spherical.

Explanation:

Let [tex]m[/tex] denote the mass of the ball. If the speed of the ball is [tex]v[/tex], the kinetic energy of the ball will be [tex](\text{KE}) = (1/2)\, m\, v^{2}[/tex].

Assume that the planet is spherical. Let [tex]r[/tex] denote the radius of the planet. Let [tex]M[/tex] denote the mass of this planet, and let [tex]G[/tex] denote the gravitational constant.

On the surface of this planet, the gravitational potential energy [tex](\text{GPE})[/tex] of this ball will be [tex](\text{GPE}) = (-G\, M\, m) / (r)[/tex]. (Note the negative sign. The ball is trapped inside the gravitational field of the planet, and it takes energy input to bring the ball out of this field.)

The ball is at its escape speed [tex]v_{e}[/tex] if the sum of [tex](\text{KE})[/tex] and [tex](\text{GPE})[/tex] at the surface of the planet is [tex]0[/tex]. In other words:

[tex](\text{KE}) + (\text{GPE}) = 0[/tex].

[tex]\begin{aligned}\frac{1}{2}\, m\, v^{2} + \frac{- G\, M\, m}{r} = 0\end{aligned}[/tex].

Rewrite this equation and solve for radius [tex]r[/tex].

[tex]\begin{aligned}\frac{G\, M\, m}{r} = \frac{1}{2}\, m\, v^{2}\end{aligned}[/tex].

[tex]\begin{aligned}r &= \frac{v^{2}}{2\, G\, M}\end{aligned}[/tex].

[tex]\begin{aligned}r &= \frac{2\, G\, M}{{v_{e}}^{2}} \\ &= \frac{2\, (6.67 \times 10^{-11}\; {\rm m^{3}\cdot kg^{-1} \cdot s^{-2})\, (1.56 \times 10^{15}\; {\rm kg})}}{(5.00\; {\rm m\cdot s^{-1}})^{2}} \\ &\approx 8.32 \times 10^{3}\; {\rm m}\end{aligned}[/tex].

False; running up stairs really requires less exertion against gravity than leisurely walking up them.

Gravity, which means "weight" in Latin, is a basic interaction in physics that causes all objects with mass or energy to be attracted to one another. By far the weakest of the four basic interactions, gravity is 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force, and 1029 times weaker than the weak interaction. As a result, it has no discernible impact on the level of subatomic particles. The motion of planets, stars, galaxies and even light are all governed by gravity, which is the most important interaction between things at the macroscopic level.

On Earth, gravity imparts weight to tangible objects, and the Moon's gravity is what causes sublunar tides in the seas.

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The force constant of the spring is  3.53 * 10^3 N/m,  the period of oscillation of the fish is 0.115 s and  the maximum speed it will reach is 0.869 m/s

Hook's law states that:

where F is the force applied on the spring, k is the spring constant, x is the stretching of the spring.

In this problem, we have

Solving the equation for k, we find the spring constant: k = 3539 N/m

The period of oscillation of a spring-mass system is

T= 2π√M/K

In this case,

m = 65.0 kg

T=2π√(65/3539) = 0.869s

k = 3539 N/m

Substituting into the formula, the period of oscillation of the mass is 0.869 sec.

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Faraday is credited with discovering that a fluctuating magnetic field causes a current to flow.

According to Faraday's Law, a current whose magnitude depends on the rate of change of the magnetic field will flow when the strength of a magnetic field changes within a loop of wire. A shifting magnetic field causes an induced current. The induced current is accompanied by an induced emf. Without a battery in the circuit, a current can be generated. The induced emf can be described using Faraday's law of induction. According to Faraday's law, an electromotive force is created when the magnetic flux or magnetic field varies over time.

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Option A is a true. An SUV strikes a motorcycle that is standing still. The motorcycle can withstand more force than the SUV since it is stationary.

Every time one object applies force to another, the other object applies an equal and opposing force to the first. His third law argues that there is an equal and opposite reaction to every action (force) in nature. If you push a truck and a vehicle with the same amount of effort, the car will accelerate faster than the truck since it is lighter. Due to the full shopping cart's greater bulk compared to the empty one, it is simpler to push one than the other.

In the early stages of having enough grip, engineers frequently discuss "power to weight ratio" because this impacts acceleration. Since it takes longer (more time) to accelerate a heavier car with the same amount of power to go the same distance, more fuel is consumed.

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The final image is found to be 2.37cm in front of the eyepiece.

The focal length of the eyepiece is 2.00 cm and it is placed at a distance of 19.00 cm in front of the objective lens.

Now, we can use the lens formula to find the position of the image,

1/v - 1/u = 1/f

Where,

v is the position of the image,

u is the position of the objective in front of the eyepiece,

f is the focal length of the eyepiece.

Now, putting values,

1/v - 1/(-19) = 1/(-3)

The focal length and u are taken negative because of the sign standard sign convention of the lens.

1/v+1/19 = -1/3

Solving further,

v = -2.38 cm

So, the final image is 2.38 cm in front of the eyepiece.

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Upon calculation the horizontal velocity of the tennis ball at A so that is just clears the net at B is found to be 39.7 ft/s

This question can be solved using newton's equation of motion.

Equations of motion in physics are equations that explain how a physical system behaves in terms of how its motion changes over time. The behavior of a physical system is described in further detail by the equations of motion as a collection of mathematical functions expressed in terms of dynamic variables. Typically, these variables are time and geographical coordinates, but they might also have momentum components.

Applying newton's equation of motion in vertical direction,

[tex]s_{y}= s_{0y} +ut+\frac{1}{2}gt^{2}+ut[/tex]

Here, u= 0

[tex]s_{y}=3ft\\ s_{0y}=7.5ft[/tex]

g= -32.2 fts⁻²

Putting in equation

3= 7.5+0-[tex]\frac{1}{2}[/tex]×32.2×[tex]t^{2}[/tex]

t= 0.5287 seconds

Applying newtons's equation in horizontal direction

[tex]s_{x}=s_{0x}+u_{x}t[/tex]

Here,

[tex]s_{x}= 21 ft\\s_{0x}= 0\\ t= 0.5287 seconds[/tex]

21= 0+[tex]u_{x}[/tex]×0.5287

[tex]u_{x}= 39.72 ft/s[/tex]

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Answer:

Newton's First Law of Motion (aka Law of Inertia)

Explanation:

The energy required to change the temperature from 26°C to 64°C is 47500 J.

Heat is a form of energy that can be transferred from one object to another due to different temperatures.

The heat required to raise the temperature is expressed by the equation:

                                          Q = m.c.ΔT

Q: Heat (Joules)

m: mass (kg)

ΔT: temperature change (°C)

c: specific heat (J/kg°C)

In the given question mass are 3 kg and the temperature change from 26°C to 64°C. (the specific heat is 4186 J/kg°C)

Q = m.c.ΔT

Q = 3 x 4186 x (64°C - 26°C)

Q = 12588 x 38°C

Q = 47720 J ≈ 47500 J

So, the energy required to change the temperature is 47500 J.

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The binding energy per nucleon of 235-U and 137-Cs is given below when a nucleus of 235u undergoes fission

235-U = 7.6 MeV

137-Cs = 8.39 MeV

What is the 235-U and 137-Cs nucleons' binding energy?

The following equation gives a nucleus' binding energy:

mc2 = BE, where BE is the binding energy.

m is a mass defect.

For 235U, c = 931.49 MeV/u is the speed of light.

A=235 m=1.9150664 BE=1.9150664 *931.49 MeV/u BE=1783.8648 MeV

The equation BE/A BE/A = 1738.648 MeV / 235 BE/A = 7.6 MeV determines the binding energy per nucleon.

Binding energy for 137-Cs is:

BE = 1.23383 u * 31.49 MeV/u, where m is the mass defect, giving 1149.3003 MeV.

The binding energy per nucleon, BE/A, is as follows:

A is 137 in the instance of 137-Cs, hence BE/A equals 1149.3003 MeV / 137 BE/A is 8.39 MeV.

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Specific heat capacity of a substance is the amount of heat required to raise the temperature by one degree Celsius of one gram of a substance. Therefore, the total energy change of this reaction is -4,594.82 kJ/mol and  reaction is exothermic reaction.

Enthalpy term is basically used in thermodynamics to show the overall energy that a matter have. Mathematically, Enthalpy is directly proportional to specific heat capacity of a substances.

ΔH = Hp - Hr

Hp = energy of the product or lattice energy = -2343.52 kJ/mol

Hr = energy of the reactant or hydration energy= 2251.3 kJ/mol

substituting all the given values in the above equation, we get

ΔH = -2343.52 kJ/mol - 2251.3 kJ

ΔH = -4,594.82 kJ/mol

Since the sing of energy is negative, so reaction is exothermic reaction.

Therefore, the total energy change of this reaction is -4,594.82 kJ/mol and  reaction is exothermic reaction.

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Yes all waves have the back and forth pattern of motion.

A wave is described as a propagating dynamic disturbance of one or more quantities that can be periodic, in which case those quantities oscillate repeatedly about an equilibrium value at some frequency.

Waves come in major types which are :

Transverse waves are like those on water, with the surface going up and down, and longitudinal waves are like of those of sound, consisting of alternating compressions and rarefactions in a medium.

All types of waves have the same fundamental properties of reflection, refraction, diffraction and interference, and all waves have a wavelength, frequency, speed and amplitude.

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In the original Milgram study, what percentage of participants displayed complete compliance, administering shocks of 450 volts About 40% that they believed were lethal.

The Milgram experiment(s) on conformity to authoritative persons were a series of social psychology research carried out by Yale University psychologist Stanley Milgram. The willingness of 40 research participants, males from various occupations and educational levels, to follow orders from an authority figure that conflicted with their own moral values was examined.

The volunteers were led to believe that they were taking part in a different experiment in which they had to administer electric shocks to a "learner." If these electric shocks had been real, they would have increased over time to lethal levels.

Unexpectedly, the experiment revealed that a very high percentage of the lab rats would fully comply with the instructions, with every person reaching 300 volts and 65% reaching the full 450 volts.

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