A cylinder with a mass M and radius r is floating in a pool of liquid. The cylinder is weighted on one end so that the axis of the cylinder stands vertically. The total length of the cylinder is L. The density of the fluid is rho.


a. When the cylinder is in equilibrium, a portion of it is submerged in the liquid. What is the vertical length h of this submerged portion? Your answer should use only the given symbols M, r, L, and rho as necessary, as well as the constant g.

b. The cylinder is now displaced a distance y from the equilibrium position, such that |y| < h, and released from rest. Let the +y-axis be upward, so that if the cylinder is pulled up, y is positive, but if it is pushed down, y is negative. Immediately after it is released, what is the y-component of the acceleration ay of the cylinder? Your answer should use only the given symbols M, r, L, y, and rho as necessary, as well as the constant g.

c. The result of part (b) implies the cylinder is now in simple harmonic motion. What is the period T of the cylinder's oscillations

it goes as follows- B> C> A> D

Bees frequently cooperate for the benefit of the colony. They occasionally may have an excessive charge on them. In the hive, four pairs of bees collide with one another. These bees can be visualized as identical conducting spheres. Sort the bees according to the size of the charge transfer's magnitude. Bees live in hives with a distinct social structure. Three varieties of bees, each with a specific job, are present in each hive. The female workers gather food and take care of the hive, while the male drones fertilize the eggs laid by the queen. Every type of bee is modified for its specific job. As they get older, the workers' tasks change.

As we can see, there are four pairs of bees, conducting spheres, and it appears that B is higher than C, which is higher than A, which is lower than D.

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Answer:

200 N

Explanation:

The force constant of the spring is 200.696 N/m & The height the object achieves when the spring releases its energy is 2.5087 m

The spring constant is the force needed to stretch or compress a spring, divided by the compressive or expansive distance. It's used to determine stability or instability in the spring, and therefore the system it's intended for. we know,

F = kx

Therefore,

k = F/x

We also know that the force being exerted on the spring is equal to the mass of the object. Hence, F = mg = 5.13 * 9.8 N = 50.174 N and we know compression due to the mass is 0.25m. Therefore,

K = 50.174/0.25 N/m

K = 200.696 N/m

Therefore, The Spring Constant is 200.696 N/m

On release, the spring potential energy gets converted to kinetic energy. Hence, on release, the height attained by the object is given by:

h = \(1/2 kx^{2}\)

We know that k=200.696 N/m and x=0.25 m. Therefore the height is:

h = \(1/2 (200.696 N/m)(0.25 m)^{2}\)

h = 2.5087 m

Therefore, the force constant of the spring is 200.696 N/m & The height the object achieves when the spring releases its energy is 2.5087 m

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Heat capacity is a physical property that measures the amount of heat energy required to raise the temperature of a substance by a certain amount. It represents the ability of a material to store thermal energy.

To find the heat capacity of this object, we can use the formula:
heat capacity = heat / (mass x change in temperature)
Plugging in the given values, we get:
heat capacity = 2100 J / (0.180 kg x 12 °C)
heat capacity = 972.2 J/(kg·°C)
Therefore, the heat capacity of this object is 972.2 J/(kg·°C).

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To find the focal length of the converging lens, we'll use the lens formula and magnification formula.

1. Lens formula: 1/f = 1/u + 1/v, where f is the focal length, u is the object distance, and v is the image distance.

2. Magnification formula: M = -(v/u) = h'/h, where M is the magnification, h' is the image height, and h is the object height.

Given information: h = 6.44 mm u = 27.7 cm = 277 mm (converted to mm) h' = -3.38 mm (negative because it's an inverted image)

Step 1: Calculate the magnification (M) using the magnification formula. M = h'/h = -3.38 / 6.44 = -0.525

Step 2: Calculate the image distance (v) using the magnification formula. v = -u * M = -277 * (-0.525) = 145.425 mm

Step 3: Find the focal length (f) using the lens formula. 1/f = 1/u + 1/v 1/f = 1/277 + 1/145.425 1/f ≈ 0.00361 + 0.00688 1/f ≈ 0.01049

Now, find f by taking the reciprocal of the sum: f ≈ 1 / 0.01049 ≈ 95.3 mm

Finally, convert the focal length to cm: f ≈ 95.3 mm / 10 = 9.53 cm So, the focal length of the lens is approximately 9.53 cm.

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Answer:

15

Explanation:

mass=?

force=30 N

m=f/a

x=30/x

2x=30

x=30/2

=15

The mass of a cat that weighs 30 Newtons would be 3.058 kilograms as the weight of anybody or object is the product of the mass of the body with the acceleration due to gravity.

It can be defined as the force by which a body attracts another body toward its center as the result of the gravitational pull of one body and another.

As given in the problem we have to find the mass of a cat that weighs 30 Newtons,

The weight of the cat = Mass of the cat × Acceleration due to gravity

30 Newtons = mass of the cat × 9.81

The mass of the cat = 30 / 9.81

                                 = 3.058 Kilograms

Thus, the mass of the cat would be 3.058 Kilograms.

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The electric flux through the given planar surface is 10.56675 Nm²/C.

Given data:

Planar surface area, A = 0.03 m²

Electric field strength, E = 704.5 N/C

Normal to surface, n = 60 degrees (the normal is oriented as shown)

The electric flux through the planar surface can be calculated using the formula,φ = E . A . cosθ

Where, E is the electric field strength

A is the area of the surface

θ is the angle between the normal to the surface

and the electric field vector Plugging in the given values,

                   φ = (704.5 N/C) x (0.03 m²) x cos 60°

                         = (704.5 N/C) x (0.03 m²) x 0.5

                          = 10.56675 Nm²/C

The electric flux through the given planar surface is 10.56675 Nm²/C.

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Answer:

A. A motor

Explanation:

Answer:

because the carpet creates more friction when sliding across which makes it slower while the slickness of the wood makes less friction

The wavelength of the radio waves in nanometers is 508 nm.

The given frequency is f = 5.90 x 10² K Hz = 5.90 x 10⁵ Hz.

We need to find the wavelength of the radio waves in nanometers.

So, let's proceed with the following formula;

v = fλ,

where,

v is the speed of light (3.00 x 10⁸ m/s),

f is the frequency (5.90 x 10⁵ Hz), and

λ is the wavelength we need to calculate.

Now, let's plug in the given values into the formula;

v = fλλ

= v / f

= 3.00 x 10⁸ m/s / 5.90 x 10⁵ Hz

= 5.08 x 10² m

As we know, 1 nm = 10⁻⁹ m

So, the wavelength in nm is;

λ = 5.08 x 10² m × 10⁹ nm/m

= 508 nm

Therefore, the wavelength of the radio waves in nanometers is 508 nm.

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Answer:

Described below

Explanation:

1) Solids: In solids, the strong attractive forces between the particles ensure that the particles are packed tightly enough and this means little or no movement between each other. However, when they experience vibration which has relationship with the kinetic energy between them

2) Liquids; In liquids due to the lesser forces of attraction between the particles, it means they tend to glide over each another but however, toward the bottom of the container they will settle. This means that the attractive forces between the liquid particles are barely strong enough to hold onto a specific volume. However, they are not strong enough to keep the molecules from sliding over one other.

3) Gases; In gases, there is almost no existing attractive force in most cases and as a result we can say the kinetic energy of the gas molecules is always greater than the attractive force between them and they are therefore far apart from each other and also move independent of each other.

The applied force is different for the two cases

The case A with a greater force involves the greatest momentum change

The case A involves the greatest force.

The initial momentum of the two ball is the same.

P = mv

where;

Since the force applied by the arm is different, the final velocity of the balls before stopping will be different.

Thus, the final momentum of each ball will be different

The impulse experienced by each ball is different since impulse is the change in momentum of the balls.

J = ΔP

The force applied by the rigid arm is greater than the force applied by the relaxed arm because the force applied by the rigid arm will cause the ball to be brought to rest faster.

Thus, we can conclude the following;

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A question is scientific if you can answer it using observations and measurements and is therefore denoted as option C.

This type of question leads to the formation of hypothesis in which careful observation is needed to answer it.

The observation may include different forms of measurements to ascertain it authenticity in this scenario.

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It will take 3.0 s

Step by step explanation:-

We want to find the time it will take the object to reach the land.

To do this, we apply one of Newtons equations of motion:

\(s = ut + \frac{1}{2}gt^{2} \)

where s= distance/height

u = initial velocity

g = acceleration due to gravity

t = time

From the given question, we have :

\(s = 180m \\ u = 45m/s \\ g = 9.8m/{s}^{2}\)

Now substitute the given values into the equation and solve for t :

\(180 = 45t + ( \frac{1}{2} \times 9.8 \times {t}^{2})\)

\( = > 180 = 45t + 4.9 {t}^{2} \)

\( = > 4.9 {t}^{2} + 45t - 180 = 0\)

Solving the above quadratic equation, using quadratic formula :

\( = > t≈3.0s;t = - 12.2s\)

Since time cannot be negative,

\(t = 3.0s\)

So, it will take 3.0 s to reach the land.

a) On a wet basis, the molar composition of the gas is approximately 0.813 mol propane, 0.055 mol n-butane, and 0.132 mol water. The ratio of mol H₂O to mol dry gas is 0.162 mol H₂O/mol dry gas.

b) The required air feed rate is approximately 65.9 kmol/h. If the combustion were only 65% complete, the required air feed rate would increase to approximately 101.4 kmol/h.

a) To calculate the molar composition on a wet basis, we convert the weight percentages to mole fractions using the molar masses of propane, n-butane, and water. The molar composition is determined by dividing the weight percentage by the respective molar mass and normalizing the values to sum up to 1. The ratio of mol H₂O to mol dry gas is determined by dividing the mol water by the sum of mols of propane and n-butane.

b) To calculate the required air feed rate, we use the stoichiometry of the combustion reaction between butane and air. The balanced equation shows that 1 mol of butane reacts with 13.5 mol of air. Considering the 25% excess air requirement, we multiply the stoichiometric air requirement by 1.25. If the combustion is only 65% complete, the remaining butane requires additional air to achieve complete combustion. Therefore, the required air feed rate increases to account for the unreacted butane.

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Bronco the skydiver, whose mass is 80 kg experiences 200 N of air resistance and gravity pulls on him with 800 N. The acceleration of his fall  7.5 m/sec².

A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.

To find the acceleration,

   F = mg

   F = 80.(10)

   F = 800 N

   air resistance = 200 N

   Net force = F - air resistance

                = 800 - 200

                =  600 N

   600 = mass . acceleration

   600 = 80 . acceleration

   acceleration = 7.5 m/sec²

Bronco the skydiver, whose mass is 80 kg experiences 200 N of air resistance and gravity pulls on him with 800 N. The acceleration of his fall  7.5 m/sec².

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Just the phone and battery should be where they should be on the photographs.

The term "matter" refers to a substance that is composed of several kinds of particles, occupies space, and has inertia. The numerous kinds of particles each have a unique mass and size, according to the fundamentals of current physics. The electron, proton, and neutron are three of the most well-known instances of material particles.

All objects with mass and volume are considered to be matter (takes up space). It is usually pretty easy to show that the everyday items we interact with have mass and occupy space.

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Answer:

2800kg

Explanation:

The Schwarzschild radius is a measure of the event horizon of a black hole, which is the point of no return beyond which nothing, not even light, can escape. It is named after the German physicist Karl Schwarzschild who first calculated it in 1916.

The formula for calculating the Schwarzschild radius is given by Rs = 2GM/c^2, where Rs is the Schwarzschild radius, G is the gravitational constant, M is the mass of the black hole, and c is the speed of light.

For a 10 solar mass black hole, we can plug in the values into the formula and get Rs = 29.96 billion km, which is approximately 30 billion km. This means that the event horizon of a 10 solar mass black hole is a sphere with a radius of 30 billion km.

To put this into perspective, the distance between the Earth and the Sun is about 150 million km, which means that the event horizon of a 10 solar mass black hole is about 200 times the distance between the Earth and the Sun.

In summary, the Schwarzschild radius of a 10 solar mass black hole is 30 billion km. This is an important measure of the size of a black hole and helps us understand the behavior of matter and energy around it.

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The inductance (L) of a series RL circuit is 0.36 H, which represents the property of the circuit to oppose changes in current flow by storing energy in a magnetic field.

In a series RL circuit, the inductance (L) affects the rate at which the current changes when the circuit is connected to a voltage source. To find the inductance, we need to consider the time it takes for the current to reach one-third of its final value after connecting the circuit to a battery.

Given:

Resistance (R) = 1.0 kW (kilowatts) = 10³ Ω (ohms)

Time (t) = 30 µs (microseconds) = 30 × 10⁻⁶ s (seconds)

The time constant (τ) of an RL circuit is given by the formula:

τ = L/R

To find the inductance (L), we can rearrange the formula as:

L = τ × R

Since we are given the time (t) it takes for the current to increase to one-third of its final value, we can calculate the time constant (τ) using the formula:

τ = t / ln(3)

Substituting the values, we have:

τ = (30 × 10⁻⁶ s) / ln(3)

Now, we can calculate the inductance (L) by multiplying the time constant (τ) by the resistance (R):

L = τ × R = (30 × 10⁻⁶ s) / ln(3) × 10³ Ω = (30 × 10⁻³ Ω·s) / ln(3)

Evaluating this expression, we find that the inductance (L) of the series RL circuit is approximately 0.36 H (henries).

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Answer:

4 A

Explanation:

From the question given above, the following data were obtained:

Voltage (V) = 12 V

Resistance (R) = 3 Ω

Current (I) =?

From ohm's law,

Voltage (V) = Current (I) × Resistance (R)

V = IR

With the above formula, we can obtain the current flowing in the circuit as illustrated below:

Voltage (V) = 12 V

Resistance (R) = 3 Ω

Current (I) =?

V = IR

12 = I × 3

Divide both side by 3

I = 12/3

I = 4 A

Therefore, the current flowing in the circuit is 4 A.

Answer:

1.0 x 10-6 N.

Explanation:

The gravitational force

Fg = G m1 m2 / r2 = (6.673 x 10-11) (50 kg) (75 kg) / (0.50 m)2 = 1.0 x 10-6 N.

Answer:

yes they are. they are one of only 4 metals that are ferromagnetic.

Answer:

To calculate the mechanical advantage of a pulley you simply have to count the number of rope sections that support whatever object you are lifting (not counting the rope that is attached to the effort)

Example:

For example, in a one pulley system the MA is 1. In a two pulley system the MA is 2. The more compound the pulley is the easier the load is to lift. If you were lifting a 600kg object with 2 pulleys you would have to use enough effort to pull 300kg to lift the 600kg object! Therefore your mechanical advantage would be 2 (600/300).

               MA= load/effort OR number of rope sections

At t = 0.5 s, the velocity of a point on the rim of the circular disk is approximately 2.4 m/s, while the acceleration is approximately 2.4 m/s².

To determine the velocity and acceleration of a point on the rim of the circular disk when t = 0.5 s, we can differentiate the equation w = (3t² + 6) with respect to time (t).

Given that the diameter of the disk is 1.6 m, the radius (r) can be calculated as half of the diameter: r = 1.6 m / 2 = 0.8 m.

Differentiating w with respect to t:

dw/dt = d(3t² + 6)/dt

dw/dt = 6t

The angular velocity (w) is the rate of change of the angular displacement with respect to time. Since the equation w = 6t represents the angular velocity, we can substitute t = 0.5 s into this equation to find the angular velocity at t = 0.5 s:

w = 6t

w = 6(0.5)

w = 3 rad/s

The linear velocity (v) of a point on the rim of the circular disk can be calculated using the formula v = rw, where r is the radius and w is the angular velocity. Substituting the values:

v = 0.8 m × 3 rad/s

v = 2.4 m/s

Therefore, when t = 0.5 s, the velocity of a point on the rim of the circular disk is 2.4 m/s.

To find the acceleration (a), we need to differentiate the linear velocity (v) with respect to time (t):

a = dv/dt

Differentiating v = rw with respect to t:

a = d(rw)/dt

a = r(dw/dt)

Substituting the values:

a = 0.8 m × (6t)

a = 4.8t m/s²

When t = 0.5 s, the acceleration of a point on the rim of the circular disk is:

a = 4.8 × 0.5

a = 2.4 m/s²

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Answer:

F = M a is the vector equation involved

F = T - M g      are the forces acting on the elevator   (scalar equation)

T - M g = M a

T = M (a + g)    remember this a scalar

If a is slowing down then it must have a positive acceleration upwards

Therefor the tension in the cable must be greater than zero

When the tension increases to M g, a has increased to zero

For a to be zero, no acceleration, T = M g

The period of the molecular vibrations caused by the pulse of sound is 0.196 microseconds, and the angular frequency is 32.03 x 10^6 radians per second.

To calculate the period and angular frequency of the molecular vibrations caused by the pulse of sound, we need to use the equation:
Angular frequency = 2π x Frequency
Period = 1 / Frequency

Given that the frequency of the ultrasound pulse is 5.10 MHz, we can calculate the angular frequency as follows:
Angular frequency = 2π x 5.10 MHz
Angular frequency = 32.03 x 10^6 radians per second

To calculate the period, we can use the following formula:
Period = 1 / 5.10 MHz
Period = 0.196 microseconds

So the period of the molecular vibrations caused by the pulse of sound is 0.196 microseconds, and the angular frequency is 32.03 x 10^6 radians per second. It's important to note that these molecular vibrations are too small to be detected by humans, but they are essential in creating the ultrasound images that are used in medical imaging.

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Answer:

4 ohms

Explanation:

Current = Voltage/resistance

2 = 8/R

2R = 8

R = 4