when the cart reached the edge of the track and stopped (before it started going back to the hand), what was the acceleration?

Answers

Answer 1

The speed increases but acceleration decreases.

In mechanics, acceleration is the price of change of the velocity of an object with respect to time. Accelerations are vector quantities. The orientation of an item's acceleration is given by means of the orientation of the net force performing on that object.

Acceleration is, rate at which pace modifications with time, in phrases of each speed and direction. A point or an item transferring in a direct line is increased if it hurries up or slows down. motion on a circle is multiplied even supposing the speed is regular, due to the fact the path is constantly changing.

Acceleration. pace is the fee of alternate of displacement. Acceleration is the charge of change of pace. speed is a vector quantity as it includes both value and course. Acceleration is also a vector amount as it's far simply the rate of trade of velocity.

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Related Questions

a cluster with a lot of type o and b stars, but no bright k or m stars, is very group of answer choices old. faint. young. poor in heavy elements. densely packed.

Answers

Very young clusters lack luminous K or M stars but have a large number of Type O and B stars.

Define Measuring the Age of a Star Cluster?

We can learn a lot from star clusters that is applicable to the study of stars in general. The fundamental justification for this is because all of the stars in a cluster are thought to have formed practically simultaneously from the same cloud of interstellar space, therefore they should all have extremely similar characteristics. Accordingly, the primary distinguishing factor among stars in a cluster is their mass, yet if we examine the characteristics of one star (age, distance, composition, etc.).

The brilliant O and B stars in the open clusters emit powerful radiation that can ionize neighboring gas and produce emission nebulae as well. The brightest stars in an open cluster make up the majority of the cluster's brightness.

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The siren of a fire engine that is driving northward at 31.0 m/s emits a sound of frequency 2160 Hz. A truck in front of this fire engine is moving northward at 19.0 m/s.
A. What is the frequency of the siren's sound that the fire engine's driver hears reflected from the back of the truck (Hz)?
B. What wavelength would this driver measure for these reflected sound waves (m)?

Answers

(a) The frequency of the siren's sound that the fire engine's driver hears reflected from the back of the truck is 2243.9Hz.

(b) The wavelength of the reflected sound waves by the listener is 0.143 m.

We use the principle of Doppler's effect to find the results.

What is the Doppler's effect?

The Doppler's effect is a phenomenon when the source of a wave and an observer move relative to each other, the frequency heard is not the same with the actual frequency.

The equation of the Doppler's effect is

f₀ = (v + v₀) fs / (v + vs)

Where

f₀ = observer frequency of soundv = speed of sound waves (340 m/s)v₀ = observer velocityvs = source velocityfs = actual frequency of sound waves

Note:

v₀ (-) if it moves away from the sound source.vs (-) if it moves closer to the observer.

There are a truck and a fire engine emitting a siren sound moving in the same direction.

The actual frequency, fs = 2160 Hz.The fire engine velocity (source), vs = 31.0 m/s.The truck velocity (observer), v₀ = 19.0 m/s.

Determine the frequency and the wavelength of the sound waves heard by the listener in the front!

We have the truck is in front of the fire engine. So, the sound source moves closer and the observer moves away. Then, frequency of the sound waves heard by the observer is

f₀ = (v - v₀)/(v - vs) × fs

f₀ = (340 - 19.0)/(340 - 31) × 2160

f₀ = (321/309) × 2160

f₀ = 2243.9 Hz

The wavelength of the sound waves heard by the observer is

λ₀ = (v - v₀) / f₀

λ₀ = (340 - 19) / 2243.9

λ₀ = 321 / 2243.9

λ₀ = 0.1430545

λ₀ = 0.143 m

Hence,

(a) The observer frequency of sound is 2243.9Hz.

(b) The wavelength of the reflected sound waves by the observer is 0.143 m.

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two wheels of mass m and radius r are ittting motionless on the top of a ramp when both wheels are released both roll down the rump under gracity

Answers

F2=2F1, as f1 is smaller by a factor of 2 due to f2 having to have twice the radius of f1 and having the same acceleration.

In mechanics, acceleration refers to the rate at which an object's velocity with respect to time varies. The vector quantity of accelerations (in that they have magnitude and direction). The acceleration of an object is determined by the direction of the net force exerted on it. Newton's Second Law states that an object's acceleration is the combined effect of two factors:

The amount of the net balance of all external forces acting on that thing is exactly proportional to the net resulting force; yet, depending on the materials used to construct it, the mass of the object is inversely related to mass.

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during what scrum event will the scrum master ask questions like: what has been our average velocity? who on the team has any upcoming vacations or work conflicts? who is responsible for what sprint tasks?

Answers

The Scrum event that will see the Scrum master asking question such as average velocity, upcoming vacations, and those responsible for sprint tasks is Sprint planning .

What are Scrum activities ?



Scrum events allow an organization to engage in processes where they are able to develop products and services which are then used to compete in the market and allow for the organization to meet its goals. There are five scrum activities or events and they are:

Sprint Sprint planning Daily scrum Sprint reviewSprint retrospective

In sprint planning, the team in question tries to work such that they can figure out how they can go about the scrum activity. The scrum master will try to find out how fast the team members have been going in terms of accomplishing goals, the availability of team members, and the responsibilities of the scrum members.

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star a and star b are both on the main sequence. star a is 28 times more luminous than star b. which star is more massive?

Answers

To find the massive stars known the luminous first.

What is luminous?

Luminous objects are those that produce their own light. Sun, candle flame, among other examples Non-luminous items are those that are unable to produce light on their own. These objects reflect light from their luminous bodies.

What is main sequence star?

Any star that is fusing hydrogen in its core and has a stable equilibrium between the inward pressure from gravity forces and the outward pressure from core nuclear fusion is considered to be in the main sequence.

Therefore, we can conclude that star A is more massive because the luminous stars are massive.

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Why are muscle and fat levels the only factors influencing flexibility impacted by personal decisions?
A.
Muscle and fat levels are mostly determined by heredity.
B.
Age, gender, and joint structure cannot be changed.
C.
Personal decisions have significant impacts on age and gender.
D.
Flexibility is not dependent upon muscle and fat levels.


Please select the best answer from the choices provided.

A
B
C
D

Answers

Answer:

B) Age, gender, and joint structure cannot be changed.

Explanation:

gimme brainliest! :-)

An object weighs 600N on moon
find it's mass on earth and moon
Find its weight on earth

Answers

Answer: 100N

Explanation:

Weight on earth = 600N

Let g= 10m/s^2 on earth

Mass on earth =  600/10 =60 kg

Now, since mass is a constant quantity so, it will remain 60 kg on the moon also.

Now, weight on moon = mg

m= mass =60 kg

g′ = acc. due to gravity on moon =  1/6th  the value on earth

So, Weight on moon =  1/6th  of the weight on earth

⇒ Weight on the moon =600 × 1/6​ = 100 N

Hope it helps and good luck!

qm.2 a particle has a velocity that is 90.0% the speed of light. if the wavelength of the particle is 1.5x10-15 m, calculate the mass of the particle.

Answers

If the wavelength of the particle is 1.5 x 10⁻¹⁵ m,  the mass of the particle will be 1.636 × 10⁻²⁷ kg

Velocity of the particle = 90.0% of c ( speed of light)

Wavelength of the particle (λ) = 1.5 × 10⁻¹⁵ m

Mass of the particle = ?

Calculate the velocity of the particle

    velocity = (90.0 / 100)(3 × 10⁸ m/s)

    velocity = (0.90)(3 × 10⁸ m/s)

    velocity = 2.70 × 10⁸ m/s

Now calculate the mass of the particle by using the following equation:

   λ = h / mv

Rearrange the equation for mass

    m = h / λv

value of h = 6.626 × 10⁻³⁴ Kg.m².s⁻¹

Put the values

    m = (6.626 × 10-34 Kg.m².s⁻¹) / (1.5 × 10⁻¹⁵ m)(2.70 × 10⁸ m/s)

    m = 1.636 × 10⁻²⁷ Kg

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2. All forms of energy can exist as either ________ or ________ energy.

Answers

Answer:

Explanation:

Comment

This depends on your grade level. Because there are only two choices needed, I would say the answer is

Potential Energy orKinetic Energy.

But recognize that when something burns, it is because of a change in chemical structure. For example CH4 + 2O2 ===> CO2 + 2H2O

Movement in the example is not as important as what is going on with the Methane Combined with the oxygen.

Answer:potential energy or kinetic energy.

Explanation: potential energy is the energy of position or condition, while kinetic energy is the energy of motion. Both forms of energy are important in understanding and analyzing the behavior and transformations of energy in various systems.

the gravitational force between two spheres is 40 n in magnitude. if the amount of each mass doubles, what is the force between the spheres? group of answer choices 80 n 10 n 20 n 160 n

Answers

The force between the spheres after each mass is doubled is 160N.

Every particle in the cosmos attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers, according to Newton's law of universal gravitation.

Coulomb's law of electrical forces, which is used to determine the strength of the electrical force developing between two charged things, is similar to Newton's law of gravitation. The force is inversely proportional to the square of the distance between the bodies under both inverse-square rules.

From newtons law of gravitation, we know that

F = (Gm₁m₂)/ r²

Initially,

Given that F₁ = 40N

F₁ = (Gm₁m₂)/ r²

F₂ = (Gm₁m₂)/ r²

Now, m₁ = 2m₁

m₂ = 2m₂

Thus,

F₂ =  (G * 2m₁ * 2m₂)/ r²

F₂ = 4 F₁

F₂ =  4 * 40N

F₂ = 160 N

The force between the spheres after each mass is doubled is 160N.

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what is a cepheid variable? what is a cepheid variable? a main-sequence star whose known luminosity makes it a good standard candle a type of luminous star whose variations in luminosity make it a good standard candle a bright source of variable x-ray emission, thought to harbor a supermassive black hole a type of galaxy whose variations in luminosity make it a good standard candle

Answers

Cepheid Variables stars are intrinsic variables which pulsate in a foreseeable way. In addition, a Cepheid star's phase (how often it pulsates) is directly related to its luminosity or brightness. Cepheid variable stars are good standard candles.

First, their luminosity is quite lofty (the most luminous Cepheids are 40,000 times more luminous than the Sun), so they can be noticed at large distances. Second, their luminosities can be determined from the Period-Luminosity Relation.

Through observations of Cepheid variables, astronomers have reckoned the distances to other galaxies. They compare the Cepheid variable's apparent brightness with its intrinsic brightness. The distinction between observed and actual brightness relents the distance.

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Answer:

a star whose luminosity pulses at a regular rate

Explanation:

got it on quiz right

A crate slides off the back of a flatbed truck that accelerated forward from rest. If the bed of the truck is frictionless, the crate falls off the back of the truck because.

Answers

The correct answer is due to Newton’s laws of motion i.e., an object at rest at rest remains at rest that’s why the crate falls back.

What governs motion, according to Newton?

Unless influenced by an imbalanced force, an item at rest stays at rest, and an object in motion keeps moving in a straight path at a constant pace. An object's acceleration is determined by its mass and the force being applied.

The crate naturally prefers to stay at rest while the truck moves ahead, so the truck will often slide beneath it and leave the crate behind.

It is all due to Newton's First Law, specifically the inertia of motion or rest.

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a stationary object of mass 4kg is set in motion by a net force of 50N. If the object attains a speed of 5m/s in time t. Calculate the value of t​

Answers

Answer: i got 0.4s

Explanation:

As the object is moving under constant force,we can apply the equation,

v=u+at where, v is the velocity attained after time t which had an initial velocity of u.

a=F/m=50/4=12.5ms^-2

Given, u=0

So, if v=5 then, t = 512.5 = 0.4s

Draw a diagram of a projectile that shows what is happening to the vertical (y) velocity of a projectile as it moves along its path . You must include what is happening to the speed of the velocity on the way up the way down and the max height.

Answers

The vertical velocity of the projectile increases but reaches zero at the maximum height and begins to decrease.

What is a projectile?

When we talk of the projectile, we are talking about the object that is moving along a parabolic path. Hence the object that is undergoing the projectile motion is going to have a curved path. Take an instance, when you kick a soccer ball, you have to notice that the ball would tend to curve as it moves up in the air and then begins to descend. That is a typical example of a projectile motion.

Now, we have to note that at the maximum height, the vertical velocity of the object would be zero. When I throw an object up, the vertical velocity of the object would continue to increase until the object reaches the maximum height where the vertical velocity is zero and then the vertical velocity of the object begins to decrease as shown in the image.

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Neutrons are a lot lower in mass than protons.

A. True
B. False

Answers

A. True.............

Answer:

False

Explanation:

As the mass of a neutron is slightly greater than the mass of a proton

A Geiger-Muller (GM) tube can be used to detect ionising radiation. How many alpha particles entering the GM tube are needed to make the counter advance by one? Give your answer in numbers, not words.

Answers

Answer:

1

Explanation:

The counter advances each time an ionising particle enters a GM tube.

Only one alpha particle entering the GM tube is needed to make the counter advance by one.

What is Geiger-Muller (GM) Counter?

A Geiger counter is a tool used to find and quantify ionized gas particle concentrations. It is widely utilized in fields including experimental physics, radiation dosimetry, and radiological defence. It consists of a metallic tube that is filled with gas and to which a high voltage supplied in multiples of 100V is applied. Alpha, beta, and gamma particles are all detected.

It is crucial to ensure that the least amount of radioactive material is delivered to human subjects when using radioactive isotopes in medical research studies on people. The radioactivity of materials must be measured with an extremely sensitive device in order to accomplish this. Geiger and Muller created a "particle detector" in 1928 that they named a "Geiger Muller Counter," or simply the "GM counter," to monitor ionizing radiation.

This  Geiger-Muller (GM) tube can be used to detect ionizing radiation. Only one alpha particle entering the GM tube is needed to make the counter advance by one.

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Two galaxies on opposite ends of the universe are moving away from the earth. Each has a velocity of 200,000 km/s relative to the earth. How fast would an observer in one of those galaxies see the other galaxy moving away?.

Answers

An observer in one of those galaxies sees the other galaxy moving away at a velocity of 400000 Km/s.

What is relative motion?

When an object has a particular velocity, then this velocity is w.r.t. frame which is known as the reference frame. When we determine the velocity of an object, the ground is considered the reference frame.

The motion of an object can be observed by the observer depending on the frame of the observer and this type of motion is relative motion.

When the two galaxies on opposite ends are moving away in opposite directions with a velocity of 200000 Km/s

The relative velocity of these two galaxies = 200000 + 200000

Relative velocity = 400000 Km/s

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if the angle from the horizontal increased, would the ball travel further away from the person? that is to say, if the angle of elevation was greater, would that make a difference in the distance from the person - further, closer, no change? be specific in your answer as to why you think this.

Answers

Let the initial velocity be u And the angle of projection is e Then, the distance between the person and the ball where it lands is called range.

If the angle with the horizontal increases Distance between the person and the ball where it lands decreases which means the ball lands closer to the person if the angle of projection increases, the range decreases.

Maximum altitude is determined by initial vertical velocity. A steeper launch angle increases the vertical velocity component, so increasing the launch angle increases the maximum altitude. The higher the degree of release, the longer the flight distance. Projectiles are launched higher, so they stay in the air longer. A horizontal component acts long on the projectile.

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The assumption that there is no energy loss is not accurate. Assuming the spring has a spring constant of 100Nm-1 and has a length change of 2 cm, the track is on a level surface, and that the final velocity of the car is 0.25 ms-1 when it reaches the end of the track, what is the percentage efficiency of the toy? Take the mass of the car to be 150 g

Answers

The toy percentage efficiency is 23%.

Solution:

The kinetic energy is:

KE = [tex]\frac{1}{2} mv^{2}[/tex]

KE = [tex]\frac{1}{2} *(150)(0.25)^2[/tex]

KE = 4.6875 J

The elastic potential energy is:

E = 0.5 x 4 x 10 = 20

E = 100 J

The percentage efficiency of the toy is found as:

%n = [tex]\frac{4.6875*100}{20}[/tex]

%n = 23%

The more the elastic material is stretched the greater the potential for elastic energy storage. The amount of elastic potential energy stored in a stretched spring can be calculated using the formula: Work is done when the spring expands and contracts.

Springs store elastic potential energy. If no inelastic deformation has occurred, the work done is equal to the stored elastic potential energy. As the spring constant increases for a constant applied force, the spring deflection decreases as the spring stiffness increases.

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select all that apply. in response to a specific stimulus, autonomic reflex arcs can trigger to help maintain homeostasis.

Answers

Internal organs unconsciously react to environmental changes as a result of reflexes, particularly autonomic reflexes, which help control homeostasis.

Why are reflexes important to maintaining homeostasis?Remember from the first module the importance of homeostasis. Reflexes help the body recognize changes and respond appropriately in order to maintain homeostasis. Reflexes happen unconsciously and automatically for a reason. Can you imagine how your life would be if you had to be conscious of the temperature of the environment you had just entered and then make conscious adjustments to maintain your internal temperature within the normal range?  To comprehend how reflexes function, we will examine the basic components of a reflex arc and how they interact to produce the desired effect.There are many different ways to classify reflexes, but for the purposes of this discussion, we'll focus on two of them: somatic reflexes, which regulate skeletal muscle, and autonomic reflexes, which regulate smooth muscle, cardiac muscle, glands, and other body parts.

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If an object is 60 centimeters high and the image is 189 centimeters high, what is the magnification?

Answers

Answer:

Explanation:

Given:

h = 60 cm

H = 189 cm

_________

K - ?

The magnification:

K = H / h

K = 189 / 60 ≈ 3.15

you throw a ball straight up with an initial velocity of 15.8 m/s. it passes a tree branch on the way up at a height of 6.81 m. how much additional time (in s) will pass before the ball passes the tree branch on the way back down?

Answers

Additional time taken before the ball passes the tree branch is 1.13s.

Here we have to find the additional time.

Given data:

Initial velocity(u) = 15.8 m/s

x is the height at which the ball reaches the greatest height after the height of 6.81m.

Height =( 6.81 + x)m

Final velocity (v) = 0

Acceleration due to gravity (g) = 9.8 m/s²

Formula:

v = u + at

0 = 15.8 - 9.8t

t = 15.8/ 9.8

 = 1.66s

Now we have:

Average velocity = Average distance/ average time

0 + 15.8/ 2 = (x + 6.81)/ 1.66

7.9 × 1.66 = x + 6.81

13.114 - 6.81 = x

x = 6.30

As the distance is 6.30.

So the additional time taken is:

Average velocity = Average distance/ Average time

0+ v/ 2 = 6.30 / t

v = 12.6/t

Now we have

v = u + at

a = v-u/t

-9.8 =( 0 - 12.6/t)/ t

9.8 = 12.6/ t²

t² = 12.6/ 9.8

  = 9/ 7

t = 3/ 2.645

 = 1.13s

Therefore the time taken is 1.13s.

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Vascular tissue helps plants transport water against the force of gravity. Because of this, plants that lack vascular tissue do not grow very tall. How is this situation similar to the information you have learned in this lesson? explain.

Answers

Because they can't move water very far, plants without vascular tissue can't get very tall. A cell wouldn't be able to bring in the materials it need if it got too big.

Vascular tissue is a multicellular conducting tissue that is intricate in structure and is present in vascular plants. Vascular tissue is primarily composed of xylem and phloem. These two tissues absorb water and nutrients inside. Two other meristems connected to vascular tissue are the vascular cambium and the cork cambium. The vascular tissue system of a particular plant consists of all of its vascular tissues.

Typically, vascular tissue has long, slender cells. Given that they act as pathways for the transportation of water, minerals, and nutrients throughout the plant, it is not unexpected that the xylem and phloem resemble pipes. Phloem's individual cells are connected end to end like the sections of a pipe.

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Numerical problems.
a) convert 300kelvin into the Celsius scale.
b) Convert 220° C into kelvin scale.
c) Convert 30° C into fahrenheit scale.
d) Convert 260° F into °C​

Answers

Answer:

a) 27 degree Celsius

b) 493.15K

c) 86 Fahrenheit

d) 126.667 degrees celsius

Explanation:

a) To convert from Kelvin scale to Celsius scale, subtract 273 from Kelvin scale

Hence, 300 - 273 = 27 degree celsius

b) The temperature T in Kelvin (K) is equal to the temperature T in degrees Celsius (°C) plus 273.15, that conversion formula:

T(K) = T(°C) + 273.15

hence, 220 + 273.15 = 493.15K

c) The formula to convert Celsius to Fahrenheit is °F = °C × (9/5) + 32

F = [ C × (9/5) + 32 ]

Given that, C = 30

F = 30 × (9/5) + 32

F = 54 + 32

F = 86

Thus, 30 °C is equivalent to 86 °F.

d) Formula

(260°F − 32) × 5/9 = 126.667°C

The 70 kg student in figure p14. 43 balances a 1200 kg elephant on a hydraulic lift. What is the diameter of the piston the student is standing on?.

Answers

The diameter of the piston the student is standing on is 0.22 times greater than that of the piston the elephant is standing on.

What is mechanical advantage of a hydraulic lift?An illustration of Pascal's law is the hydraulic system.By exerting a modest force on the small piston, we can generate a bigger force on the large piston.At each piston, the ratios of force to area must be the same.Three practical tools that make use of Pascal's law are hydraulic brakes, lifts, and presses.

Given parameters:

Mass of the student: m = 70 kg.

Mass of the elephant: M = 1200 kg.

Let the diameter of the piston the student is standing on is d.

and  the diameter of the piston the elephant is standing on is D.

Using Pascal's law,

Weight of the student ÷ area  of the piston the student is standing on = Weight of the elephant ÷ area  of the piston the elephant is standing on.

⇒ 70 kg × g / π d² = 1200 kg × g / π D²

⇒ 1400 d² = 70 D²

⇒ d= 0.22D.

Hence,  the diameter of the piston the student is standing on is 0.22 times greater than that of the piston the elephant is standing on.

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a lamina occupies the part of the disk in the first quadrant and the density at each point is given by the function . a. what is the total mass? b. what is the moment about the x-axis, ? c. what is the moment about the y-axis, ? d. where is the center of mass? ( , ) e. what is the moment of inertia about the origin, ?

Answers

The center of mass of the lamina would be in the middle of the axis and the mass of the lamina is 25.

For this, we will use the polar coordinates. According to the change of coordinates, where r and theta are the new parameters. Given a point (x,y) in the plane, r is the distance from (x,y) to the origin and theta is the angle formed between the line that joins the origin and the point, and the x-axis.

        We need to describe the region D in terms of the new parameters. Replacing the values of x,y in the given inequality, we get that . Since and r>0 we get that r<=5. On the other side, in order to describe the whole region of the first quadrant, we need to sweep the angle theta from 0 to. With that, we can calculate the mass of the lamina as follows here, the extra r appears as the Jacobian coordinates.

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9. what happens to the internal pressure in a fluid flowing in a horizontal pipe when its speed increases? when its speed decreases?

Answers

The pressure decreases when the speed increases then internal pressure in a fluid flowing in a horizontal pipe its speed decreases The pressure increases when the speed decreases.

What is Pressure?

The physical force used to apply pressure on an object is defined as such. Per square inch of an item, a force is delivered perpendicularly to its surface. For pressure, the fundamental formula is F/A. (Force per unit area). The Pascal is the unit of pressure (Pa). The four different types of pressure are absolute, atmospheric, differential, and gauge pressure.'Pressure' is the term used to describe the thrust (force) applied to a surface per unit area. The ratio of force to area is another way to describe it (over which the force is acting).The layer of gases that surrounds the earth's atmosphere creates a pressure that is known as "atmospheric pressure."

However, 101325 Pa is what it is at sea level.

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a person slaps her leg with her hand, which results in her hand coming to rest in a time interval of 2.25 ms2.25 ms from an initial speed of 3.25 m/s3.25 m/s . what is the magnitude of the average contact force exerted on the leg, assuming the total mass of the hand and the forearm to be 1.55 kg1.55 kg ?

Answers

The magnitude of the average contact force exerted on the leg by the person is 2238.8N.

A person slaps her leg with her hand which results her hand to come to rest in a time interval of 2.25 millisecond from an initial speed of 3.25m/s.

According to second law of motion of Newton,

The average force applied by a body can be given by the change in momentum per unit time of the body.

So, we can write,

F = M∆V/t

Putting values,

F = 1.55 x 3.25 x 10³/2.25

F = 2238.8 N.

So, the magnitude of the average contact force exerted on the leg is 2238.8N.

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The natural abundance of si-28 (mass = 27. 98 amu) is 92. 23%. For si-29 (mass = 28. 98 amu), it is 4. 67%, and for si-30 (mass = 29. 97 amu), it is 3. 10%.

Answers

28.11 u is the Average atomic mass of Silicon.

Average atomic mass of Si

= 28×92.25+29×4.65+30×3.10÷100

=28.11 u

The mass of the components that make up an element's atom is referred to as its atomic mass. One-twelfth of the mass of the carbon-12 atom, which has an assigned atomic mass of 12 units, is expressed as a multiple of 1.992646547 1023 gram, or more precisely as 1.992646547 gram. One atomic mass unit is equivalent to 1.660539040 1024 grams on this scale (amu). The atomic mass unit is occasionally referred to as the dalton in honor of English scientist John Dalton (Da).

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a spotlight on the ground shines on a wall 12 m away. if a man 2 m tall walks from the spotlight toward the building at a speed of 1.1 m/s, how fast (in m/s) is the length of his shadow on the building decreasing when he is 4 m from the building? (round your answer to one decimal place.)

Answers

When he is 4 m away from the building, the speed at which his shadow lengthens is -0.41 m/s.

What do you mean by angles?

An angle is a shape that is made up of two rays or lines that have a shared terminal. The name "angle" comes from the Latin word "angulus," which means "corner." The common terminal of the two rays—known as the vertex—is referred to as an angle's sides. The angle in the plane does not always need to be in Euclidean space.

Given,

Distance of man from building = x

∴ initially, x = 12

dx/dt = -1.1 m/s

Let,

Shadow height = y

Now,

Solve for [tex]\frac{dy}{dt}[/tex] : when x=4

From the diagram it seen similar triangles with similar base/height ratios,

[tex]\frac{2}{12-x}[/tex] = [tex]\frac{y}{12}[/tex]

y = [tex]\frac{24}{12-x}[/tex]

[tex]\frac{dy}{dt}[/tex] = [tex]\frac{24}{(12-x)^{2} }[/tex] × [tex]\frac{dx}{dt}[/tex]

At x= 4,

dy/dt becomes:

[tex]\frac{24}{(12-4)^{2} }[/tex] × (-1.1)

∴ y = -0.41 m/s

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