Ritalin and the pain medication Demerol have a high risk of dependence but may be used for medicinal purposes under a doctor's supervision. These substances are _____ of the CSA list.

Answers

Answer 1

Ritalin and Demerol are both controlled substances that have a high risk of abuse and dependence.

What is the list?

Schedule II drugs are believed to have a high abuse potential that could lead to severe psychological or physical dependence. They do, however, occasionally have other known medical applications and can be prescribed by a licensed healthcare provider.

Ritalin is an example of a stimulant, whereas Demerol is an example of an opioid. Thus the drugs that have been mentioned here are drugs that are strictly controlled.

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Related Questions

What is the period of a mass-spring system with the following characteristics?

What is the period of a mass-spring system with the following characteristics?

Answers

the period of a mass-spring system with the  characteristics can be calculated using the formula T = 2π√(m/k), where m is the mass of the object and k is the spring constant. the period of the mass-spring system with the given characteristics is approximately 3.14 seconds.

A mass-spring system has the following characteristics: A spring that is initially stretched or compressed has an oscillatory motion around its equilibrium position. This is referred to as a mass-spring system.The period of the mass-spring system is the time it takes for one complete cycle, including compression and extension. The period is given by the equation

`T = 2π * √(m/k)`,

where T is the period, m is the mass attached to the spring, and k is the spring constant. Let's consider an example to better understand this formula: Suppose a mass of 5 kg is attached to a spring with a spring constant of 20 N/m. What is the period of the system?

T = 2π * √(m/k) = 2π * √(5/20) = 2π * √(1/4) = 2π * (1/2) = π ≈ 3.14s

Therefore, the period of the mass-spring system with the given characteristics is approximately 3.14 seconds.

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When jumping straight down, you can be seriously injured if you land stiff-legged. One way to avoid injury is to bend your knees upon landing to reduce the force of the impact. A 63.5-kg man just before contact with the ground has a speed of 7.89 m/s. (a) In a stiff-legged landing he comes to a halt in 3.99 ms. Find the magnitude of the average net force that acts on him during this time. (b) When he bends his knees, he comes to a halt in 0.205 s. Find the magnitude of the average net force now. (c) During the landing, the force of the ground on the man points upward, while the force due to gravity points downward. The average net force acting on the man includes both of these forces. Taking into account the directions of the forces, find the magnitude of the force applied by the ground on the man in part (b).

Answers

Answer:

a)  F = 1.26 10⁵ N, b)  F = 2.44 10³ N, c)   F_net = 1.82 10³ N  directed vertically upwards

Explanation:

For this exercise we must use the relationship between momentum and momentum

         I = Δp

         F t = p_f -p₀

a) It asks to find the force

as the man stops the final velocity is zero

         F = 0 - p₀ / t

the speed is directed downwards which is why it is negative, therefore the result is positive

         F = m v₀ / t

         F = 63.5 7.89 / 3.99 10⁻³

         F = 1.26 10⁵ N

b) in this case flex the knees giving a time of t = 0.205 s

          F = 63.5 7.89 / 0.205

          F = 2.44 10³ N

c) The net force is

         F_net = Sum F

         F_net = F - W

         F_net = F - mg

let's calculate

         F_net = 2.44 10³ - 63.5 9.8

         F_net = 1.82 10³ N

since it is positive it is directed vertically upwards

its the one with the minion profile I wish they weren't boooorn

Answers

boy do not say that , who knows

Night terrors and nightmares are
really the same event.
True
False

Answers

False

“Sleep terrors differ from nightmares. The dreamer of a nightmare wakes up from the dream and may remember details, but a person who has a sleep terror episode remains asleep. Children usually don't remember anything about their sleep terrors in the morning”

10. A plane is flying through very dense clouds with no visibility. The pilot's
instruments tell her that she is flying at a heading of 54 knots West by
103 knots South. What is the pilot's total velocity?

Answers

The pilot's total velocity is 116.3 knots in the direction of 62.3⁰.

What is the pilot's total velocity?

The pilot's total velocity is calculated by applying the principle of relative velocity.

The total velocity is also the resultant velocity and the magnitude of the pilot's total velocity is calculated by applying Pythagoras theorem as follows;

R = √ (V₁² + V₂²)

R =  √ (54² + 103²)

R = 116.3 knots

The direction of the velocity vector is calculated as follows;

tan θ = (103 knots) / (54 knots)

θ = tan⁻¹ (103/54)

θ = 62.3⁰

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1. What is an asteroid that is pulled off course by a planet's gravity and orbits around that planet called

Answers

Answer:

I don't know but take a guess from these

Explanation:

Trojan Asteroids

Moons

Satellites

trojan asteroids revolves around the planet due to gravitational force of that planet.

An asteroid that is pulled by a gravitational force of planet and orbits around that planet is called trojan asteroids. These trojan asteroids are present around the Jupiter planet. The Jupiter has a large population of trojan asteroids revolving around the planet.

The gravitational force of the planet compels the asteroid to move around the planet and prevent it from going away to the atmosphere so we can conclude that trojan asteroids revolves around the planet due to gravitational force of that planet.

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Consider 4 charges placed at the corners of a square with side 1.25m as shown. What are the magnitude and direction of the electrostatic force on Q1 resulring from other three charges?
(Note: Please put your final answer in 4 decimal places.). pls answer:)​

Consider 4 charges placed at the corners of a square with side 1.25m as shown. What are the magnitude

Answers

Answer:

 F = 2,8289 i ^ + 1,0909 j ^) 10⁻² N

F = 3.0226 10⁻² N ,  θ  = 21.16º

Explanation:

For this exercise we use Coulomb's law

         F = k q₁q₂ / r₁₂²

We also use that the force is a vector magnitude, so we must calculate each component of the force , see the adjoint for the direction of the vectors

X axis

          Fₓ = -F₁₄ + F₁₃ₓ

         

Y axis

        \(F_{y}\) = F₁₂ -F_{13y}

let's look for the expression for each force

where the side of the square is a = 1.25 m

  F₁₂ = k Q₁Q₂ / a²

  F₁₄ = k Q₁Q₄ / a²

the distance between 1 and 3 is

         d = √(a² + a²) = a √2

   F₁₃ = k Q₁Q₃ / d²

let's use trigonometry to find the components

              cos 45 = F₁₃ₓ / F₁₃

              F₁₃ₓ = F₁₃ cos 45

              F₁₃ₓ = k Q₁Q₃ / 2a²

              sin 45 = F_{13y} / F₁₃

              F_{13y} = F₁₃ sin 45

              F_{13y} = k Q₁Q₃ / 2a²  sin 45

 

Taking all terms, we substitute in the force for each axis

X axis

          Fₓ = - k Q₁Q₄ / a² + k Q₁Q₃ / 2a₂ cos 45

          Fₓ = k Q₁ / a² ( -Q₄ + Q₃ /2   cos 45)

          Fₓ = 9 10⁹ 1.5 10⁻⁶ / 1.25²   (- 4.5 10⁻⁶ + 3.5/2  cos 45  10⁻⁶)

          Fₓ = 8.64 10³ (3.2626 10⁻⁶)

          Fₓ = 2.8189 10⁻² N

Y axis

          F_{y} = k Q₁Q₂ / a² - k Q₁Q₃ /2a²   sin 45

          F_{y} = k Q₁ / a² (Q₂ - Q₃ /2 sin45)      

          F_{y} = 9 10⁹ 1.5 10⁻⁶/ 1.25²    (2.5 10⁻⁶ - 3.5/2   sin 45  10⁻⁶)

          F_{y} = 8.64 10³ (1.26256 10⁻⁶)

          F_{y} = 1.0909 10⁻² N

The result can be given in two ways

1) F = Fₓ i ^ + F_{y} j ^

     F = 2,8289 i ^ + 1,0909 j ^) 10⁻² N

2) in the form of a module and an angle, for which we use the Pythagorean theorem and trigonometry

       F = √ (Fₓ² + F_{y}²)

       F = 10⁻² √ (2,8189² + 1,0909²)

       F = 3.0226 10⁻² N

   

       tan θ = F_{y} / Fx

       θ = tan⁻¹ (F_{y} / Fₓ)

       θ = tan⁻¹ (1.0909 / 2.8189)

        θ  = 21.16º

Consider 4 charges placed at the corners of a square with side 1.25m as shown. What are the magnitude

Which graph shows the change in velocity of an object in free fall?

Which graph shows the change in velocity of an object in free fall?

Answers

Answer:

The graph of the velocity of an object in free fall would look like a straight line sloping downward. As the object falls, its velocity increases at a constant rate, so the graph of its velocity versus time will be a straight line with a negative slope. This is because acceleration due to gravity is a constant -9.8 meters per second squared, so the velocity of a free-falling object will increase by 9.8 meters per second every second.

Therefore, the graph that shows the change in velocity of an object in free fall is a straight line with a negative slope. Here is an example of such a graph:

Free Fall Velocity Graph

5. Hilda is trying to move a 40 kg couch across a level floor and pushes with a horizontal force of
150 N, but the couch does not move. What is the minimum coefficient of static friction with the
floor? Assume the acceleration due to gravity is g = 9.8 m/s2

Answers

The minimum coefficient of static friction with the floor is 0.3846.

To find the minimum coefficient of static friction with the floor, we need to consider the forces acting on the couch. In this case, the force of gravity is pulling the couch downward with a magnitude of mg, where m is the mass of the couch (40 kg) and g is the acceleration due to gravity (9.8 m/s²).

Since the couch does not move, the force of static friction between the couch and the floor must be equal in magnitude but opposite in direction to the horizontal pushing force of 150 N.

Therefore, we have the equation F_friction = F_push, where F_friction is the force of static friction.

The force of static friction can be calculated using the formula F_friction = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force.

Since the couch is on a level floor and is not accelerating vertically, the normal force N is equal in magnitude but opposite in direction to the force of gravity, which is mg.

Substituting the values into the equation, we have μs * mg = 150 N.
Solving for μs, we get μs = 150 N / (mg).
Substituting the given values, we have μ_s = 150 N / (40 kg * 9.8 m/s²).
Simplifying, we find that μs = 0.3846.

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A 8.00-kg object is hung from the bottom end of a vertical spring fastened to an overhead beam. The object is set into vertical oscillations having a period of 1.70 s. Find the force constant of the spring.

Answers

Answer:

109.32 N/m

Explanation:

Given that

Mass of the hung object, m = 8 kg

Period of oscillation of object, T = 1.7 s

Force constant, k = ?

Recall that the period of oscillation of a Simple Harmonic Motion is given as

T = 2π √(m/k), where

T = period of oscillation

m = mass of object and

k = force constant if the spring

Since we are looking for the force constant, if we make "k" the subject of the formula, we have

k = 4π²m / T², now we go ahead to substitute our given values from the question

k = (4 * π² * 8) / 1.7²

k = 315.91 / 2.89

k = 109.32 N/m

Therefore, the force constant of the spring is 109.32 N/m

(b) Which has more mass: 50 cm of gold or 50 cm of aluminum? Explain.

Answers

Gold’s molar mass is about 196 while aluminum is about 27, thus 50cm of gold has more mass

The metal wire is stretched so that its cross-section is still circular but its total length is now 10 meters. What is the resistance of the wire after stretching

Answers

I don’t know I think about 20 meters but I’m probably wrong I just need to do this so someone can answer my question

A 50gram bracelet is suspected of not being pure gold. It is dropped into a glass of water and 4 cm3of water overflows. Is the bracelet pure gold? How do you know?

Answers

Since, density of the bracelet is not equal to the density of gold, then, the bracelet is not pure gold.

To know if the bracelet is pure gold, we calculate the density of the bracelet and compare it to the density of pure gold (19.3 g/cm³).

That is, for the bracelet to pure gold,

Density of bracelet ≈ 19.3 g/cm³

What is Density?

Density can be defined as the ratio of the mass and the volume of a substance.

The formula of Density is give as

D = m/v................... Equation 1

⇒ Where:

D = Density of the braceletm = mass of the braceletv = volume of the bracelet

From the question,

⇒ Given:

m = 50 gv = 4 cm³ (an object displace an amount of water equal to it's own volume)

⇒ Substitute these values into equation 1

D = 50/4D = 12.5 g/cm³

Hence, since the density of the bracelet is not equal to the density of gold, then, the bracelet is not pure gold.

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Which of the following best compares the structures in protists and fungi that allow these organisms to explore their environment. Question 2 options: Protists and fungi move using cilia, flagella, and hyphae. Some protists move using cilia and flagella. Fungi do not move but have fast growing hyphae. Protists move using hyphae. Some fungi move using cilia, and flagella. Neither protists nor fungi have cilia, flagella, and hyphae. They obtain energy only if the food source moves by them.

Answers

Answer:

Some protists move using cilia and flagella. Fungi do not move but have fast growing hyphae.

Explanation:

trust me

a rectangular container measuring 20cmX20cmX30cm is filled withn water.What is the mass of the voulme of water in kilogram and in grams?

Answers

Answer:

12,000 grams = 12 kg

Explanation:

Volume V = 20 x 20 x 30 cm³ = 12,000 cm³

density of water d = 1 g/cm³

so the mass is 12,000 grams = 12 kg

A lowest A on a piano has a frequency of 27.5 HZ if the tension in the 2.00m string is 308N and one half wavelength occupies the spring what is the mass of the wire

Answers

The mass of the wire of lowest A on a piano is 0.00165 kg.

The frequency of a vibrating string is given by the equation:

f = (1/2L) * sqrt(T/μ)

where f is the frequency of the string, L is the length of the string, T is the tension in the string, and μ is the linear mass density of the string (mass per unit length).

We know the frequency of the lowest A on a piano is 27.5 Hz. We also know that one half wavelength occupies the string, so the length of the string is half the wavelength:

L = (1/2) * λ

The wavelength of a sound wave is given by:

λ = 2L/n

where n is the number of nodes (points of zero displacement) in the wave. For the lowest A on a piano, n = 1, so we can write:

λ = 2L

Substituting this into the equation above for L, we obtain:

L = λ/2

Now we can substitute these values into the first equation:

27.5 = (1/2)(λ/2) * sqrt(308/μ)

Simplifying, we get:

λ = 4L

308/μ = 4(27.5)^2 (1/4)

μ = 0.000824 kg/m.

Since μ = m/L, where m is the mass of the wire and L is its length, we can find the mass of the wire by multiplying the linear mass density by the length of the string:

m = μL

The length of the string is given as 2.00 m, so we can write:

m = 0.000824 kg/m * 2.00 m = 0.00165 kg

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You are asked to design a spring that will give a 1110 kg satellite a speed of 3.55 m/s relative to an orbiting space shuttle. Your spring is to give the satellite a maximum acceleration of 5.00g. The spring's mass, the recoil kinetic energy of the shuttle, and changes in gravitational potential energy will all be negligible.
(a) What must the force constant of the spring be?
(b) What distance must the spring be compressed?

Answers

Answer:

Explanation:

Kinetic energy of satellite = 1/2 m v²

= .5 x 1110 x 3.55²

= 6994.39 J

This energy comes from the elastic energy of  compressed spring

elastic energy = 1/2 k d² where k is elastic constant and d is compression in spring .

1/2 k d²  = 6994.39 J

kd² = 13988.77 --------------------------- (1)

force created by spring = k d

acceleration = force / mass

= k d / 1110

Given ,

k d / 1110  = 5 x g = 5 x 9.8 = 49

kd = 54390  ------------------------------------------------- ( 2 )

dividing ( 1 )  and ( 2 )

d =  13988.77 / 54390

= .25719 m

= 25.72 cm

kd = 54390

k x .25719 m = 54390

k = 211477.9 N /m

an7. Pressure is calculated by dividing force by theover which the force is exerted.Which state of matter will hold its shape without a container?QPressure is calculated by dividing force by the “what”over which the force is exerted?

Answers

The pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

Then, the missing word is area.

4. Two people each have a mass of 55 kg. They are both in an
elevator that has a mass of 240 kg. When the elevator
begins to move, the people and the elevator have an upward
acceleration of 1.00 m/s2. What is the net force that acts on
the elevator as it accelerates upward at 1.00 m/s2?

Answers

Answer:

350 N

Explanation:

F=ma

\(f = force \\ m = mass \\ a = acceleration\)

\(m = 2(55kg) + 240kg \\ a = 1.0 \frac{m}{ {s}^{2} } \)

Force = 350 Newtons

The net force acting on the elevator would be 350 Newtons as it accelerates upward at 1.00 m/s2.

What is Newton's second law?

Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.

The mathematical expression for Newton's second law is as follows

F = ma

As given in the problem two people each have a mass of 55 kg. They are both in an elevator that has a mass of 240 kg. When the elevator begins to move, the people and the elevator have an upward acceleration of 1.00 m/s2, then we have to find the net force acting on the elevator,

The net force acting on the elevator,

F = ma

F =(2×55 + 240)×1

  = 350 Newtons

Thus, the net force acting on the elevator would be 350 Newtons as it accelerates upward at 1.00 m/s2

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1. A student moves a box of books down the hall by pulling on a rope attached to the box. The student
pulls with a force of 185N, at an angle 25 degrees above the horizontal. The box has a mass of 35 kg.
What is the value of uk?

Answers

Answer:

the value of the uk is 400kg

Explanation:

**NEED ANSWER ASAP, H.W QUESTION**
If the proton proton chain produces gamma ray photons, why are the majority of photons we observe from the sun at visible wavelengths?

Answers

The bombardment of the gamma rays with the particles in outer space reduces the energy thus what we see is mostly visible light of lower energy.

What is nuclear fusion?

We know that nuclear fusion is the process by which two light nuclei are combined in order to obtain a heavier nucleus with the emission of a tremendous mount of energy. Due to the tremendous amount of energy that is required when we are carrying out a fusion reaction, it does occur only in the sun.

The  proton proton chain produces gamma ray photons. We know that gamma rays have a very high energy but the energy of the gamma photons is reduced as it is bombarded with the particle in the atmosphere.

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Set local ground level to 700 ft, and record the inches of mercury.

What is the altimeter reading in inches of mercury (from the Kollsman window)?

Answers

The main way in which an altimeter measures the altitude of an object is by calculating the location's air pressure.

What is an Altimeter?

This refers to the instrument that is used to measure the altitude of an object when it is at a fixed level.

Hence, we can see that an altimeter should NOT be confused with a barometer, because although they both measure pressure, a barometer calculates the change in air pressure and elevation based on available weather.

Please note that your question is incomplete so I gave you a general overview to help you get a better understanding of the concept.

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Set local ground level to 700 ft, and record the inches of mercury.What is the altimeter reading in inches

A 14.0 Kg ball is dropped from a building, the building has aheight of 255 m. What is the Potential energy of the ball?

Answers

Given data

*The given mass of the ball is m = 14.0 kg

*The given height is h = 255 m

*The value of the acceleration due to gravity is g = 9.8 m/s^2

The formula for the potential energy of the ball is given as

\(U_p=mgh\)

Substitute the known values in the above expression as

\(\begin{gathered} U_p=(14.0)(9.8)(255) \\ =34986\text{ J} \end{gathered}\)

Hence, the potential energy of the ball is 34986 J

A roller coaster is at a peak of 20m and has a mass of 900kg. What is the potential energy of the roller coaster?
O 100000 J
10000 J
O 9.8 J
O 176400 J

Answers

The potential energy of the roller coaster is 176,400 J (joules).

The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.

In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).

Using the formula, we can calculate the potential energy:

PE = mgh

= (900 kg)(9.8 \(m/s^2\))(20 m)

= 176,400 J

Therefore, the potential energy of the roller coaster is 176,400 J (joules).

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Find the Magnitude of the resultant vector (the actual
path of the boat).
The picture is a little blurry, so here are the stats:
Velocity of the boat is 0.75 m/s
Velocity of the river is 1.2 m/s

Answers

The magnitude of the resultant vector, representing the actual path of the boat, is approximately 1.42 m/s.


To find the magnitude of the resultant vector, we need to consider the boat's velocity and the velocity of the river. The boat's velocity is given as 0.75 m/s, and the river's velocity is given as 1.2 m/s.

Since the boat is moving in a river, we can think of the boat's velocity as a combination of two velocities: its own velocity and the velocity of the river. The resultant vector represents the actual path of the boat, considering both velocities.

To calculate the resultant vector, we can use vector addition. The magnitude of the resultant vector can be found by taking the square root of the sum of the squares of the boat's velocity and the river's velocity. Mathematically, we have:

Resultant magnitude = √(boat velocity^2 + river velocity^2)

Plugging in the given values, we have:

Resultant magnitude = √(0.75^2 + 1.2^2)

= √(0.5625 + 1.44)

= √2.0025

≈ 1.42 m/s

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A stone is dropped from the top of a high cliff with zero initial velocity. In which system is the net momentum zero as the stone falls freely

Answers

Answer:

A system that includes the stone and the earth.

Explanation:

If the system of being dropped from the height of the cliff consists of just the stone alone, then it means that its momentum will certainly undergo changes as it falls freely. However, If the system is now expanded to include not only the stone but also the Earth, then it implies that the momentum of the stone which is in the downward direction will be equal and opposite to the momentum of the Earth in the upwards direction towards the stone. Therefore, the momentum will cancel out and net momentum will be zero.

A system of stone and earth can result to a net zero momentum.

Conservation of linear momentum

The principle of conservation of linear momentum states that the sum of the initial momentum is equal to the sum of final momentum.

\(m_1u_1 + m_2 u_2 = m_1v_1 + m_2 v_2\)

A system that consists a linear system of stone and earth can result to a net zero momentum.

Thus, a system of stone and earth can result to a net zero momentum.

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Which of the following is NOT an important phenomenon that commonly erodes and weathers exposed rock outcrops to form sedimentary material?
a) Lightning
b) Wind
c) Rain
d) Freezing/Thawing

Answers

Answer:

Explanation:

While each of these can cause erosion and weathering, lightning is probably the least important as it occurs less frequently and affects a much smaller surface area when it strikes.

Wind is not very effective by itself, but it can carry abrasives which work to degrade rock surfaces. It covers a very large area at once so the net effect can be moderate to large especially desert areas where plants are not readily available to disrupt the flow.

Rain covers huge areas and is quite common.

Freezing/Thawing cycles cover large areas and are quite common in the temperate and arctic latitudes and even in tropical altitudes.

Attached is a photo taken atop Half Dome in Yosemite National Park showing two of thousands of divots in the rock there caused by lightning strikes. The current in the lightning heats the stone causing water trapped in it to flash to steam. The increased pressure inside the stone can overwhelm the material strength and blow rock chunks over a fairly good sized area. This is a fairly rapid weathering and erosion when it occurs, but that is typically limited to a few dozen days per year and occurs mostly on high ground where lightning is more likely to strike earth.

Which of the following is NOT an important phenomenon that commonly erodes and weathers exposed rock


What is Energy in physics?

Answers

Answer:

Energy, in physics, the capacity for doing work. It may exist in potential, kinetic, thermal, electrical, chemical, nuclear, or other various forms. There are, moreover, heat and work—i.e., energy in the process of transfer from one body to another.

Explanation:

Hope this helps!

A warning buoy A warning buoy is observed to rise every 4.3 s as crests of waves pass by it.

(a) What is the period of these waves?is observed to rise every 4.3 s as crests of waves pass by it.

Answers

A warning buoy is observed to rise every 4.3 s as crests of waves pass by it. The period of these waves is (T) = 4.3s

What is period?

The period defines the quantity or the required time to complete one single oscillation. It has a synonym called time period. It can be measured in Seconds.

How can we calculate the period?

According to the question,

A warning buoy is observed to rise every 4.3 s as crests of waves pass by it.

According to the definition of time period, time between two consecutive peaks of the oscillation called the time period.

So, According to the question the period of these waves is (T) = 4.3s

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A student pushes a baseball of m = 0.15 kg down onto the top of a vertical spring that has its lower end fixed to a table, compressing the spring a distance of d = 0.18 meters from its original equilibrium point. The spring constant of the spring is k = 690 N/m. Let the gravitational potential energy be zero at the position of the baseball in the compressed spring. !
What is the ball’s velocity, in meters per second, at half of the maximum height relative to the equilibrium point?

Answers

The ball's velocity at half of the maximum height relative to the equilibrium point is approximately 1.727 m/s.

How do you calculate the ball's velocity at half the maximum height?

To solve this problem, we make useof the law of conservation of energy. The initial potential energy of the system (when the ball is at its highest point before being released) is equal to the final potential energy (when the ball reaches half of its maximum height above the equilibrium point) plus the final kinetic energy.

Initial potential energy = mgh = 0.15 kg x 9.81 m/s² x 0.18 m = 0.26523 J

At half of the maximum height, the ball has traveled a distance of 0.09 meters above the equilibrium point.

Final potential energy = mgh = 0.15 kg x 9.81 m/s² x 0.09 m = 0.132615 J

To find the final kinetic energy, we can use the fact that the spring potential energy at half of the maximum height is equal to the initial potential energy minus the final potential energy:

Spring potential energy = (1/2)kx² = (1/2)(690 N/m)(0.18 m - 0.09 m)² = 0.008415 J

Final kinetic energy = Initial potential energy - Final potential energy - Spring potential energy

Final kinetic energy = 0.26523 J - 0.132615 J - 0.008415 J = 0.1242 J

Finally, we can use the equation for kinetic energy to find the velocity of the ball at half of the maximum height:

Final kinetic energy = (1/2)mv²

v = \(\sqrt{(2 x Final kinetic energy / m) }\)= \(\sqrt{(2 x 0.1242 J / 0.15 kg)}\) = 1.727 m/s

Therefore, the ball's velocity at half of the maximum height relative to the equilibrium point is approximately 1.727 m/s.

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