what will be the speed of a solid sphere of mass 2.0 kilograms and radius 15.0 centimeters when it reaches the bottom of a incline of length 5.0 meters. Assume the sphere starts from rest and rolls without slipping.

Answer:

Average power output of insect is 2.42W

Explanation:

Workdone by constant force during displacement is given by:

W= F× d cos theta

Where theta is angle between F and d.

Power output due to the force over the interval time is given by:

P= Workdone/change in time

Ginen:

Mass of insect,m= 7.0g= 7/1000 = 0.07kg

Downward force applied by insect,F= 2mg

Distance moved by the wing each stroke=1.5cm=1.5/100= 0.015m

W= F× d cos theta

Where theta=0° since force is in the same direction as the displacement.

W= 2mg×d

W= 2× 0.07 × 9.8 × 0.015

W= 0.02058J

Power output = W/ change in time

Since wings make 117strokes each second time interval is 1/117 = 8.5×10^-3seconds

Power= 0.02058/(8.5×10^-3)

Power= 2.42W

Answer:

[tex]T_1=0.24y[/tex]

Explanation:

Using Kepler's third law, we can relate the orbital periods of the planets and their average distances from the Sun, as follows:

[tex](\frac{T_1}{T_2})^2=(\frac{D_1}{D_2})^3[/tex]

Where [tex]T_1[/tex] and [tex]T_2[/tex] are the orbital periods of Mercury and Earth respectively. We have [tex]D_1=0.39D_2[/tex] and [tex]T_2=1y[/tex]. Replacing this and solving for

[tex]T_1^2=T_2^2(\frac{D_1}{D_2})^3\\T_1^2=(1y)^2(\frac{0.39D_2}{D_2})^3\\T_1^2=1y^2(0.39)^3\\T_1^2=0.059319y^2\\T_1=0.24y[/tex]

Final answer:

A year on Mercury is approximately 88 Earth days long, which means it is about 0.241 Earth years, due to Mercury's average distance from the Sun being 0.39 times that of Earth's.

Explanation:

The student's question relates to the orbital period of Mercury compared to Earth's, given its average distance from the Sun. Mercury’s orbit around the Sun takes approximately 88 Earth days, which constitutes a Mercury year. This is calculated using Kepler's third law of planetary motion, which relates the orbital period of a planet to its average distance from the Sun (orbital semi-major axis).

Because Mercury is 0.39 times as far from the Sun as Earth is, its orbital period is significantly shorter than Earth's. Earth's average distance from the Sun is approximately 1 astronomical unit (AU), making it the basis for measuring distances in our solar system. Therefore, a year on Mercury, in Earth years, is 88/365, or about 0.241 Earth years.

Answer: Pitch

Explanation:

Pitch of sound is defined as the factor that monitors the sound quality through produced vibrations rate.It helps in determination of sounds tone in terms highness or lowness.

According to the question,Enrico is finding difficulty in judging the difference between pitch sound of tuba and piccolo as per their tone in terms of high or low.

Enrico is having trouble telling the difference between the sound of a tuba and the sound of a piccolo. Even though a piccolo produces much briefer, faster sound waves than does a tuba, he has trouble picking out the differences in the pitch of these sounds.

Pitch: Pitch is the perceptual attribute of sound that allows us to distinguish between different frequencies. The sound of a tuba and a piccolo are different primarily because they produce sound waves at different frequencies. A tuba produces lower frequency sound waves (lower pitch), while a piccolo produces higher frequency sound waves (higher pitch). If Enrico is having trouble telling the difference between the sound of a tuba and a piccolo, it suggests he is having trouble distinguishing between their pitches.

Loudness: Loudness refers to the perceived volume or intensity of a sound. While the tuba and piccolo can be played at different volumes, the primary distinguishing factor between them is not loudness but pitch.

Hue: Hue is a term used in the context of color, not sound. It refers to the distinct characteristic of color that allows us to differentiate between colors such as red, blue, and green.

Amplitude: Amplitude refers to the height of the sound wave and is related to the loudness or volume of the sound. While amplitude can affect how loud a sound is, it does not directly differentiate between the characteristic sounds of a tuba and a piccolo.

Therefore, the appropriate term for distinguishing between the sounds of different instruments, such as a tuba and a piccolo, is pitch.

The complete question is:

Enrico is having trouble telling the difference between the sound of a tuba and the sound of a piccolo. Even though a piccolo produces much briefer, faster sound waves than does a tuba, he has trouble picking out the differences in the of these sounds.

O pitch

O loudness

O hue

O amplitude

Final answer:

The buoyant force experienced by an object submerged in a fluid is determined by the Archimedes' principle. When floating in the denser water of the Dead Sea, the buoyant force is greater than one's weight.

Explanation:

The buoyant force experienced by an object submerged in a fluid is determined by the Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. When a person floats in fresh water, the buoyant force acting on them is equal to their weight. However, when they float higher in the denser water of the Dead Sea, the buoyant force that acts on them is greater than their weight. Therefore, the correct answer is (a) greater than their weight.

Final answer:

The buoyant force acting on you when you float in the denser water of the Dead Sea is equal to your weight, which is consistent with Archimedes' principle. The correct option is c.

Explanation:

When you float higher in the denser water of the Dead Sea, the buoyant force that acts on you is: c) equal to your weight. Archimedes' principle tells us that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces. Given that the Dead Sea has a higher density due to its salt content, you displace less water to experience a buoyant force that equals your weight, compared to fresh water. As a result, you float higher in the Dead Sea, but the buoyant force itself remains equal to your weight. Hence, Option c is correct.

Explanation:

Below is an attachment containing the solution.

Answer:

The maximum height of the ball after the bounce is 1.2 m

Explanation:

Potential Energy = mass * Height * acceleration of gravity

PE=mgh

= 0.2 x 9.8 x 1.5

P.E = 2.94 J

During bounce of ball 0.60 J of energy is lost. So

  2.94 - 0.6 = 2.34 J

now  new energy is 2.34

New P.E = mgh

2.34 = 0.2 x 9.8 x h

h = 2.34 / 0.2 x 9.8

h =  1.2 m

The maximum height of the ball after the bounce is 1.2 m

Explanation:

Given:

Mass = 0.2 kg

Height = 1.5 m

Potential energy of the drop, PE = m × g × h

= 0.2 x 9.81 x 1.5

= 2.94 J

After the drop, 0.6 J of energy is dissipated, so amount of energy left

= 2.94 - 0.6

= 2.34 J

This energy is eqal to thenew potential energy which is:

m × g × h = 2.34

0.2 × 9.81 × h = 2.34

= 2.34/1.962

= 1.19 m.

Answer:

The work done on the canister by the 5.0 N force during this time is

54.06 Joules.

Explanation:

Let the initial kinetic energy of the canister be

KE₁ = [tex]\frac{1}{2} mv_1^{2}[/tex] = [tex]\frac{1}{2} *3*3.6^{2}[/tex] = 19.44 J in the x direction

Let the the final kinetic energy of the canister be

KE₂ = [tex]\frac{1}{2} mv_2^{2}[/tex] = [tex]\frac{1}{2} *3*7.0^{2}[/tex] = 73.5 J in the y direction

Therefore from the Newton's first law of motion, the effect of the force is the change of momentum and the difference in energy between the initial and the final

= 73.5 J - 19.44 J = 54.06 J

Explanation:

Below is an attachment containing the solution.

Final answer:

The horizontal component of the normal force, represented as FNsinθ, provides the centripetal force necessary for a car to round a circular curve on a banked turn without friction.

Explanation:

When a car is rounding a circular curve on a banked turn, the force that provides the centripetal force necessary to keep the car moving on the circular path is the horizontal component of the normal force exerted on it by the road. This can be represented as FNsinθ, where θ is the banking angle. The weight of the car, mg, acts vertically downwards and does not contribute to the centripetal force in this ideal frictionless scenario. For ideal banking, where the angle is perfect for the speed and radius of the turn, the net external force equals the horizontal centripetal force required for circular motion. Therefore, the horizontal component of the normal force is the only force component that acts towards the center of the curvature, providing the centripetal acceleration.

Answer:

The magnitude of the final velocity is 14.14 m/s

Explanation:

The horizontal component of the final velocity and vertical component of the final velocity, forms a perpendicular vector. To determine the magnitude of the final velocity, we sum the two vectors.

To add two perpendicular vector, Pythagoras principle is used.

[tex]V^2 = V_x^2 +V_y^2\\\\V = \sqrt{V_x^2 +V_y^2}\\\\V = \sqrt{(10)^2 +(-10)^2} =14.14 m/s[/tex]

The magnitude of the final velocity is 14.14 m/s

The unstretched length of the spring is 0.15 m

Explanation:

Given-

Length of the stretched spring, [tex]x_{f}[/tex] = 20 cm = 0.2 m

K = 200 N/m

U = 0.25 J

unstretched length of the spring, x₀ = ?

We know,

U = [tex]\frac{1}{2} (k)[/tex] (Δx)²

Δx = [tex]x_{f}[/tex] - x₀

Δx = 0.2 - x₀

0.25 = 100 (0.2 - x₀)²

0.0025 = (0.2 - x₀)²

0.05 = 0.2 - x₀

x₀ = 0.15 m

Therefore, the unstretched length of the spring is 0.15 m

Answer:

Explained below:

Explanation:

Range of Motion is the measurement of action throughout a specific joint or body part. If your goniometer breaks, no need to worry because an inclinometer is also helpful to measure the range of motion in a joint by measuring the joint angles at length and flexion and in order to verify that there is improvement being made on rising the range of motion in a joint, the physical therapist measures the joint angle before the treatment and keep on doing to do so over time.

It is possible to measure a range of motion by using a protractor and a ruler.

Motion or movement is a measure to indicate the distance that travels a particular object and/or material.

In conclusion, it is possible to measure a range of motion by using a protractor and a ruler.

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Answer:

a) 5.51m/s² b) 192.94N c) 1.38m each

Explanation:

Given two boxes of masses m1 = 35kg and m2 = 45kg hung vertically from opposite ends of a rope passing over a rigid horizontal metal rod, we will analyze the forces acting on each body.

According Newton's second law, Force = mass ×acceleration

The forces acting on body of mass m1 are the tension (T) and the frictional force (Ff) which opposes the tension.

Taking the sum of horizontal forces acting on mass m1, we will have;

T +(-Ff) = m1a

T - Ff = m1a... (1)

For the mass m2, the forces acting on the body are in the vertical direction and this forces are the weight (W) acting downwards and the tension(T) acting upwards. The sum of the forces in the body is given as ;

W + (-T) = m2a

W-T = m2a ...(2)

Since W = mg, equation 2 will become;

m2g - T = m2a...(2)

Solving equation 1 and 2 simultaneously to get the tension and the acceleration, we have;

T - Ff = m1a ... 1

m2g - T = m2a ... 2

Since friction is negligible, Ff = 0

Adding the two equation will give;

m2g-Ff = m2a+m1a

Since Ff =0

m2g = (m2+m1)a

a = m2g/m1+m2

a = 45(9.8)/45+35

a =441/80

a = 5.51m/s²

b) Substituting a = 5.51 into equation 1 to get the tension T in the rope will give;

T = m1a

T = 35×5.51

T = 192.94N

c) since velocity = displacement/time

Displacement = velocity × time

To get the velocity, since acceleration = velocity/time,

Velocity = acceleration ×time

Velocity = 5.51× 0.5

Velocity = 2.76m/s

Displacement of each box will be the same since they are moving with the same acceleration.

Displacement = 2.76m/s × 0.5s

Displacement of each boxes = 1.38m

The acceleration of the boxes is 0.98 m/s^2, the tension in the rope is 376.3 N, and the displacement of each box after 0.5 seconds is 0.12 m.

This question deals with the physics of motion, particularly involving concepts of mass and friction. Given that the two boxes with different masses m1=35kg and m2=45kg are hung vertically from opposite ends of a rope over a rigid horizontal metal rod, and stating negligible friction, we can compute:  

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Answer:

[tex]8000\ N[/tex]

Explanation:

The question is incomplete.

The complete question would be

B) Suppose the magnitude of the gravitational force between two spherical objects is 2000 N when they are 100 km apart. What is the gravitational force [tex]F_g[/tex] between the two objects described in Part B if the distance between them is only 50 km.

Given gravitational force between two object [tex]F_g=2000\ N[/tex] when objects are placed [tex]100\ km[/tex] apart.

We need to determine gravitational force when they are kept [tex]50\ km[/tex] apart.

As we know the gravitational force [tex]F_g[/tex] is inversely proportional to the square of distance between objects [tex](d)[/tex].

[tex]F_g=\frac{K}{d^2}[/tex]

Where [tex]K=Gm_1m_2[/tex] that will be constant. Because the mass of the object remain same in both cases. And [tex]G[/tex] is already gravitational constant.

Given,

[tex]2000=\frac{K}{100^2}\\ So,\ K=2000\times 100^2[/tex]

Let [tex]F'_g[/tex] is the force between objects when they were kept [tex]50\ km[/tex] apart.

[tex]F'_g=\frac{K}{50^2} \\\\F'_g=\frac{2000\times 100^2}{50^2}\\ \\F'_g=2000\times 4=8000\ N[/tex]

So, [tex]8000\ N[/tex] is the gravitational force when two objects were kept [tex]50\ km[/tex] apart.

The gravitational force between two objects can be calculated using Newton's law of gravitation formula, which requires knowledge of both objects' masses and the distance between them. Without exact masses of the objects in the question, it's not possible to provide a numeric answer, but generally, an increased distance leads to a decreased gravitational force.

Calculating Gravitational Force Between Two Objects

To calculate the gravitational force (Fg) between two objects using Newton's law of gravitation, you need to know the masses of the two objects and the distance between them. The formula to use is F = Gm1m2 / r2, where F is the gravitational force, G is the gravitational constant (6.673x10-11 N·m²/kg²), m1 and m2 are the masses of the objects, and r is the distance between their centers. If the masses of the objects are not provided in the question, you cannot calculate the force accurately. However, assuming identical conditions to the provided reference, where two objects have a mass of 50 kg each and are 0.50 meters apart, and you change the distance to 50 km (50,000 meters), the gravitational force will be significantly smaller due to the increase in distance according to the inverse square law of gravitation.

If you had the exact masses, the gravitational force at the new distance of 50 km could be calculated directly using the formula by substituting the known values for mass and distance. The result would show how much less the gravitational force is at the greater distance compared to the initial 0.50 meters. This calculation demonstrates the concept that as distance increases, the gravitational force between two masses decreases rapidly.

Answer:

Intensity of beam 18 feet below the surface is about 0.02%

Explanation:

Using Lambert's law

Let dI / dt = kI, where k is a proportionality constant, I is intensity of incident light and t is thickness of the medium

then dI / I = kdt

taking log,

ln(I) = kt + ln C

I = Ce^kt

t=0=>I=I(0)=>C=I(0)

I = I(0)e^kt

t=3 & I=0.25I(0)=>0.25=e^3k

k = ln(0.25)/3

k = -1.386/3

k = -0.4621

I = I(0)e^(-0.4621t)

I(18) = I(0)e^(-0.4621*18)

I(18) = 0.00024413I(0)

Intensity of beam 18 feet below the surface is about 0.2%

Answer:

The answer to the question is

A tilted bed is said to have a _dip____, describing the angle that the bed forms with the horizontal plane--and a strike, the compass direction that lies at right angles to the tilted bed.

Explanation:

The dip of a tilted bed, describes the acute angle a tilted bed makes with the horizontal plane, by stating the numerical value of the angle from 0 to 90 degrees  as well as pointing out the orientation of the downward dipping direction in the orientation towards N, S, E, W

The strike line represents the line formed to represent the intersection of a feature of a bed  such as the bed rock surface with a horizontal plane.

The dip and the strike line of a tilted bed are always at right angles to each other on a geologic map.

A tilted geological layer's angle with the horizontal is called the 'dip' and the line it forms intersecting with the horizontal at 90 degrees is the 'strike'. These measurements help determine the orientation of rock layers suffering from deformation.

A tilted bed is said to have a dip, describing the angle that the bed forms with the horizontal plane—and a strike, the compass direction that lies at right angles to the tilted bed. The dip is a measure of the steepest angle of descent relative to the horizontal plane and indicates the direction in which water would flow down the plane. The strike, on the other hand, is the direction of the line formed by the intersection of a rock layer's surface with the horizontal plane, which is always perpendicular to the dip direction. Survey instruments like a Brunton Compass are commonly used by geologists to measure strike and dip accurately to understand feature orientations within geological formations.

Answer:

The greater the masses of two objects, the greater the resultant gravitational force; the greater the distance between the two objects, the smaller the resultant gravitational force.

Explanation:

The gravitational force between two objects is an attractive force, whose magnitude is:

[tex]F=G\frac{m_1 m_2}{r^2}[/tex]

where

G is the gravitational constant

m1, m2 are the masses of the two objects

r is the distance between the objects

From the equation above, we observe that:

- The magnitude of the force is directly proportional to the product of the masses

- The magnitude of the force is inversely proportional to the square of the distance between the masses

Therefore, we can say that:

The greater the masses of two objects, the greater the resultant gravitational force; the greater the distance between the two objects, the smaller the resultant gravitational force.

Final answer:

The gravitational force between two objects increases with the masses and decreases with the distance between them. The correct terms for the blanks are 'stronger' for the effect of mass and 'weaker' for the effect of distance.

Explanation:

The question is related to the concept of gravitational force in physics. We know from Newton's law of universal gravitation that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This can be represented by the formula:

[tex]F_{gravity} = G \frac{ (M_1 M_2)}{R^2}[/tex],

where [tex]F_{gravity}[/tex] is the gravitational force, G is the gravitational constant, [tex]M_1[/tex] and [tex]M_2[/tex] are the masses of the two objects, and R is the distance between the centers of the two objects.

Thus, the sentence correctly filled out would be: The greater the masses of two objects, the stronger the resultant gravitational force; the greater the distance between the two objects, the weaker the resultant gravitational force.

Answer:

The answer for this one is that wood is the oldest mean of energy and it is also cheap that is why people in less developed coubtries use wood as a primary energy source.

Explanation:

The Developing countries depends on the wood and other forest goods for their everyday cooking and heating needs, prompting the public to assist with tropical deforestation and insecurity through the usage of these tools.

Both ideas— that forest-derived energy is mainly used in the developed nation and its value in the energy portfolios of advanced economies is negligible— fail to catch

Final answer:

People in less developed countries rely on wood and biomass for energy because it's inexpensive and accessible; however, this reliance can lead to deforestation and pollution. In contrast, developed nations are seeing an increased biomass use due to rising fossil fuel costs, though they have a greater mix of energy sources.

Explanation:

People in less developed countries often use wood as a primary energy source for multiple reasons. Wood and other forms of biomass, such as animal dung, are inexpensive, relatively efficient, and readily available. These sources of energy are crucial for domestic uses including heating, sanitation, and cooking. In areas where electricity and modern fuels are not accessible or are too costly, biomass is a vital resource. Additionally, due to rapid population growth and poverty, some regions have a higher demand for firewood as they lack alternative energy sources. This reliance often leads to environmental issues like deforestation, as the use of wood outpaces the replenishment of forests.

Furthermore, in developed nations, the consumption of energy includes a mix of sources with a declining reliance on biomass due to access to electricity and other modern energy forms. However, as fossil fuel prices increase and availability declines, biomass use is also growing in these nations. Despite being renewable, the environmental impact of biomass as an energy source includes deforestation and the release of harmful pollutants such as carbon monoxide and particulate matter from burning wood.

Explanation:

Below is an attachment containing the solution.

The rider is rising at a speed of approximately 15.71 m/min when the rider is 9 m above ground level on a Ferris wheel with a radius of 5 m rotating at a rate of one revolution every 2 minutes.

To find the speed at which the rider is rising, we can use the concept of angular velocity. The angular velocity of the Ferris wheel can be calculated by taking the circumference of the circle formed by the rider's position and dividing it by the time it takes to complete one revolution. In this case, the circumference is equal to 2π multiplied by the radius of the Ferris wheel. The time it takes to complete one revolution is given as 2 minutes.

The formula for angular velocity is ω = θ/t, where ω is the angular velocity, θ is the angle swept, and t is the time taken. Since one revolution is equal to 360 degrees or 2π radians, the angular velocity can be calculated as:

ω = (2π rad)/(2 min) = π rad/min

Now, to find how fast the rider is rising, we can use the relationship between linear velocity (v) and angular velocity (ω) given by v = rω, where r is the radius of the Ferris wheel. In this case, the radius is given as 5 m. Plugging in the values, the linear velocity is:

v = (5 m)(π rad/min) = 5π m/min ≈ 15.71 m/min

Therefore, when the rider is 9 m above ground level, the rider is rising at a speed of approximately 15.71 m/min.

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Explanation:

Stars form in the Milky Way at a rate of about 1 solar mass per year, which means it would take a few hundred billion years for all gas to be turned into stars, far exceeding the universe's age of 14 billion years. Pulsars and supernova events influence this star-forming process and the interstellar medium.

Astronomers have estimated that new stars form in our galaxy, the Milky Way, at a rate of about 1 solar mass per year. If we consider the amount of interstellar gas available to form new stars, and no new gas was added, we can calculate how long it would take for all the gas to be converted into stars. Given that the Milky Way contains about a few hundred billion solar masses of gas, it would take a few hundred billion years for all the interstellar gas to be used up at the current rate of star formation, which is significantly longer than the age of the universe (14 billion years).

Stars, including pulsars, form and die within the galaxy at varying rates. For example, one new pulsar is born approximately every 25 to 100 years, aligned with the rate of supernovae occurrences. Supernova explosions contribute to the recycling of interstellar material, affecting star formation and the interstellar medium.

Answer:

A solid moment of inertia is  [tex]I = \frac{mr^2}{2}[/tex].

Here, both the solid cylinder and the cylindrical shell have the same mass, the same radius, and turn on a horizontal, friction-less axle.

The solid cylinder has less inertia than the cylindrical shell, and it requires less torque to rotate, meaning that the solid cylinder weight block falls faster than the cylindrical shell itself.

Fill in the blanks, in order.

Gravitational potential energy, Translation kinetic energy, Kinetic energy;

Hallow, Solid, Hallow, Solid;

Hallow, Transitional kinetic energy, Hallow

Answer:

The answer to the queations are;

A) The block attached to the solid cylinder would hit the ground first.

B) By the time the blocks reach the ground, they have transformed identical amounts of _gravitational potential_______energy into_____rotational kinetic________ energy of the cylinders. energy of the blocks and _______translational kinetic_____But the moment of inertia of a ____hollow______cylinder is higher than that of a ____solid_______ cylinder of the same mass, so more of the energy of the system is in the form of rotational kinetic energy for the ______hollow_____________cylinder than for the ___solid_______ one. This leaves less energy in the form of translational kinetic energy for the ____hollow________cylinder. But it is the ____translational kinetic________ energy that determines the speed of the block. So the block moves more slowly for the system with the ______hollow______cylinder, and so its block reaches the ground last.

Explanation:

To solve the question, we note that

The total energy of motion of the moving cylinders is equal to

K[tex]_{TOT[/tex] = 1/2·m·v² + 1/2·I·ω²

Where

m = Mass

v = Velocity

ω = Angular velocity

I = moment of inertia where I for hollow cylinder = MR² and

I for solid cylinder = 1/2·MR².

Therefore we have

K[tex]_{TOT[/tex] for solid cylinder = 1/2·m·v² + 1/2·I·ω² = 1/2·m·v² + 1/2·1/2·MR²·ω²

= 1/2·m·v² + 1/4·MR²·v²/r² = 1/2·m·v² + 1/4·M·v² = 3/4·m·v²

For the hollow cylinder, we have

K[tex]_{TOT[/tex] = 1/2·m·v² + 1/2·MR²·ω² = 1/2·m·v² + 1/2·MR²·v²/r² = 1/2·m·v² + 1/2·m·v²

= m·v²

From conservation of energy the initial potential energy is transformed into potential energy as follows

PE = m·g·h

Where:

m = Mas

g = Gravitational acceleration

h = height

Therefore

For the solid cylinder 3/4·m·v² = m·g·h and  v² = [tex]\frac{3}{4} \frac{m*g*h}{m}[/tex] and v  = [tex]\sqrt{\frac{4}{3} gh}[/tex]

For the hollow cylinder m·v² = m·g·h and  v² = [tex]\frac{m*g*h}{m}[/tex] and v  = [tex]\sqrt{gh}[/tex]

This shows that the solid cylinder has a higher downward velocity and the block attached to the solid cylinder would hit the ground first

B) By the time the blocks reach the ground, they have transformed identical amounts of _gravitational potential_______energy into_____rotational kinetic________ energy of the cylinders. energy of the blocks and _______translational kinetic_____But the moment of inertia of a ____hollow______cylinder is higher than that of a ____solid_______ cylinder of the same mass, so more of the energy of the system is in the form of rotational kinetic energy for the ______hollow_____________cylinder than for the ___solid_______ one. This leaves less energy in the form of translational kinetic energy for the ____hollow________cylinder. But it is the ____translational kinetic________ energy that determines the speed of the block. So the block moves more slowly for the system with the ______hollow______cylinder, and so its block reaches the ground last.

Answer:

0.247 J = 247 mJ

Explanation:

From the principle of conservation of energy, the workdone by the applied force, W = kinetic energy change + electric potential energy change.

So, W = ΔK + ΔU =1/2m(v₂² - v₁²) + q(V₂ - V₁) where m = mass of particle = 5.4 × 10⁻² kg, q = charge of particle = 5.10 × 10⁻⁵ C, v₁ = initial speed of particle = 2.00 m/s, v₂ = final speed of particle = 3.00 m/s, V₁ = potential at surface A = 5650 V, V₂ = potential at surface B = 7850 V.

So, W = ΔK + ΔU =1/2m(v₂² - v₁²) + q(V₂ - V₁)

          = 1/2 × 5.4 × 10⁻²kg × ((3m/s)² - (2 m/s)²) + 5.10 × 10⁻⁵ C(7850 - 5650)

          = 0.135 J + 0.11220 J

          = 0.2472 J

          ≅ 0.247 J = 247 mJ

The required flow work of the compressor is calculated using the flow work equation and the ideal gas law. First, we determine the final volume using the ideal gas law. Then we substitute these figures into the flow work equation, giving the result as 8.08 kJ/kg.

The flow work required by the compressor is calculated using the equation

flow work = pressure * volume.

Given the initial pressure P1 = 120 kPa, volume V1 = 6 L and final pressure P2 = 1000 kPa,

we can substitute these values into the equation.

However, the volume at the end of compression is not given. To find this, we need to use the ideal gas law, P1V1/T1=P2V2/T2,

where T1 is the initial temperature and T2 is the final temperature.

Convert the temperatures to kelvins (T1 = 22 + 273 = 295 K, T2 = 400 + 273 = 673 K) and volume to m3 (V1 = 6 / 1000). Solving for V2 gives V2 = P1V1T2 / P2T1 = 0.00147 m3.

Now, substituting again into the flow work equation gives

flow work = (1000 kPa)(0.00147 m3) = 1.47 kJ.

This is the energy per unit volume, to find it per unit mass, divide it  by the specific volume

v2 = V2 / m = R*T2 / P2 = 0.182 m3/kg,

Therefore, the required flow work = 1.47 kJ / 0.182 kg = 8.08 kJ/kg.

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The flow work required by the compressor is approximately 622.476 kJ/kg.

The flow work required by the compressor is given by the equation:

[tex]\[ w_{flow} = \int_{1}^{2} v \, dp \][/tex]

where [tex]\( v \)[/tex] is the specific volume of the air and [tex]\( dp \)[/tex] is the differential pressure change. For an ideal gas, the specific volume can be calculated using the ideal gas law:

[tex]\[ v = \frac{RT}{p} \][/tex]

where [tex]\( R \)[/tex] is the gas constant, [tex]\( T \)[/tex] is the absolute temperature in Kelvin, and [tex]\( p \)[/tex] is the pressure.

Given:

- Initial pressure [tex]\( p_1 = 120 \)[/tex] kPa

- Final pressure [tex]\( p_2 = 1000 \)[/tex] kPa

- Initial temperature [tex]\( T_1 = 22 + 273.15 = 295.15 \)[/tex] K (converting from Celsius to Kelvin)

- Final temperature [tex]\( T_2 = 400 + 273.15 = 673.15 \)[/tex] K

- Gas constant [tex]\( R = 0.287 \) kPa/m^3/kg/K[/tex]

Since the process is adiabatic and the air is being compressed, we can assume that the specific volume at the initial state [tex]\( v_1 \)[/tex] can be calculated using the initial conditions:

[tex]\[ v_1 = \frac{RT_1}{p_1} \][/tex]

Substituting the values:

[tex]\[ v_1 = \frac{0.287 \times 295.15}{120} \][/tex]

[tex]\[ v_1 = \frac{84.80}{120} \][/tex]

[tex]\[ v_1 = 0.7067 \text{ m}^3/\text{kg} \][/tex]

The flow work can be approximated if we assume the process to be isothermal at the inlet temperature (which is a common simplification for flow work calculation):

[tex]\[ w_{flow} = v_1(p_2 - p_1) \][/tex]

Substituting the values:

[tex]\[ w_{flow} = 0.7067(1000 - 120) \][/tex]

[tex]\[ w_{flow} = 0.7067 \times 880 \][/tex]

[tex]\[ w_{flow} = 622.476 \text{ kJ/kg} \][/tex]

Answer:

26 L

Explanation:

According to the first law of thermodynamics, for an ideal gas:

[tex]\Delta U=Q-W[/tex]

where

[tex]\Delta U[/tex] is the change in internal energy of the gas

Q is the heat absorbed by the gas

W is the work done by the gas

The internal energy of a gas depends only on its temperature. Here the temperature of the gas is kept constant (330 K), so the internal energy does not change, therefore

[tex]\Delta U=0[/tex]

So we have

[tex]Q=W[/tex]

The heat added to the gas is

[tex]Q=1.7 kJ = 1700 J[/tex]

So this is also equal to the work done by the gas:

[tex]W=1700 J[/tex]

For a process at constant temperature, the work done by the gas is given by

[tex]W=nRT ln\frac{V_2}{V_1}[/tex]

where:

n is the number of moles

R is the gas constant

T is the temperature of the gas

[tex]V_1[/tex] is the initial volume

[tex]V_2[/tex] is the final volume

In this problem, we have:

W = 1700 J is the work done by the gas

n = 2.00 mol

T = 300 K is the gas temperature

[tex]V_1=19 L[/tex] is the initial volume of the gas

And solving the equation for V2, we find the final volume of the gas:

[tex]V_2=V_1 e^{\frac{W}{nRT}}=(19)e^{\frac{1700}{(2.0)(8.314)(330)}}=26 L[/tex]

Answer:

The stickiness in the inner walls allows them to be easily coated with the desired antigens, this translates in the use of a smaller amount of antigen. If the walls weren't sticky there's a possibility the antigen won't stick to them and therefore the result of the ELISA can be a false negative.

I hope you find this information useful and interesting! Good luck!

Answer:

Acceleration, a= 1.65m/s^2

Acceleration is downward.

Explanation:

y: N- m1gcosalpha=0

x: Ff- FT- m1gsinalpha= m1× alpha

Ff= uN= um1gcosalpha

FT=m2g

Acceleration ,a = g(ucosalpha- (m2/m1)-sin alpha)

a= (m2/m1) + sinalpha= 1.976

Cos alpha= 0.766

U2= 2.8

a= g(2.8×0.766)- 1.976)

a= g× 0.1688

a= 9.8× 0.1688

a=1.65m/s^2

Answer:

Using a good pair of binoculars, you observe a section of the sky where there are stars of many different apparent brightnesses. You find one star that appears especially dim. This star looks dim because it is farther away or it has a small radius.

Explanation:

Apparent magnitude in astronomy is the apparent brightness of a star that is seen from the Earth, that brightness can variate according to the distance at which the star is from the Earth or due to its radius.

That can be demonstrate with the next equation:

[tex]F = \frac{L}{4\pi r^2}[/tex] (1)

Where F is the radiant flux received from the star, L its intrinsic luminosity and r is the distance.

For example, an observer sees two motorbikes approaching it with its lights on but one of the motorbikes is farther, so the light of this one appears dimmer, even when the two lights emit the same amount of energy per second.  

That is because the radiant flux decreases with the square distance, as can be seen in equation 1.

In the other hand, a bigger radius means that the gravity in the surface of the star will be lower, allowing that light can escape more easily:

[tex]g = \frac{GM}{R^2}[/tex] (2)

Where g is the surface gravity in the star, G is the gravitational constant, M is the mass of the star and R is the radius of the star.

Answer:

Galileo

Explanation:

Galileo formulated the law of free falling bodies that distance traveled by falling bodies are proportional to the squares of the time elapsed.

Galileo confirmed the model of  heliocentric universe given previously by Copernicus that the whole universe revolves around the sun . His observation of movement of Venus helped him prove this model.

Answer:

x2=0.732m

Explanation:

We can calculate the spring constant using the equilibrium equation of the block m1. Since the spring is in equilibrium, we can say that the acceleration of the block is equal to zero. So, its equilibrium equation is:

[tex]m_1g-k\Delta x_1=0\\\\\implies k=\frac{m_1g}{\Delta x_1}\\\\k=\frac{(7.5kg)(9.8m/s^{2})}{0.84m-0.69m}=490N/m[/tex]

Then using the equilibrium equation of the block m2, we have:

[tex]m_2g-k\Delta x_2=0\\\\\\implies x_2=x_0+\frac{m_2g}{k} \\x_2=0.69m+\frac{(2.1kg)(9.8m/s^{2})}{490N/m}= 0.732m[/tex]

In words, the lenght x2 of the spring when the m2 block is hung from it, is 0.732m.

Answer:

[tex]2.4\times 10^{12}[/tex]

Explanation:

We are given that

Speed of light,v=[tex]2.998\times 10^8 m/s[/tex]

Diameter of ring,d=92 m

Radius,r=[tex]\frac{d}{2}=\frac{92}{2}=46 m[/tex]

Current, I=0.40 A

We have to find the number of electrons in the beam.

We know that

Current,I=[tex]\frac{q}{t}[/tex]

Where q= ne

[tex]e=1.6\times 10^{-19} C[/tex]

Using the formula

[tex]0.40=\frac{1.6\times 10^{-19}n}{\frac{2\pi r}{v}}[/tex]

[tex]0.40=\frac{1.6\times 10^{-19}n\times v}{2\pi r}[/tex]

[tex]0.40=\frac{1.6\times 10^{-19}n\times 2.998\times 10^8}{2\pi\times 46}[/tex]

[tex]n=\frac{0.40\times 2\pi\times 46}{1.6\times 10^{-19}\times 2.998\times 10^8}=2.4\times 10^{12}[/tex]