Consider the bead threaded on a circular hoop of Example 7.6 (page 260), working in a frame that rotates with the hoop.
a) Find the equation of motion of the bead, and check that your result agress with Equation (7.69).
b) Using a free-body diagram, explain the result (7.71) for the equillibrium positions.

Given that the speed of light in substance A is x times greater than the speed of light in substance B, the ratio of n_A to n_B in terms of x is:

n_A / n_B = 1 / x

Given that the speed of light in substance A is x times greater than the speed of light in substance B, we can represent this relationship as:

v_A = x * v_B

To find the ratio n_A / n_B in terms of x, we need to consider the refractive index formula:

n = c / v

Where n is the refractive index, c is the speed of light in a vacuum, and v is the speed of light in the medium.

For substance A:
n_A = c / v_A

For substance B:
n_B = c / v_B

Now, we'll divide n_A by n_B:

(n_A / n_B) = (c / v_A) / (c / v_B)

As c (the speed of light in vacuum) is constant, it cancels out:

(n_A / n_B) = (1 / v_A) * (v_B / 1)

We know that v_A = x * v_B, so let's substitute this:

(n_A / n_B) = (1 / (x * v_B)) * (v_B / 1)

The v_B terms cancel out: (n_A / n_B) = 1 / x

So the ratio of n_A to n_B in terms of x is: n_A / n_B = 1 / x

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We have that The Density and Volume is given as

\(\rho=0.67\\\\\V=30cm^3\)

The factors that affect Density are Mass and Volume

From the question we are told that

The piece of wood shown above has a mass of 20 grams.

Wood parameters

2cm

5cm

3cm

Generally the equation for the Volume  is mathematically given as

\(V=L*B*H\\\\\V=2*5*3\\\\V=30cm^3\)

Generally the equation for the Density is mathematically given as

\(\rho=\frac{m}{v}\\\\\\rho=\frac{20}{30}\\\\\rho=0.67\)

Therefore the factors that affect Density are Mass and Volume

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Answer:

2.286 km/s²

Explanation:

Since acceleration a = (v - u)/t where u = initial horizontal velocity of ball = 0 m/s (since it starts from rest), v = final horizontal velocity of ball at serve = 73.14 m/s and t = time taken for serve = 32.0 ms = 0.032 s

Substituting the values of the variables into the equation, we have

a = (v - u)/t

a = (73.14 m/s - 0 m/s)/0.032 s

a = 73.14 m/s/0.032 s

a =  2285.625 m/s²

a = 2.285625 km/s²

a ≅ 2.286 km/s²

So, the x - component of the ball's acceleration during the serve is 2.286 km/s²

Answer:

P = 5880  J

Explanation:

Given that,

The mass of the block, m = 30 kg

The block is sitting at a height of 20 m.

The block will have gravitational potential energy. The formula for gravitational potential energy is given by :

\(P=mgh\\\\=30\times 9.8\times 20\\\\=5880\ J\)

So, the required potential energy is equal to 5880  J.

Answer:

4. y = 2.38333t - 26.55 is the answer.

b) 6.83 years, which corresponds to approximately 2.165 years as measured by someone on the spaceship.

According to special relativity, time dilation occurs when an object is moving relative to an observer. Time dilation means that time appears to pass more slowly for the moving object compared to a stationary observer.

In this scenario, the spaceship is traveling at a speed of 0.9640c, which is 0.9640 times the speed of light. We want to find out how long the trip takes as measured by someone on the spaceship, which means we need to consider time dilation.

The time dilation factor, γ, is given by the equation:

γ = 1 / √(1 - (v^2 / c^2))

where v is the velocity of the spaceship and c is the speed of light.

Substituting the given values:

γ = 1 / √(1 - (0.9640c)^2 / c^2)

= 1 / √(1 - 0.9298)

= 1 / √(0.0702)

≈ 3.160

This means that time appears to pass approximately 3.160 times slower for someone on the spaceship compared to someone in the Earth's rest frame.

Now, let's consider the time it takes for the trip in the Earth's rest frame. We'll denote this time as t_earth.

Given that the spaceship takes t_earth to travel between the two planets as measured in the Earth's rest frame, the time it takes for someone on the spaceship, t_ship, can be calculated by:

t_ship = t_earth / γ

Substituting the provided answer options:

a) t_earth = 2.79 years

t_ship = 2.79 years / 3.160 ≈ 0.883 years

b) t_earth = 6.83 years

t_ship = 6.83 years / 3.160 ≈ 2.165 years

c) t_earth = 39.5 years

t_ship = 39.5 years / 3.160 ≈ 12.50 years

d) t_earth = 28.8 years

t_ship = 28.8 years / 3.160 ≈ 9.13 years

Based on the calculations, the correct answer is option b) 6.83 years, which corresponds to approximately 2.165 years as measured by someone on the spaceship.

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Answer:

Because the bumpers are a crumple zone.

The maximum torque is approximately 0.62 Nm when the motor is spinning.

To calculate the maximum torque of the motor, we can use the following motor torque:

τ = N * B * A * I * sin(θ)

where:

τ is torque and

N is the torque Number of turns of the coil,

B magnetic force,

A is the area of ​​the coil,

I is the current through the coil,

θ is the angle of the magnets and normal coils.

Given:

Number of turns, N = 25

Magnetic field strength, B = 0.030 T

Length of one side of the square coil, l = 4.

8 cm = 0.048 m

Resistor, R = 34 Ω

Voltage, V = 7.7 V

Let's first use Ohm's law to calculate the current through the coil:

I = V / R

V 4 = 3. ≈ 0.226 A

Now let's calculate the area of ​​the coil:

A = l^2

= (0.048 m)^2

= 0.002304 m^2

Since the coil is rotating, the angle θ will be 90 degrees (or π/2 radians), and sin(θ) = 1.

Now calculate the torque:

τ = N * B * A * I * sin(θ)

= 25 * 0.030 T * 0.002304 m^2 * 0.

226 A * 1

≈ 0.617 Nm

The maximum torque of the engine is approx. 0.62 Nm.

The maximum torque is approximately 0.62 Nm when the motor is spinning.

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Astronomers would use the method of "spectroscopic parallax" to find the distance to a remote quasar.

Explanation:

Spectroscopic parallax is a technique used to determine the distance to a celestial object using its spectrum. In this method, astronomers analyze the spectrum of a quasar and compare it to the spectrum of a nearby star with a known luminosity. By comparing the two spectra, they can determine the quasar's luminosity, and then use that information to calculate its distance using the inverse square law. This method is particularly useful for distant objects, like quasars, which are too far away to be measured using traditional parallax methods.

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Answer:

It maybe 1600

Explanation:

Because it's near to 1500 in the line.

The circumference of the circle after t seconds = 25.12 t

Given data,

The radius of each circular wave will increase by four centimeters per second (cm/s)

In 1 second of circular wave radius = 4cm

In 1*t second of circular wave radius = 4t cm

As a result, the radius of the circular wave after t seconds is 4t cm.

We already know that the circumference of a circle is given by = 2πr, where r is the circle's radius.

As a result, the radius of a circular wave after t seconds is = 2π * radius of a circular wave after t seconds = 2π * 4t

                                                    = 8πt

( Taking π = 3.14 )

As a result, the circumference of the circle after t seconds = 8πt

                                                                                                     = 3.14t

                                                                                                   = 25.12t

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The following statements are true: the force on the fullback is the same magnitude but in the opposite direction as the force on the defensive back, and the total momentum before and after the collision are the same.

When a fullback hits a defensive back, the forces exerted on both players are equal in magnitude but opposite in direction according to Newton's third law of motion. This law states that for every action, there is an equal and opposite reaction. Therefore, the force on the fullback is the same magnitude as the force on the defensive back, but they act in opposite directions.

However, according to the law of conservation of momentum, the total momentum of the system (the fullback and the defensive back) remains constant if no external forces are present. Therefore, the total momentum before the collision is the same as the total momentum after the collision.

In summary, the force on the fullback is the same magnitude but in the opposite direction as the force on the defensive back. Additionally, the total momentum before and after the collision remains the same, in accordance with Newton's third law and the law of conservation of momentum.

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The heat of the surroundings is  - 4482 J.

A calorimeter is a device in which that is no exchange of heat between the device and the environment. In other words, there could only be exchange of heat when the a substance has been put inside the calorimeter.

We know that in a calorimeter;

Heat of the surrounding =  Heat of the system

That implies that they are of the same magnitude but of opposite direction hence the heat of the system is - 4482 J.

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Answer:

5000°A

Explanation:

If it is right answer so please mark me as brainleist anwer as ur wish

Answer:

Mark Brainliest

Explanation:

Electromagnetic waves are not like sound waves because they do not need molecules to travel. This means that electromagnetic waves can travel through air, solid objects and even space.

17.01 m/s is the car’s velocity .

s=ut+at²/2

s-at²/2=ut

u=s-at²/2÷t

u=312/18.4

u=17.01 m/s

"The rate at which an item changes its location" is described by a vector number called velocity. Imagine someone walking swiftly, one step forward, one step back, and starting each step from the same location. Velocity is a vector quantity. Therefore, velocity is cognizant of direction. The direction must be taken into account when determining an object's velocity. A velocity of 55 miles per hour is not adequate information. It is necessary to account for the direction in order to accurately describe the object's velocity. Simply put, the direction of the velocity vector represents the motion of the object.

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Answer: L

Explanation: L is the specific latent heat for a particular substance (kJ kg−1 or in BTU lb−1), either Lf for fusion, or Lv for vaporization.

Answer:The hypothesis (or hypotheses) for this experiment would be :

1) Experiment of motion( movement) can be performed in this lab.

2) Experiment of motion( movement) can be performed better in this lab.

3)  Only experiments of motion( movement) can be performed in this lab.

4) Experiment of motion( movement) can be performed more accurately in this lab.

5) No experiment of motion( movement) can be performed in this lab.

Explanation:

The hypothesis (or hypotheses) for this experiment would be :

Experiment regarding motion( movement) can be performed in this lab.

And Conclusion would be:

This lab is for motion.

We can only conclude that this lab is for motion when we find out that the motion experiments can be performed better or with higher accuracy or none other experiment can be carried out as easily as the motion experiment.

We only conclude when we test the hypothesis .

The hypothesis can be tested in a number of ways such as showing better results, or showing negative results of the said statement.

So there can be a few hypotheses as follows.

1) Experiment of motion( movement) can be performed in this lab.

2) Experiment of motion( movement) can be performed better in this lab.

3)  Only experiments of motion( movement) can be performed in this lab.

4) Experiment of motion( movement) can be performed more accurately in this lab.

5) No experiment of motion( movement) can be performed in this lab.

Explanation:

The speed of 5 kg ball is 10.2 m/s

Given data:

The mass of cart 1 is m₁=3 kg.

The speed of cart 1 moving east is v₁=17 m/s.

The mass of other cart is m₂=5 kg.

Since the carts stick together, and comes to rest their final velocity is zero, i.e., v=0.

Applying the conservation of momentum between the carts as,

Here, v₂ is the speed of 5kg cart. Since the cart 2 moving in west direction therefore v₂=-v₂.

Substitute all the values in above equation,

Thus, the speed of 5 kg ball is 10.2 m/s.

Final answer: 10.2 m/s

Answer:

b

Explanation:

negativity sure ans bro

Answer:

During an experiment, a student moves a cell from pure water to salted water. ... It will release water and shrivel. It will release water and burst.

Assuming that the standard deviation is known to be 1.1, for a mean of 1080 samples, it can be said that the data supports the claim that the current ozone level is insufficient at the 0.02 level.

Step 1 of 5: Enter the hypotheses:

Null hypothesis (H0): The current ozone level is sufficient (μ = 7.0 ppm)

Alternative hypothesis (H1): The current ozone level is insufficient (μ < 7.0 ppm)

Step 2 of 5: Enter the value of the z-test statistic:

To find the z-test statistic, we'll use the formula:

z = (X' - μ) / (σ / √n)

where:

X' = sample mean = 6.9 ppm

μ = population mean = 7.0 ppm

σ = standard deviation = 1.1 ppm

n = sample size = 1080

Substituting the values into the formula:

z = (6.9 - 7.0) / (1.1 / √1080)

z = -0.1 / (1.1 / 32.863)

z ≈ -0.1 / 0.033157

z ≈ -3.018

Step 4 of 5: Enter the decision rule:

Since the alternative hypothesis is one-tailed (μ < 7.0 ppm), we need to compare the z-test statistic with the critical value for the given significance level.

At a significance level of 0.02, the critical value can be found using a z-table or a calculator. For a one-tailed test, the critical value is approximately -2.055.

Step 5 of 5: Enter the conclusion:

The z-test statistic (-3.018) is smaller than the critical value (-2.055). Therefore, we reject the null hypothesis.

Conclusion: The data supports the claim that the current ozone level is insufficient at the 0.02 level.

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Explanation:

a) i) Calculation of the friction force:

The friction force can be determined using the equation:

friction force = coefficient of friction * normal force

The normal force is equal to the weight of the object, which can be calculated as:

normal force = mass * gravitational acceleration

where the gravitational acceleration is approximately 9.8 m/s².

normal force = 75 kg * 9.8 m/s² = 735 N

friction force = 0.4 * 735 N = 294 N

ii) Calculation of the acceleration of the body:

Now, we can calculate the acceleration using Newton's second law:

net force = mass * acceleration

Since the applied force and the friction force act in opposite directions, the net force can be calculated as:

net force = applied force - friction force

net force = 300 N - 294 N = 6 N

mass = 75 kg

6 N = 75 kg * acceleration

acceleration = 6 N / 75 kg = 0.08 m/s²

b) Explanation:

In part (a), we calculated the friction force to be 294 N and the acceleration of the body to be 0.08 m/s². The positive acceleration indicates that the body is moving in the direction of the applied force.

The friction force opposes the motion of the body and acts in the opposite direction to the applied force. In this case, the applied force of 300 N is greater than the friction force of 294 N. As a result, the net force acting on the body is 6 N in the direction of the applied force.

The small net force of 6 N, compared to the body's mass of 75 kg, results in a relatively low acceleration of 0.08 m/s². This indicates that the body will accelerate slowly in the direction of the applied force due to the presence of friction.

Overall, the friction force and the resulting acceleration of the body are determined by the coefficient of friction (μ) and the mass of the object. In this case, the body experiences a relatively high friction force, leading to a small acceleration.

Answer:

B

Explanation:

Answer: According to Newton’s 1st law, the truck must be in equilibrium.

At the end of the eighth second with the constant velocity of 5.5 m/s the skater will have travelled a distance of 44 meters from the initial point of reference and his position will be 44 meters from initial position.

Velocity is a vector that presents change in displacement per unit time constant velocity implies that the change in displacement will remain the same every second.

Position is a word that is referenced to the displacement that object has covered in a certain direction where as displacement is the shortest distance between two points.

Given:

Initial constant velocity = 5.5 m/s

According to the question this velocity remains constant throughout the motion.

To find the position of the status on the 8th 2nd after the skater passes the initial point can be found by using the displacement time formula.

Displacement = constant velocity × time

Substituting value in the displacement time formula we get.

Position at eighth second from the initial point = 5.5 × 8

Position at eighth second from the initial point = 44 meter

Therefore, at the end of the eighth second with the constant velocity of 5.5 m/s the skater will have travelled a distance of 44 meters from the initial point of reference and his position will be 44 meter from initial position.

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The power absorbed by each element can also be calculated using Ohm's Law: P = V^2/R.

To calculate the power absorbed by each circuit element in the diagram below, use Ohm's Law and the Power equation. First, find the voltage v and the currents i1 and i2:

V = 120V
i1 = (V - 30) / 22 = (120-30) / 22 = 4.545A
i2 = (V - 15) / 12 = (120-15) / 12 = 9.167A

Then, use the Power equation to calculate the power for each element

Power absorbed by 30Ω: P = V*i1 = 120*4.545 = 545.4W
Power absorbed by 22Ω: P = V*i2 = 120*9.167 = 1098.04W
Power absorbed by 15Ω: P = V*i2 = 120*9.167 = 1098.04W
Power absorbed by 12Ω: P = V*i2 = 120*9.167 = 1098.04W

The power absorbed by each element can also be calculated using Ohm's Law: P = V^2/R.

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The centripetal force on the electron in the first orbit of the hydrogen atom would be 81.75 x 10⁻⁹.

The main points of Bohr's model of atom are -

Given is that an electron (e⁻) (m = 9.1 x 10⁻³¹ kg) moving at 2.18 x 10⁶ m/s (in a Bohr orbit in the H atom).

The radius of first Bohr orbit of hydrogen atom is -

{r} = 0.529 A˚ = 0.529 x 10⁻¹⁰ m.

The centripetal force on the electron in the first orbit of the hydrogen atom would be -

F = mv²/r

F = (9.1 x 10⁻³¹)(2.18 x 10⁶)²/0.529 x 10⁻¹⁰

F = 81.75 x 10 ⁻³¹ ⁺ ¹² ⁺ ¹⁰

F = 81.75 x 10⁻⁹

Therefore, the centripetal force on the electron in the first orbit of the hydrogen atom would be 81.75 x 10⁻⁹.

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Answer:its 1.9 10^26

Explanation: