A 100 kg cart goes around the inside of a vertical loop of a roller coaster. The radius of the loop is 3 m and the cart moves at a speed of 6 m/s at the top. The force exerted by the track on the cart at the top of the loop is half the cart's mass, how fast is cart moving in m/s?

Answer:

785.398 W

444.5698 m

Explanation:

I = Intensity of sound

r = Distance

The intensity of sound is given by

[tex]\beta=10log\frac{I}{I_0}\\\Rightarrow 130=10log\frac{I}{10^{-12}}\\\Rightarrow 13=log\frac{I}{10^{-12}}\\\Rightarrow 10^{13}=\frac{I}{10^{-12}}\\\Rightarrow I=10^{-12}\times 10^{13}\\\Rightarrow I=10\ W/m^2[/tex]

Power

[tex]P=IA\\\Rightarrow P=I4\pi r^2\\\Rightarrow P=10\times 4\pi\times 2.5^2\\\Rightarrow P=785.398\ W[/tex]

The power output of the speaker is 785.398 W

If [tex]\beta=85\ db[/tex]

[tex]\beta=10log\frac{I}{I_0}\\\Rightarrow 85=10log\frac{I}{10^{-12}}\\\Rightarrow 8.5=log\frac{I}{10^{-12}}\\\Rightarrow 10^{8.5}=\frac{I}{10^{-12}}\\\Rightarrow I=10^{-12}\times 10^{8.5}\\\Rightarrow I=10^{-3.5}\ W/m^2[/tex]

[tex]P=IA\\\Rightarrow P=I4\pi r^2\\\Rightarrow r=\sqrt{\frac{P}{I4\pi}}\\\Rightarrow r=\sqrt{\frac{785.398}{10^{-3.5}\times 4\pi}}\\\Rightarrow r=444.5698\ m[/tex]

The distance would be 444.5698 m

To calculate the power output of the speaker, we can convert the sound level from decibels to intensity and then use the formula for spherical spreading of sound. To find the distance where the sound level is 85 dB, we can use the same formula and solve for the distance.

To calculate the power output of the speaker, we first need to convert the sound level from decibels to intensity. We can use the formula I = Io * 10^(B/10), where I is the intensity, Io is a reference intensity, and B is the sound level in decibels. With Io = 10^-12 W/m² and B = 130 dB, we can find I. Since the sound spreads in a sphere, we can use the formula I = P / (4πr²), where P is the power output of the speaker and r is the distance. We know I and r, so we can solve for P.

Using the same formula, we can find the distance r where the sound level is 85 dB. We are given the intensity I and the sound level B, so we can solve for r using the formula r = sqrt(P / (4πI)).

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This Physics problem involves two parts using Newton's law of gravitation. For part (a) calculate the gravitational force between the 32 kg object and each of the other objects, and then find the net force. For part (b), set the forces as equal and solve for the appropriate distance, considering the force direction.

To solve these particular physics problems, which are based on Newton's law of gravitation, the following formula can be used: F = G* (m1*m2)/ r^2, where F stands for force, G is the gravitational constant (approximately 6.67 x 10^-11 N(m/kg)^2), m1 and m2 are masses of the objects and r is the distance between them.

For part (a) of the question, we need to calculate the gravitational force between the 32 kg object and each of the other objects, and then find the net force. And for part (b), we set the forces as equal and solve for the appropriate distance.

Remember, it is important to take into account the direction of the force. The two larger weights will each exert a force on the 32 kg weight that tries to pull it towards them. That means that if you measure distance from one of the larger weights, the forces exerted by it will be positive, and the forces from the other weight will be negative.

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Answer:

a

Explanation:

The most reasonable conclusion of the above phenomenon is that water is a poor conductor of heat. Basically water is an insulator. The heat from surface to the bottom of the beaker will take a lot of time. Moreover, no convection current is formed so, heat might not even reach the bottom surface. Hydrogen bonding also play a vital role in determining the thermal properties of water.

hence option A is correct

The most reasonable conclusion from the observation that only the surface of the water in a beaker boils is that water is a poor conductor of heat, which leads to inefficient heat transfer through its body. So the correct option is a.

If a beaker of water is placed under a broiler, with the observation that only the surface layer boils while the water at the bottom of the beaker remains close to the initial temperature, it can be concluded that water is a poor conductor of heat. This phenomenon happens because heat is not efficiently transferred through the body of the water from the hot surface at the top to the cooler sections below. In this scenario, the heat from the broiler predominantly warms the water by radiation directly at the surface, but the lack of conduction prevents the lower part of the water from reaching the boiling point.

Heat conduction in materials depends on the kinetic energy transfer between molecules. Good conductors, like metals, allow for a rapid heat flux due to the effective transfer of energy during molecular collisions. In contrast, poor conductors experience less efficient energy transfer, resulting in a slower rate of heat flow. Additionally, convection could play a role in heat distribution, but in this case, the observation that only the surface boils suggests conduction is the limiting factor for heat transfer to the bottom of the beaker.

Answer:

a. 2.64 m/s

b. 5.9 m/s

c. 997.92 m3

Explanation:

As this is steady flow, the mass flow rate is constant, and so is the product of flow velocity and cross-sectional area

av = 0.077 * 3.6 = 0.2772 m3/s

We can calculate the speed at various areas by dividing the product above by area

a.[tex]v_1 = 0.2772 / a_1 = 0.2772 / 0.105 = 2.64 m/s[/tex]

b.[tex]v_2 = 0.2772 / a_2 = 0.2772 / 0.047 = 5.9 m/s[/tex]

c. Since the volume discharge rate is 0.2772 cube meters per second. In 1 hour, or 60 * 60 = 3600 seconds, the total volume of water discharged would be

0.2772 * 3600 = 997.92 m3

A water pipe with a varying cross-sectional area has a flow rate of 0.277 m³/s at one point. Over one hour, the pipe discharges 1000 m³ of water.

a. Since the water is incompressible, the volume flow rate at all points in the pipe must remain constant. This means that the product of the cross-sectional area and the fluid velocity must be the same at every point.

Using the continuity equation, we can calculate the fluid velocity at points 2 and 3:

V1 * A1 = V2 * A2

3.60 m/s * 7.70×10−2 m2 = V2 * 0.105 m2

Solving for V2:

V2 = (3.60 m/s * 7.70×10−2 m2) / 0.105 m2

V2 ≈ 2.64 m/s

Similarly, for point 3:

V1 * A1 = V3 * A3

3.60 m/s * 7.70×10−2 m2 = V3 * 0.047 m2

Solving for V3:

V3 = (3.60 m/s * 7.70×10−2 m2) / 0.047 m2

V3 ≈ 5.898 m/s

b. To calculate the volume of water discharged from the open end of the pipe in 1.00 hour, we need to determine the volume flow rate and multiply it by the time.

Volume flow rate = Cross-sectional area * Fluid velocity

Volume flow rate = 0.047 m2 * 5.898 m/s

Volume flow rate ≈ 0.277 m³/s

Volume of water discharged in 1.00 hour:

Volume flow rate * Time

0.277 m³/s * 3600 s/hour

≈ 999.12 m³

Since the volume of water discharged in 1.00 hour is close to 1000 m³, we can round it to 1000 m³.

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Answer:2155 J

Explanation:

Given

Change in Internal energy [tex]\Delta U=-1477 J[/tex] i.e. decrease in Internal Energy

Heat added to system [tex]Q=678 J[/tex]

According First law for a system

[tex]dQ=dU+dW[/tex]

[tex]678=-1477+dW[/tex]

[tex]dW=2155 J[/tex]

Thus 2155 J of work is done by system                      

Answer:

Maximum height attained by the ball will be h = 28.416 m

Explanation:

We have given initial speed of the ball u = 23.6 m /sec

At maximum height velocity will be zero so final velocity v = 0 m/sec

Acceleration due to gravity [tex]g=9.8m/sec^2[/tex]

From law of motion we know that [tex]v^2=u^2-2gh[/tex]

[tex]0^2=23.6^2-2\times 9.8\times h[/tex]

h = 28.416 m

So maximum height attained by the ball will be h = 28.416 m

Answer:

[tex]\rho=4.02\times 10^{-8}\ \Omega-m[/tex]

Explanation:

Let us assume that the radius of the wire, r = 0.8 mm = 0.0008 m

EMF of the battery, V = 12 V

Slope of I versus 1/d, m = 600 A-m

The resistance of any material is given by :

[tex]R=\rho \dfrac{d}{A}[/tex]

d is the length of wire

Since, [tex]I=\dfrac{V}{R}[/tex]

[tex]I=\dfrac{VA}{\rho d}[/tex]

[tex]I=\dfrac{VA}{\rho}.(\dfrac{1}{d})[/tex]

[tex]y=slope\times x[/tex]

[tex]\dfrac{VA}{\rho}=600[/tex]

[tex]\rho=\dfrac{VA}{600}[/tex]

[tex]\rho=\dfrac{12\times \pi \times (0.0008)^2}{600}[/tex]

[tex]\rho=4.02\times 10^{-8}\ \Omega-m[/tex]

So, the resistivity of the material of which the wire is made is [tex]4.02\times 10^{-8}\ \Omega-m[/tex].

The slope of the I vs. 1/d graph represents the resistivity of the wire's material. The given slope is 600 A*m, therefore, the resistivity of the material this wire is made of is 600 Ω*m.

The slope of the I vs. 1/d graph is equal to the resistivity of the material the wire is made of. In this case, the slope is given as 600 A*m, so this means the resistivity of the material the wire is made of is 600 Ω*m. This is derived from Ohm's law V=IR which when arranged as I = V/R, indicates that the slope of the graph is the resistance. Since, the resistance R of a cylindrical conductor is directly related to the resistivity (ρ) of the material as R = ρL/A, where L is the length and A is the cross-sectional area, the slope is a representation of this relationship hence representing resistivity.

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Answer:

Gold, Platinum and Uranium

Explanation:

A star is nothing but a huge ball of gas. Specifically, Hydrogen, the simplest element of nature. A star is in equilibrium because its immense mass causes it to collapse towards itself, squeezing those hydrogen nuclei or protons, and the union of the protons in its nucleus causes the star to explode, releasing energy. As long as these nuclear reactions exist (the same ones that human beings can cause with their hydrogen bombs), the star will remain in equilibrium.

Protons have a positive charge and tend to repel. But inside the stars they are so tight (there is a lot of pressure and temperature), that they can't avoid crashing. At that time, the electromagnetic force is defeated by what physicists call Strong Force, which holds together protons and neutrons forming more complex atoms. In a typical star, the protons join to form the next element in the periodic table: Helium, consisting of 2 protons and two neutrons. It is a rare element on Earth and was discovered in the Sun rather than on our planet. Hence his name, from the Greek Helios, the sun god.

However, the mass of the sum of the protons that bind to form Helium is less than the total mass of Helium. What happen? Are the laws of physics inside the stars not fulfilled? What happens is impossible to understand if one is born before Albert Einstein, but today it is very easy to explain. The mass that we lack, has actually become energy. The German physicist Albert Einstein (1879-1955) discovered that mass and energy are equivalent while formulating his Theory of Relativity. In fact, let me, for once, write a mathematical equation of an unparalleled beauty:

E = mc2

This equation tells us that the energy E is equal to the mass m times the square of a constant c; that constant c is the speed of light, approximately 300,000 km / s. That is, a very small mass, such as a proton, is equivalent to a very large energy, since the numerical factor by which the mass is multiplied is a very large number. And that energy is what the stars release, the one that our Sun emits and gives us life.

When Hydrogen is depleted, the star collapses until the pressure and temperature increase enough for Helium to fuse with itself; the cycle is repeated and the star ends up generating Carbon, Oxygen, Nitrogen, Silicon, Iron. As you can see, the stars are factories of atoms. When the star explodes, even heavier atoms are generated, such as Gold, Platinum, Uranium, elements that abound on our planet. And they abound, because the Sun is a second or third generation star: that is, it was born from the remains of other stars' explosions, along with the materials that make up our planet, the rest of the planets, the asteroids, the comets, the interstellar dust and ourselves.

Answer:

It is known as the centripetal vector directed to the centre of the fictious circumference

The acceleration vector of a particle in uniform circular motion always points towards the center of the circle

The total acceleration vector of a particle in uniform circular motion always points towards the center of the circle. It is directed perpendicular to the velocity vector and its magnitude is given by [tex]a = v^2/r,[/tex] where v is the magnitude of the velocity vector and r is the radius of the circle.

For example, when a car is moving in a circular path on a banked turn, the acceleration vector points towards the centre of the turn, keeping the car on the circular track. In summary, the acceleration vector of a particle in uniform circular motion is always directed towards the centre of the circle and its magnitude is given by [tex]a = v^2/r,[/tex]

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Answer: The Sun is at the center of the solar system and the planets move around it.

Explanation:

During the Middle Ages, it was believed that the Earth remained motionless, occupying the center of a universe subject to uniform circular motion where Earth was the only world. All this because the only accepted idea was that of Ptolemy.  

Until the Polish astronomer Nicolaus Copernicus proposed that the Earth annually orbits the Sun and rotates once a day on its own axis.  He also dared to affirm that the other planets also orbited the Sun as a fixed point. This meant the Earth was no longer unique, nor did it occupy the center of the known universe.  

On the other hand, Galileo observed Venus with his telescope and found out it presented phases (such as those of the moon) together with a variation in size; observations that are only compatible with the fact that Venus rotates around the Sun and not around Earth.

These observations and discoveries were presented by Galileo to the Catholic Church (which supported the geocentric theory at that time) as a proof that completely refuted Ptolemy's geocentric system and affirmed Copernicus' heliocentric theory.

It is important to note, this was the main reason for Galileo to be arrested.

Answer:

Explanation:

Given to find the pressure

v = 12.6 m/s , A = 3.0m * 1.8 m = 54 m^2

p air = 1.3 kg/m^3

F = 1/2 * p *v^2 *A

F = 1/2 *1.3 kg/m^3 * (12.6 m/s)^2 * 54m^2

F = 5572.476 N

The stress and the pressure can find across the area

α = F /A

α = 5572.476 N / 54 m^2

α = 103.194 Pa

Answer:

[tex]\omega=32.14\ rad/s[/tex]

Explanation:

Given that,

The compression in the spring, x = 0.0647 m

Speed of the object, v = 2.08 m/s

To find,

Angular frequency of the object.

Solution,

We know that the elation between the amplitude and the angular frequency in SHM is given by :

[tex]v=\omega\times A[/tex]

A is the amplitude

In case of spring the compression in the spring is equal to its amplitude

[tex]\omega=\dfrac{v}{A}[/tex]

[tex]\omega=\dfrac{2.08\ m/s}{0.0647\ m}[/tex]

[tex]\omega=32.14\ rad/s[/tex]

So, the angular frequency of the spring is 32.14 rad/s.

Final answer:

An ionic bond is the electrostatic attraction that holds together ions with opposite charges in an ionic compound, such as sodium and chlorine forming table salt.

Explanation:

The electrostatic attraction that binds oppositely charged ions together is known as an ionic bond. This type of chemical bond is fundamental in the formation of ionic compounds where electrons are transferred from one atom to another, such as the formation of table salt from sodium and chlorine.

Ions are created when atoms either lose or gain electrons, leading to the formation of cations (positively charged) and anions (negatively charged). The electrostatic attraction between these ions of opposite charge results in a stable ionic structure. For instance, a sodium ion (Na+) will form a stronger ionic bond with a 2+ charge than with a 1+ charge due to the increased electrostatic attraction.

Answer:

d) Decrease, increase, remain constant

Explanation:

If one tire has a slow leak, the air pressure within the tire will_DECREASE____with time due to outflow of air , the surface area between the tire and the road will__INCREASE__in time,due to flattening of tire.

The net force the tire exerts on the road will_REMAIN CONSTANT____in time. It is so because force does not depend upon area. It is pressure which depends upon area. As there is no change in the weight of the car , force on the road will remain constant.

Answer: 16.9cm/s

Explanation:

According to the principle of conservation of linear momentum which states that the sum of momentum of bodies before collision is equal to the sum of their momentum after collision.

Momentum = mass × velocity of the body

Let m1 be mass of the first body= 12g

m2 be mass of the second body= 29cm/s

v1 be velocity of the first body= 24g

v2 be velocity of the second body= 14cm/s.

Note that both objects will move with a common velocity (v) after collision. Using the formula

m1v1 + m2v2 = m1v +m2v

12(24) + 29(14) = (12+29)v

288+406 = 41v

694 = 41v

v = 694/41

v = 16.9cm/s

To find the velocity of the slower object after the elastic collision, we can use the conservation of momentum and kinetic energy equations. By plugging in the given values and solving the system of equations, we can determine the final velocities of both objects.

In an elastic collision, the total momentum of the system is conserved. To find the velocity of the slower object after the collision, we can use the equation:

mass₁ × velocity₁ + mass₂ × velocity₂ = mass₁ × final_velocity₁ + mass₂ × final_velocity₂

Plugging in the values, we have:

12g × 29 cm/s + 24g × 14 cm/s = 12g × final_velocity₁ + 24g × final_velocity₂

Converting the masses to kg, and solving for final_velocity₂:

0.012 kg × (29 cm/s) + 0.024 kg × (14 cm/s) = 0.012 kg × (final_velocity₁) + 0.024 kg × (final_velocity₂)

0.348 kg cm/s + 0.336 kg cm/s = 0.012 kg × final_velocity₁ + 0.024 kg × final_velocity₂

0.684 kg cm/s = 0.012 kg × final_velocity₁ + 0.024 kg × final_velocity₂

Since the collision is elastic, the total kinetic energy of the system is conserved. This means that the final kinetic energy of the system is equal to the initial kinetic energy.

Using the formula for kinetic energy:

(1/2) × mass₁ × (velocity₁)² + (1/2) × mass₂ × (velocity₂)² = (1/2) × mass₁ × (final_velocity₁)² + (1/2) × mass₂ × (final_velocity₂)²

Plugging in the values:

(1/2) × 0.012 kg × (29 cm/s)² + (1/2) × 0.024 kg × (14 cm/s)² = (1/2) × 0.012 kg × (final_velocity₁)² + (1/2) × 0.024 kg × (final_velocity₂)²

0.012 kg cm²/s² + 0.024 kg cm²/s² = 0.012 kg × (final_velocity₁)² + 0.024 kg × (final_velocity₂)²

0.036 kg cm²/s² + 0.336 kg cm²/s² = 0.012 kg × (final_velocity₁)² + 0.024 kg × (final_velocity₂)²

0.372 kg cm²/s² = 0.012 kg × (final_velocity₁)² + 0.024 kg × (final_velocity₂)²

We now have a system of two equations with two unknowns. Solving this system will give us the final velocities of both objects after the collision.

Answer:

[tex]r_k=0.5r_e[/tex]

Explanation:

[tex]M_e[/tex] = Mass of Earth

[tex]M_k[/tex] = Mass of Kardashia = [tex]4M_e[/tex]

[tex]R_e[/tex] = Radius of Earth

[tex]R_k[/tex] = Radius of Kardashia

Gravitational force of Earth on object

[tex]F_e=\frac{GM_em}{r_e^2}[/tex]

Gravitational force of Kardashia on object

[tex]F_k=\frac{GM_km}{r_k^2}\\\Rightarrow F_k=\frac{G4M_e}{r_k^2}[/tex]

The gravitational force i.e., the weight of the body is same on both the planets

[tex]F_e=F_k[/tex]

If the same particle is used then the mass will also be equal

Dividing the forces

[tex]\frac{F_e}{F_k}=\frac{\frac{GM_em}{r_e^2}}{\frac{G4M_e}{r_k^2}}\\\Rightarrow 1=4\frac{r_k^2}{r_e^2}\\\Rightarrow r_k^2=\frac{1}{4}r_1^2\\\Rightarrow r_k=\frac{1}{2}r_e\\\Rightarrow r_k=0.5r_e[/tex]

The radius of the planet Kardashia is half of the radius of Earth

Answer:a) Each is at same temperature

Explanation:

According to the zeroth law of thermodynamics when two objects are in thermal equilibrium with the third one then they are at thermal equilibrium with each other thus they all are at the same temperature.

Here Also objects are in thermal Equilibrium then they should be at the same temperature.

As Internal Energy is an Extensive Property that depends on the amount of gas Present thus two gases at thermal Equilibrium can have different Temperatures.        

Final answer:

Objects at thermal equilibrium are at the same temperature, by the principle of thermal equilibrium and the Zeroth law of thermodynamics. This equilibrium does not require the objects to have the same internal energy or heat content.

Explanation:

For objects at thermal equilibrium, the correct statement is that each is at the same temperature. This is directly derived from the principle of thermal equilibrium, which states when two or more objects are in thermal contact and no heat flows between them, they are considered to be in thermal equilibrium. According to the Zeroth law of thermodynamics, if object A is in thermal equilibrium with object B, and object A is also in thermal equilibrium with object C, then objects B and C are in thermal equilibrium with one another. This invariably leads to the understanding that all objects at thermal equilibrium share the same temperature, but not necessarily the same internal energy or the same amount of heat.

While the law of conservation of energy ensures that the total energy in an isolated system remains constant, how this energy is distributed among objects (in terms of internal energy or heat) can vary significantly based on each object's specific heat capacity, mass, and other factors. Therefore, the correct answer to the question is: a. Each is at the same temperature.

Answer: At the period that's between its peaks of brightness and its luminosity.

Explanation:

The two observable properties of a cepheid variable that are directly related to one another at the period between its peaks of brightness and its luminosity. The period-luminosity relation allows us to determine its luminosity from the period between its peaks of brightness. In astronomy, a period-luminosity relation is a relationship linking the luminosity of pulsating variable stars with their pulsation period. The popular relation, for Classical Cepheid variables, is also called Leavitt's law

Answer:

3 x 10^18 kg

Explanation:

Time period, T = 3 days = 86400 x 3 = 259200 seconds

r = 7 x 10^5 m

Let M be the mass of planet

Use the formula of time period of satellite

[tex]T = 2\pi \sqrt{\frac{r}{GM}}[/tex]

Where, G be the universal gravitational constant.

[tex]M=\frac{4\pi ^{2}r^{3}}{GT^{2}}[/tex]

By substituting the values

[tex]M=\frac{4\times 3.14 \times 3.14\times \left ( 7\times 10^{5} \right )^{3}}{6.67\times 10^{-11}\times 259200\times 259200}[/tex]

M = 3 x 10^18 kg

Thus , the mass of planet is 3 x 10^18 kg.

Answer:

As a result of the violent revolts in france in july 1830 gave up the throne and fled for Great Britain.

Explanation:

Following Charles X taking the throne of France, he strengthened the power of the clergy and the monarchy. In 1830, Charles X attempted to suppress the Constitution, suspend Parliament, and shut down the press. The press disobeyed and encouraged mobs to protest. The protests got violent and fearing for his life, Charles X stepped down from the throne and took his family to Great Britain.

Answer:

Bird's speed immediately after swallowing = 4.52 m/s

Explanation:

Here momentum is conserved.

Initial momentum = Final momentum

Mass of bird = 300 g = 0.3 kg

Velocity of bird = 5.5 m/s

Mass of insect = 10 g = 0.01 kg

Velocity of insect = -25 m/s ( opposite to the motion of bird)

Initial momentum = 0.3 x 5.5 + 0.01 x -25 = 1.4 kgm/s

Final mass = 0.3 + 0.01 = 0.31 kg

Initial momentum = Final momentum = 1.4 kgm/s

                 1.4 = 0.31 x Bird's speed immediately after swallowing

         Bird's speed immediately after swallowing = 4.52 m/s

The speed of the bird immediately after swallowing, measured by an observer on the ground, is 4.52 m/s.

Momentum of a object is the force of speed of it in motion. Momentum of a moving body is the product of mass times velocity.

When the two objects collides, then the initial collision of the two body is equal to the final collision of two bodies by the law of conservation of momentum.

A 300 g bird flying along at 5.5 m/s sees a 10g insect heading straight toward it with a speed of 25 m/s (as measured by an observer on the ground, not by the bird).

Let suppose the bird's speed immediately after swallowing is v' m/s. Thus, by the conservation of momentum,

[tex](m_1v_1)+(m_2v_2)=(m_1+m_2)v'[/tex]

Put the values,

[tex](0.3\times5.5)+(0.01\times(-25))=(0.3+0.01)v'\\v'=4.52\rm\; m/s[/tex]

Thus, the speed of the bird immediately after swallowing, measured by an observer on the ground, is 4.52 m/s.

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Answer:

[tex]0.57 ms^{-1}[/tex]

Explanation:

k = spring constant of the spring = 40 Nm⁻¹

A = amplitude of the simple harmonic motion = 4 cm = 0.04 m

m = mass of the block attached to spring = 0.20 kg

w = angular frequency of the simple harmonic motion

Angular frequency of the simple harmonic motion is given as [tex]w = \sqrt{\frac{k}{m} } \\w = \sqrt{\frac{40}{0.20} }\\w = 14.14 rads^{-1}[/tex]

[tex]v[/tex] = Speed of the block as it pass the equilibrium point

Speed of the block as it pass the equilibrium point is given as

[tex]v = A w\\v = (0.04) (14.14)\\v = 0.57 ms^{-1}[/tex]

Final answer:

The speed of a 0.20-kg block attached to a spring and released from a displacement of 4.0 cm on a frictionless surface is calculated to be 0.4 m/s when it passes through the equilibrium point, using conservation of mechanical energy.

Explanation:

The question involves calculating the speed of a block when it passes through the equilibrium point after being released from a displacement in a setup involving harmonic motion. In this case, we use the principle of conservation of mechanical energy. The total mechanical energy in a system, including potential and kinetic energy, remains constant if only conservative forces are doing work. Since the surface is frictionless and the only force doing work is conservative (spring force), the potential energy stored in the spring when the block is displaced is fully converted into kinetic energy when the block passes through the equilibrium position.

The potential energy stored in the spring at the maximum displacement is given by ½*k*x², where k is the spring constant (40 N/m) and x is the displacement (0.04 m). Thus, PE = 0.5 * 40 * (0.04)² = 0.032 J. At the equilibrium point, all this potential energy is converted into kinetic energy (KE = 0.5 * m * v²), allowing us to solve for v (speed). Rearranging KE = PE gives v = [tex]\sqrt{(2*PE/m)[/tex]. Plugging in the values, v = [tex]\sqrt{2*0.032/0.20[/tex] = 0.4 m/s.

Final Answer:

The angle θ at which the wheel comes to rest is approximately θ = tan^(-1)(μ), where μ is the coefficient of static friction. The minimum coefficient of static friction required to prevent slipping is μ = tan^(-1)(m_wheel / m_cylinder), where m_wheel is the mass of the wheel and m_cylinder is the mass of the cylinder.

Explanation:

In this scenario, the forces involved include the gravitational force acting on both the wheel and the cylinder and the tension in the cord. The component of the gravitational force parallel to the incline causes the wheel to roll, and the frictional force opposes slipping. At the point where the wheel comes to rest, the net force along the incline is zero.

Using the equilibrium condition, the gravitational force component along the incline is balanced by the frictional force. This gives us the equation: m_wheel * g * sin(θ) = μ * m_wheel * g * cos(θ), where g is the acceleration due to gravity. Simplifying, we find μ = tan(θ).

To find the minimum coefficient of static friction, we can substitute the masses of the wheel and cylinder: μ_min = tan^(-1)(m_wheel / m_cylinder). This represents the point where the wheel will come to rest without slipping. The tan^(-1) function gives the angle at which the static friction is just sufficient to prevent slipping, and this corresponds to the minimum coefficient of static friction required.

Answer:

10 m/s

Explanation:

mass, M = 2000 kg

Power, P = 100 kW = 100000 W

inclination, θ = 30°

g = 10 m/s^2

Let the velocity is v.

P = F x v

where, F is force and v be the velocity

100000 = mg Sin 30 x v

100000 = 2000 x 10 x 0.5 x v

v = 10 m/s

Thus, the speed is 10 m/s.

Answer:

Fusion of hydrogen to helium

Explanation:

The sun produces its energy mainly by fusing hydrogen nuclei to form helium.

In the sun 4 hydrogen nuclei join to form one of helium, this fusion releases a lot of energy and because this fusion occurs in large quantities, this is where the energy of a star like our sun is produced, and that is the reason of its plasma state.

The energy produced in the fusion is received on earth in the form of electromagnetic radiation.

Answer:

D. Nothing will happen; the seesaw will still be balanced.

Explanation:

D. Nothing will happen; the seesaw will still be balanced. Since both toruqes or momentums respect to the center have changed in the same amount (one-half their original distance) the seesaw will remain balanced, if the children change distance in a different amount then it will be out of balance

D. Nothing will happen; the seesaw will still be balanced.

The force acting on a system with static equilibrium is 0

[tex] \large {\boxed {\bold {\sum F = 0}} [/tex]

(forces acting as translational motion only, not including rotational forces)

[tex] \displaystyle \sum F_x = 0 \\\\\ sum F_y = 0 [/tex]

For objects undergoing rotation, the equilibrium must be met

[tex] \large {\boxed {\bold {\sum \tau = 0}} [/tex]

A heavy boy (Hb) and a lightweight girl (Lg) are balanced on a mass-less seesaw

Because there is a balance of rotation, the torque equation:

Στ = 0

Hb.r1-Lg.r2 = 0

Hb.r1 = Lg.r2 (equation 1)

If they both move forward so that they are one-half their original distance from the pivot point, then the distance of the two children to the pivot point is reduced to half

Then the torque equation:

[tex]\rm Hb\times \dfrac{r_1}{2}= Lg\times \dfrac{r_2}{2}\\\\Hb\times r_1=Lg\times r_2[/tex]

This equation remains the same as equation 1, so the seesaw will still be balanced.

tangential force

https://brainly.com/question/2175648

displacement of a skateboarder

brainly.com/question/1581159

The distance of the elevator

brainly.com/question/8729508

Answer

Given,

Frequency of the ultrasonic pulse = 30 kHz

Speed of the sound = v = 343 m/s

wavelength of the wave emitted = ?

using formula

     [tex]v = \nu \lambda[/tex]                    

     [tex]\lambda= \dfrac{v}{\nu}[/tex]                  

     [tex]\lambda= \dfrac{343}{30\times 10^3}[/tex]

     [tex]\lambda=11.43 \times 10^{-3}\ m[/tex]          

     [tex]\lambda=11.43\ mm[/tex]                    

time taken for a pulse  that reflects off an object 3.0 m away to make a round trip                                                

   [tex]time = \dfrac{\Delta x}{\Delta v}[/tex]

   [tex]time = \dfrac{2\times 3}{343}[/tex]

            t = 0.01749 s

            t = 17.49 ms

The motion detector uses ultrasonic waves to measure distance by timing the round trip of a sound wave. Distance is calculated using the speed of sound and the time taken for the echo to return, and the calculation requires a division by 2 to account for the round trip. Calibration is important for accuracy as the speed of sound changes with temperature.

The motion detector described is a classic example of how ultrasonic waves can be used to measure distance. A similar principle is applied in an automatic focus camera, which generates ultrasonic sound waves, captures their reflections off objects, and calculates the distance based on the time delay of the returning waves. The speed of sound in air at 20 ℃ is approximately 344 m/s. Therefore, if a sound wave returns after 0.150 seconds, we can calculate the distance to the object as follows:

Distance = Speed of Sound × Time / 2
Distance = 344 m/s × 0.150 s / 2
Distance = 25.8 meters
This calculation takes into account that the sound wave must travel to the object and back, making the total distance twice the distance we want to measure, hence the division by 2.

The ultrasonic range finder and technologies such as radar and Doppler shift applications in traffic law enforcement rely on similar concepts of wave reflection and frequency shifts to measure distance and speed.

To understand the effects of temperature on the calibration of such devices, the room temperature is required because the speed of sound in air changes with temperature, potentially influencing the accuracy of these measurements.

Answer:

l=24.8 cm

Explanation:

The period of a simple pendulum is given by

[tex]T= 2\pi\sqrt{\frac{l}{g} }[/tex]

l= length of pendulum

g= acceleration due to gravity

taking square on both the sides we get

[tex]T^2= 4\pi^2\frac{l}{g}[/tex]

This can be rewritten as

[tex]l = \frac{T^2}{g}4\pi^2[/tex]

now substituting T= 1 and g= 9.8

[tex]l = \frac{1^2}{9.8}4\pi^2[/tex]

l= 0.248 m = 24.8 cm

Final answer:

The length of a pendulum with a period of 1.00 s can be calculated using the formula L = (T^2/g)π^2, resulting in a length of approximately 0.999 m or 99.9 cm.

Explanation:

The period of a pendulum is determined by its length and the acceleration due to gravity, and it is independent of factors such as mass or amplitude. The period is given by the formula T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

In the given question, the period of the pendulum is 1.00 s. To find the length of the pendulum, we can rearrange the formula and solve for L: L = (T^2/g)π^2.

Using a standard value for acceleration due to gravity of 9.8 m/s^2, we can substitute the values to find the length of the pendulum: L = (1.00 s^2 / 9.8 m/s^2)π^2. Evaluating this expression, we find that the length of the pendulum is approximately 0.999 m, or 99.9 cm.

Answer:  The correct answer is :  have entered into G0

Explanation:  G0 is the fifth phase, it is named because it is out of the cycle, it is still for an undefined time when new cells are not needed and in this phase the cell is not in division and has lost the ability to perform mitosis.

Answer:

Option (a)

Explanation:

Impulse is defined as the change in momentum of the body. It is a vector quantity and its SI unit is Kg m/s.

mass of ball, m = 0.4 kg

initial velocity, u = - 30 m/s

Final velocity, v = + 20 m/s

Initial momentum, pi = mass x initial velocity = m u = 0.4 x (- 30) = - 12 kg m/ s

Final momentum, pf = mass x final velocity = mv = 0.4 x 20 = 8 Kg m /s

Change in momentum = final momentum - initial momentum = 8 - (- 12 )

So, impulse = 20 kg m /s right

Option (a) is correct

Final answer:

The impulse of the net force on the ball during its collision with the wall is the change in momentum, coming to 32 kg·m/s to the right, leading to option E) none of the above as the correct answer.

Explanation:

The impulse of the net force on a ball during its collision with the wall can be calculated using the change in momentum of the ball, which is equal to the impulse imparted to it. If the ball has a mass of 0.40 kg and changes its velocity from 30 m/s to the left (which we can consider as a negative direction) to 20 m/s to the right (a positive direction), we need to take into account the magnitude and the direction of this change.

The initial momentum of the ball is given by the product of its mass and its initial velocity, which is -0.40 kg × 30 m/s (the negative sign indicates the initial leftward direction). The final momentum after the collision is 0.40 kg × 20 m/s. The impulse is the difference between the final and initial momentum: (0.40 kg × 20 m/s) - (-0.40 kg × 30 m/s), which equals 20 kg·m/s + 12 kg·m/s or 32 kg·m/s to the right. Therefore, the correct answer is E) none of the above.