A 3.9-m-diameter merry-go-round is rotating freely with an angular velocity of 0.70 rad/s. Its total moment of inertia is 1320 kg.m. Four people standing on the ground, each of mass 70 kg suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now? What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?

Answer:

40kg

Explanation:

that the answer

The density of water expressed in SI unit is 1000.3 kg/m³

Density is defined as the ratio of mass per unit volume.

where M is the mass of the object and V is the volume occupied by the object

As we know that 1 slug = 14.593 kg

So 1.94 slug = 1.94 × 14.593 kg

Also 1 ft³ = 0.0283 m³

On converting slug/ft³ to kg/m³

= (1.94 slug/ ft³) * (14.593/1 slug) * (1/0.0283 )

= 1000.3 kg/m³

Therefore the density in SI unit is 1000.3 kg/m³.

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When a pipe is filled with a liquid of higher density than air, the frequency of the normal modes of the pipe decreases.

This is due to the fact that the speed of sound is proportional to the square root of the ratio of the bulk modulus to the density of the medium in which it travels.

When the density of the medium inside the pipe increases, the velocity of sound decreases, causing the frequency of the normal modes to decrease.

he wavelength of the sound waves inside the pipe is shortened due to the increase in density, resulting in a lower frequency of the normal modes.

The frequency of the normal modes of a pipe is influenced by a variety of factors, including the diameter and length of the pipe, as well as the speed of sound in the medium inside the pipe. T

he frequency of the normal modes is inversely proportional to the length of the pipe, with longer pipes producing lower frequencies.

In the case of a pipe filled with a liquid of higher density than air, the frequency of the normal modes would be lower than if it were filled with air.

This is because the speed of sound in the liquid would be lower than in air, resulting in a decrease in the frequency of the normal modes.

When a pipe is filled with a liquid of higher density than air, the frequency of the normal modes of the pipe decreases.

This is due to the fact that the speed of sound in the liquid is lower than in air, resulting in a decrease in the frequency of the normal modes.

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The correct way to compare two strings in C++ is by using the s1.compare(s2) function. The function returns an integer value that indicates whether the two strings are equal or if one is greater or less than the other.

Let's understand how the s1.compare(s2) function works. The function takes two arguments - the first is the string s1 that we want to compare, and the second is the string s2 that we want to compare s1 with. The function returns an integer value that indicates the result of the comparison.

If s1 is greater than s2, the function returns a positive integer value. If s1 is less than s2, the function returns a negative integer value. And if s1 is equal to s2, the function returns 0.The function compares the two strings lexicographically, that is, it compares the corresponding characters of the two strings starting from the first character.

If the characters at the same position in both strings are equal, it moves on to compare the next character, and so on until it finds a mismatched character. Then it returns the difference between the ASCII values of the two mismatched characters.Here is an example of using the s1.compare(s2) function:```#include
#include
using namespace std;
int main()
{
   string s1 = "hello";
   string s2 = "world";
   int result = s1.compare(s2);
   if (result == 0)
       cout << "s1 and s2 are equal" << endl;
   else if (result > 0)
       cout << "s1 is greater than s2" << endl;
   else
       cout << "s1 is less than s2" << endl;
   return 0;
}```In the above example, we compare two strings s1 and s2 using the s1.compare(s2) function. Since s1 is less than s2 lexicographically, the function returns a negative integer value, and we print "s1 is less than s2".I hope this helps!

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a)A ball is thrown at an angle of 40 degrees, the ball reach the height  is 8.24m

b)Time taken by the ball in the air is 2.620 s.

c) far form the edge of the building will it land is 86.24m.

a) Maximum height is given as :

H = (v₀ sinθ)²/2g

H = (20 x 0.642)²/(2 x 9.8)

H = 8.24m

b) Time taken by the ball :

T = 2v₀ sinθ/g

T = (2x 20 x 0.642)/9.8

T = 2.620 s

c) far form the edge of the building will it land:

range is calculated as :

R = v₀ sin2θ/g

R = (20 x 0.022)/9.8

R = 86.24m

a)A ball is thrown at an angle of 40 degrees, the ball reach the height  is 8.24m

b)Time taken by the ball in the air is 2.620 s.

c) far form the edge of the building will it land is 86.24m.

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The movement described in the question is known as toe walking. Toe walking is a gait abnormality where the individual walks on the balls of their feet or the toes, rather than using their heels to touch the ground first. It is a common behavior seen in children, especially in their early stages of walking, but it usually resolves on its own without any treatment.

However, in some cases, toe walking may persist and can cause various complications such as muscle tightness, tendon shortening, and difficulties in balance and coordination.

Toe walking can be a sign of an underlying neurological condition, such as cerebral palsy or autism, or it can be caused by tightness in the calf muscles, a short Achilles tendon, or structural problems in the feet. Treatment options include physical therapy, stretching exercises, orthotics, and in rare cases, surgery. Early intervention is essential to prevent any long-term complications associated with toe walking.

In summary, toe walking is a common movement observed in children, but it can indicate underlying medical conditions that require attention. If you notice persistent toe walking in your child, it is best to seek medical advice to ensure timely intervention and treatment.

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The maximum net charge that can be placed on the spherical conductor before dielectric breakdown occurs can be found using the formula: Q = 4πε₀r²E where Q is the charge, ε₀ is the electric constant (8.854 × 10^-12 F/m), r is the radius of the conductor, and E is the dielectric strength of the air.

Substituting the given values, we get:

Q = 4π(8.854 × 10^-12)(0.72)^2(3 × 10^6) = 5.05 × 10^-6 C or 5.05 µC (to three significant figures)

The magnitude of the potential of the sphere when it carries this maximum charge can be found using the formula:

V = kQ/r

where V is the potential, k is the Coulomb constant, Q is the charge, and r is the radius of the conductor.

Substituting the given magnitude, we get:

V = (8.98755 × 10^9)(5.05 × 10^-6)/(0.72) = 6.27 kV (to two significant figures)

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The magnitude of the potential of the sphere when it carries the maximum charge is 16.4 kV.

Q_max = 4πε_0R²E_max

Q_max = 4π(8.854 × \(10^{-12}\) F/m)(0.72 m)^2(3 × \(10^{6}\) V/m)

= 4.02 × \(10^{-6}\) C

= 4.02 µC

V = Q/(4πε_0R)

V = (4.02 × \(10^{-6}\) C)/(4π(8.854 × \(10^{-12}\)F/m)(0.72 m))

= 16.4 kV

A charge is a fundamental property of matter that describes the electric force that an object can exert on other objects. It is a scalar quantity that can be positive or negative, and its unit of measurement is the Coulomb (C).

The charge can exist in two types: positive and negative. Positive charges are carried by protons, while negative charges are carried by electrons. The total charge of an isolated system is always conserved, meaning that it cannot be created or destroyed, only transferred or redistributed among objects. Electric charge plays a critical role in a wide range of physical phenomena, including the behavior of atoms and molecules, the functioning of electrical circuits, and the interactions between particles in the universe.

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Answer:

f = 5 Hz

Explanation:

use f = speed / wavelength

f = 100 m/s / 20 m

f = 5 Hz

Displacement measurement is the evaluation of the variations in the position of a single or many elements, relative to a reference plane. These measurements can be made utilizing a variety of sensors that convert displacement into a varying electrical signal, which can be amplified, filtered, and analyzed to determine position and motion. The piezoelectric sensor is a transducer that transforms mechanical energy into electrical energy. It can be used for displacement measurement.

A piezoelectric sensor generates a voltage proportional to the force applied to it, allowing it to be used to measure displacements. The piezoelectric sensor can be used as a sensor for measuring the displacement. It works on the principle of piezoelectric effect. The piezoelectric effect can be explained as when a mechanical stress is applied to a crystal, it generates a voltage across the crystal that is proportional to the mechanical stress applied to the crystal. When the stress is released, the voltage disappears. Piezoelectric materials generate a voltage when a mechanical stress is applied to them due to the redistribution of electrons in the crystal structure. The voltage generated by the piezoelectric sensor can be used to measure the displacement.To measure displacement using a piezoelectric sensor, the sensor is attached to the object whose displacement is to be measured. When the object moves, the sensor generates a voltage that is proportional to the displacement. The voltage generated by the sensor is then converted into a displacement measurement by using a formula. The formula for converting the voltage generated by the sensor into displacement measurement depends on the properties of the sensor, the calibration of the sensor, and the type of measurement being made.

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Answer:

88 %

Explanation:

The rate of heat loss by a conducting material of thermal conductivity K, cross-sectional area,A and thickness d with a temperature gradient ΔT is given by

P = KAΔT/d

The total heat lost by the styrofoam wall is P₁ = K₁A₁ΔT₁/d₁ where K₁ =thermal conductivity of styrofoam wall 0.033 W/m-K, A₁ = area of styrofoam wall = 17 m², ΔT₁ = temperature gradient between inside and outside of the wall and d₁ = thickness of styrofoam wall = 0.20 m

The total heat lost by the glass window is P₂ = K₂A₂ΔT₂/d₂ where K₂ =thermal conductivity of glass window pane wall 0.96 W/m-K, A₂ = area of glass window pane = 0.15 m², ΔT₂ = temperature gradient between inside and outside of the window and d₂ = thickness of glass window pane = 7 mm = 0.007 m

The total heat lost is P = P₁ + P₂ = K₁A₁ΔT₁/d₁ + K₂A₂ΔT₂/d₂

Now, since the temperatures of both inside and outside of both window and wall are the same, ΔT₁ = ΔT₂ = ΔT

So, P = K₁A₁ΔT/d₁ + K₂A₂ΔT/d₂

Since P₂ = K₂A₂ΔT₂/d₂ = K₂A₂ΔT/d₂is the heat lost by the window, the fraction of the heat lost by the window from the total heat lost is

P₂/P = K₂A₂ΔT/d₂ ÷ (K₁A₁ΔT/d₁ + K₂A₂ΔT/d₂)

= 1/(K₁A₁ΔT/d₁÷K₂A₂ΔT/d₂ + 1)

= 1/(K₁A₁d₂÷K₂A₂d₁ + 1)

= 1/[(0.033 W/m-K × 17 m² × 0.007 m ÷ 0.96 W/m-K × 0.15 m² × 0.20 m) + 1]

= 1/(0.003927/0.0288 + 1)

= 1/(0.1364 + 1)

= 1/1.1364

= 0.88.

The percentage is thus P₂/P × 100 % = 0.88 × 100 % = 88 %

The percentage of heat lost by window of the total heat is 88 %

The equivalent resistance between points A and B in the diagram is 22 Ω

We shall begin by obtaining the equivalent resistance in parallel (i,e the three 6 Ω resistor). Details below:

1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃

1/Rₜ = 1/6 + 1/6 + 1/6

1/Rₜ = 3/6

1/Rₜ = 1/2

Rₜ = 2 Ω

Finally, we shall determine the equivalent resistance between A and B (i.e series arrangement). Details below:

R = R₁ + R₂ + R₃ + R₄ + R₅ + R₆ + R₇ + R₈ + R₉ + R₁₀ + R₁₁

R = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2

R = 22Ω

Thus, we can conclude that the equivalent resistance is 22 Ω

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Answer:

a = 30 km / h²

Explanation:

Dado que

Velocidad inicial, u = 70 km / h

Velocidad final, v = 95 km / h

Tiempo, t = 30 s = 0.1 h

Lo sabemos

v = u + a t

a = aceleración

Ahora poniendo los valores en la ecuación anterior

\(95 = 70 + a \ times 0.1 \)

\(a = \ dfrac {95-70} {0.1} = 30 \ km / h ^ 2 \)

Por lo tanto, la aceleración será

a = 30 km / h²

Answer:

A lightbulb has 25 W stamped on it. What does this mean?:

These labels mean that each lightbulb has Its respective power delivered to It when It Is connected to a constant

Explanation:

Answer:

Explanation:

The formula for this is designed around the fact that momentum must be conserved:

\([(m_{ball1}*v_{ball1})+(m_{ball2}*v_{ball2})]_b=[(m_{ball1}+m_{ball2})v_{both}]_a\)

This is because they sitck together after they collide. Filling in:

[(3*10)+(5*2)] = [3 + 5]v and

30 + 10 = 8v so

40 = 8v and

v = 5

They are both moving east at a velocity of 5 m/s since they stuck together.

Our ability to perceive movement when reading "message boards" that are used in advertising is based on:

Our ability to perceive movement in advertising is based on apparent movement. This is a phenomenon in which an object appears to be moving when it is actually stationary.

This is often used in advertising to create the illusion of movement, which can make the message on the "message boards" more eye-catching and memorable. Apparent movement is also commonly used in animation, where a series of still images are shown in rapid succession to create the illusion of movement.

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Answer:

20 m

Explanation:

by the formula,

                         \(2aS = V_{f}^{2} - V_{i}^2\)

                         2 x 10 x S = 20^2 - 0

                         20S = 400

                         \(S = \frac{400}{20}\)

                          S = 20 m  

Answer:

Vf=20m/s

Vi=10m/s

a=2m/s^2

t=?

Vf=Vi+at

a=Vf-Vi/t

t=Vf-Vi/a

t=20-10/2

t=10/2

t=5seconds.

It will take approximately 1.98 seconds for the object to hit the ground after Sandra throws it into the air with an initial vertical velocity of 38 ft/s from a platform 30 ft above the ground.

Step 1: Identify the given information.
Initial vertical velocity (v0) = 38 ft/s (upward)
Initial height (h0) = 30 ft
Final height (hf) = 0 ft (ground level)

Step 2: Use the following kinematic equation to relate the heights, initial vertical velocity, and time (t) for a falling object:
hf = h0 + v0*t - (1/2)*g*t²

Here, g is the acceleration due to gravity, which is approximately 32 ft/s² for objects near Earth's surface.

Step 3: Plug in the given values and solve for time (t).
0 = 30 + 38*t - (1/2)*32*t²

Step 4: Rearrange the equation to get a quadratic equation.
0 = -16t² + 38t + 30

Step 5: Solve the quadratic equation for t using the quadratic formula or factoring, if possible.
t ≈ 1.98 s (ignoring the negative root since time cannot be negative)

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The deflection angle is 37.29º if the prism was made of polystyrene plastic.

What is a laser beam?

Laser beam is a light beam propagating dominantly in one direction.

It is a beam of radiation produced from a laser.

Here given that,

refraction index of glass, n1= 1.52

refraction index of polystyrene plastic, n2 = 1.59

deflection angle, B = 22.6º

For the second surface,

B  = 45º - 22.6º

B  = 22.40º

Now from the formula of Snell's law:

n1 sinФ = n2 sin B

sin B / sinФ = n1 / n2

sinФ = (sin 22.40º) * ( 1/ 1.59)

Ф = 37.29º

Hence,

The deflection angle is 37.29º if the prism was made of polystyrene plastic.

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To find the speed of the original object, we can use the conservation of momentum. The total momentum before the disintegration is equal to the total momentum after the disintegration.

The total momentum before the disintegration is given by the sum of the momentum of the two fragments in the x and y directions: To find the speed of the original object, we need to calculate the magnitude of the total momentum before the disintegration.

Magnitude of the total momentum before disintegration = \(sqrt((1.75 MeV/c)² + (2.00 MeV/c)²)sqrt((1.75 MeV/c)² + (2.00 MeV/c)²)\) Once we have the magnitude of the total momentum before disintegration, we can use the equation:

Total momentum before disintegration = (mass of the original object) *

(speed of the original object)

Rearranging the equation, we can solve for the speed of the original object:

Speed of the original object = (Magnitude of the total momentum before disintegration) / (mass of the original object)

Please note that the units of MeV/c are used for momentum and MeV/c² for mass in this problem.

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Answer: Destructive interference

Explanation: Noise-cancelling headphones cancel out unwanted sound by creating an opposing sound wave that mimics the noise you want to get rid of, but just 180° out of phase.

Noise-cancelling headphones use destructive interference to cancel out external sounds. When sound waves travel, they create areas of high and low pressure as they oscillate. The headphones work by creating a sound wave that is the exact opposite of the external sound wave, causing the two waves to cancel each other out. This is known as destructive interference. By using this technique, noise-cancelling headphones are able to reduce or eliminate the amount of external sound that reaches the ear of the listener.

Answer:

Ionic bonds are formed between cation and anions . A cation is formed when a metal ion loses valence electron while an anion is formed when a non-metal gains a valence electron.

The speed of the fluid near the right-hand end of the tube is approximately 10.06 m/s.

Bernoulli's equation is a fundamental principle in fluid mechanics that relates the pressure, velocity, and height of a fluid in a flow. It states that for an incompressible fluid flowing in a steady state through a pipe of varying cross-sectional area, the total energy of the fluid (consisting of pressure energy, kinetic energy, and potential energy) remains constant along any streamline of the flow. Mathematically, the equation is:

P + (1/2)ρv² + ρgh = constant

To find the speed of the fluid near the right-hand end of the tube, we can use the Bernoulli's equation, which relates the pressure and velocity of a fluid in a flow:

P₁ + (1/2)ρv₁² = P₂ + (1/2)ρv₂²

where P1 and v1 are the pressure and velocity of the fluid at the left hand end of the tube (where the pipe is wider), and P2 and v2 are the pressure and velocity at the right-hand end (where the pipe is narrower).

We can redo this equation to solve for v₂:

v₂ = sqrt(2*(P₁-P₂)/ρ + v₁²)

where sqrt denotes the square root.

Using the given values:

A₂/A₁ = 0.46

dP = 27.6 Pa

ρ = 2.93 kg/m³

We can find the pressure at the left hand end using the fact that the pressure is the same at the same height, and the fluid is incompressible, so its density is constant:

P₁ = P₂ + dP = P₂ + 27.6 Pa

The area ratio gives us:

A₂ = 0.46*A₁

Now we need to find v₁. We can use the continuity equation, which states that the mass flow rate (ρAv) is constant in an incompressible fluid:

ρ₁A₁v₁ = ρ₂A₂v₂

where ρ1 is the density of the fluid at the left hand end, which is the same as ρ₂, and A₁ and A₂ are the pipe's cross-sectional areas at the left and right ends, respectively.

Substituting A₂ = 0.46 × A₁ and simplifying, we get:

v₁ = (0.46)² × v₂

Substituting this into the Bernoulli's equation, we get:

P₁ + (1/2)ρv₁² = P₂ + (1/2)ρv₂²

Substituting P₁ = P₂ + 27.6 Pa and v₁ = (0.46)² × v₂, and solving for v₂, we get:

v₂ = √((227.6)/(0.46^2ρ) + (0.46)⁴ × v₂²/ρ)

Simplifying this equation, we get:

v₂= √((227.6)/(0.46^2ρ × (1-0.46⁴)))

Substituting the given values, we get:

v₂ = √((227.6)/(0.46²²°⁹³ × (1-0.46⁴))) = 10.06m/s

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Explanation:

70N-40N=30N

The amplitude of the motion is 1.0 mm, the maximum velocity of the blade is 753.6 mm/s, and the magnitude of maximum acceleration of the blade is 1.81 × 10⁵ mm/s².

Distance moved by the blade= 2.0 mm

Frequency = 120 Hz

Simple Harmonic Motion

In simple harmonic motion, the displacement of the object is a sinusoidal function of time where the frequency of oscillation is same as the frequency of the motion of the object. Therefore, the displacement of the object as a function of time is given as,

x(t) = Asin(2πft)

where,

x(t) = displacement of object as a function of time t.

A = amplitude of the object.

f = frequency of the object.

t = time period.

a)Amplitude

The amplitude of the motion is given by,A = maximum displacement from mean position.

The amplitude of the motion is,A = 1.0 mm

Max displacement from mean position= Amplitude= 1.0 mm

b) The maximum speed of the blade is given by,

v = (2πf)A

where,

v = maximum velocity of the blade

A = amplitude of motion

f = frequency of motion

Therefore,

v = (2πf)A

= 2 × 3.14 × 120 × 1.0

= 753.6 mm/s

So, the maximum velocity of the blade is 753.6 mm/s.

c) The maximum acceleration of the blade is given by,

a = (2πf)²A

where,

a = maximum acceleration of the blade

A = amplitude of motion

f = frequency of motion

Therefore,

a = (2πf)²A

= (2 × 3.14 × 120)² × 1.0

= 1.81 × 10⁵ mm/s²

So, the magnitude of maximum acceleration of the blade is 1.81 × 10⁵ mm/s².

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