The density of water is 1. 0 g/cm3. How many kilograms of water does a submerged 120-cm3 block displace? Recall that 1. 0 g/cm3 weights 9. 8 N on earth. What is the buoyant force on the block?

When a drinking straw is placed in water and the opening is covered with a finger, lifting the straw out of the water causes some water to remain inside. This is due to combination of atmospheric pressure and cohesion.

When the straw is placed in water and the opening is covered, the air inside the straw is trapped. As the straw is lifted out of the water, the weight of the water column inside the straw creates a partial vacuum. Atmospheric pressure, which is exerted equally in all directions, pushes the water upward to fill the empty space created by the rising column of air inside the straw. This pressure from the surrounding air keeps the water suspended inside the straw.

Additionally, cohesion, the attractive force between water molecules, plays a role. Water molecules tend to stick together due to their polar nature. As the straw is lifted, the cohesive forces between the water molecules help maintain the column of water by forming a continuous chain-like structure from the water in the glass to the water in the straw. This cohesion, combined with the pressure from the surrounding air, allows the water to remain inside the straw.

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Answer:

17640

Explanation:

Power = workdone/time

Power = (force x displacement)/time

Power = (mg x 60)/60

Power = (1800 x 9.8 x 60)/60

=> power = 17640 watt

-- impurities in the water

-- air pressure is higher than standard

The angular frequency of the light wave is approximately 3.769 x 10¹⁵ rad/s.

The propagation constant (β) of a light wave is related to the angular frequency (ω) and the speed of light (c) by the equation β = ω/c. In this case, we are given the propagation constant as 1.256 x 10⁷ m⁻¹ and the speed of light as 3.00 x 10⁸ m/s.

Rearranging the equation, we can solve for ω by multiplying β by c. Plugging in the values, we find,

ω = (1.256 x 10⁷ m⁻¹) × (3.00 x 10⁸ m/s)

ω ≈ 3.769 x 10¹⁵ rad/s.

Therefore, the angular frequency of the light wave is approximately 3.769 x 10¹⁵ rad/s.

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We can see here that when a high operating kilovoltage is used, a. Low subject contrast; many shades of gray.

A dental image refers to a visual representation or picture of the teeth, gums, and surrounding structures in the oral cavity.

Dental images are typically captured using various imaging techniques and equipment to assist in the diagnosis, treatment planning, and monitoring of dental conditions.

A high kilovoltage setting produces an image with decreased or low contrast; the radiograph exhibits many shades of gray. This is because the higher energy x-rays are better able to penetrate tissue, resulting in less variation in the absorption of x-rays by different tissues.

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The turning-point angles of the swing are approximately 0.567°.

To find the turning-point angles of the swing, we can use the concept of conservation of mechanical energy. At the turning points, the kinetic energy of the child is maximum, while the potential energy is zero.

Length of the ropes (L) = 3.3 m

Speed of the child (v) = 0.80 m/s

At the turning points, the total mechanical energy is conserved and can be expressed as the sum of kinetic energy and potential energy:

E = KE + PE

At the highest point (when the ropes are vertical), the entire mechanical energy is in the form of potential energy, given by:

E = mgh

At the lowest point (when the ropes are horizontal), the entire mechanical energy is in the form of kinetic energy, given by:

E = (1/2)mv²

Since the mass of the child cancels out, we can equate the two expressions for mechanical energy:

mgh = (1/2)mv²

Simplifying, we get:

h = (1/2)v²/g

Substituting the given values:

h = (1/2)(0.80 m/s)² / 9.8 m/s²

h ≈ 0.0327 m

Now, we can find the turning-point angles using trigonometry. The turning-point angle (θ) is related to the height (h) and the length of the ropes (L) by:

sin(θ) = h/L

Substituting the values:

sin(θ) = 0.0327 m / 3.3 m

θ ≈ 0.0099 radians

Converting radians to degrees:

θ ≈ 0.0099 radians * (180° / π radians)

θ ≈ 0.567°

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Answer:

As we navigate down a group the atoms get bigger and bigger with more and more electrons. This means the outermost electrons get further and further away from the positively charged nucleus.

Answer:

As we navigate down a group the atoms get bigger and bigger with more and more electrons. This means the outermost electrons get further and further away from the positively charged nucleus

Hope this helps!!!!

The required solids concentration is 2000 mg/L, which corresponds to option b. 100 mg/L.

PPM (parts per million) is a unit of concentration that represents the number of parts of a substance per million parts of the total solution. In this case, the solids concentration of 2000 ppm means there are 2000 parts of solids per million parts of the wastewater sample.

To convert ppm to mg/L (milligrams per liter), we can assume that 1 ppm is equivalent to 1 mg/L. Therefore, the solids concentration is 2000 mg/L, which corresponds to option b. 100 mg/L.

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The economic impact resulting from the collapse of two large power grids and 130 million people being without power for two months due to a 4800 nT/min geomagnetic storm disturbance in the United States would be substantial, likely amounting to billions of dollars.

1. Loss of productivity: The major factor contributing to the economic impact would be the loss of productivity during the two-month period. Without power, businesses, industries, and essential services would be severely disrupted, leading to a decline in output and economic activity.

To estimate the economic impact, we need to consider the following factors:

a. GDP per capita: According to the World Bank, the United States' GDP per capita was approximately $63,416 in 2020.

b. Average number of working days in two months: Assuming an average of 22 working days per month, we have a total of 44 working days affected by the power outage.

c. Workforce participation rate: As of September 2021, the U.S. labor force participation rate was around 61.6%.

d. Affected population: Given that 130 million people are without power, we need to calculate the percentage of the workforce among them. Assuming the workforce participation rate remains constant, the affected workforce can be estimated as follows:

Affected workforce = Workforce participation rate * Affected population

Affected workforce = 0.616 * 130,000,000

Affected workforce  ≈ 79,976,000

e. Loss of productivity per day: To estimate the loss of productivity per day per worker, we can divide the GDP per capita by the average number of working days in a year:

Loss of productivity per day per worker = GDP per capita / 365

Loss of productivity per day per worker  ≈ $63,416 / 365

Loss of productivity per day per worker   ≈ $173.63

f. Total loss of productivity: The total loss of productivity during the two-month period can be calculated by multiplying the loss of productivity per day per worker by the number of affected working days and the affected workforce:

Total loss of productivity = Loss of productivity per day per worker * Number of affected working days * Affected workforce

                        ≈ $173.63 * 44 * 79,976,000

                        ≈ $610,964,195,520

Additional costs: The economic impact would also include additional costs incurred due to the power outage, such as emergency response efforts, infrastructure repairs, and the financial burden on individuals and businesses.

Based on the calculations, the economic impact resulting from the collapse of two large power grids and 130 million people being without power for two months due to a 4800 nT/min geomagnetic storm disturbance would be estimated at approximately $610.96 billion in terms of loss of productivity alone.

This estimate does not include the additional costs associated with the power outage, which would likely further increase the economic impact.

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The examination of radial and tangential fracture lines on glass struck by two projectiles in sequence can provide both the refractive index of the glass and the sequence of impact.

Glass fractures in a distinct pattern when subjected to impact. Radial and tangential fracture lines can be observed on the glass surface, and by examining their characteristics, valuable information can be derived. Firstly, the refractive index of the glass can be determined by analyzing the angles and spacing of the fracture lines. This information is useful for forensic investigations and determining the type of glass involved. Secondly, by studying the sequence and intersection points of the fracture lines, it is possible to determine the order in which the projectiles struck the glass. This can provide crucial insights into the dynamics of the event and aid in reconstructing the sequence of events accurately.

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The intensity of the fire alarm is approximately 3.16 × 10²⁴ in units of watts per square meter (W/m²) rounded to the nearest hundredth.

To find the intensity of a fire alarm that measures 125 dB loud, we can rearrange the formula for loudness to solve for intensity.

The formula for loudness in decibels is given by:

L = 10 log (I / (10⁻¹²))

Where:

L is the loudness in decibels

I is the intensity of the sound

We can rewrite the formula to solve for I:

I = 10^((L / 10) + 12)

In this case:

Loudness (L) = 125 dB

Substituting the value of L into the formula, we have:

I = 10^((125 / 10) + 12)

I ≈ 10^(12.5 + 12)

I ≈ 10^(24.5)

I ≈ 3.16 × 10²⁴

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When the length of a pendulum is 1.00 m, the period reaches its minimum value when the displacement (x) is 28.87 cm. At a location with a gravitational acceleration of [tex]9.800 m/s²[/tex], this minimum period is 1.525 seconds.

The period of a simple pendulum is determined by its length (l) and the gravitational acceleration (g) at its location. The relationship between the period (T) and the length of the pendulum is given by the equation:

[tex]T = 2\pi \sqrt(l/g)[/tex]

In this case, we are given that the length of the pendulum (l) is 1.00 m. To find the minimum value of the period, we need to determine the corresponding displacement (x). The displacement is the maximum distance the pendulum swings away from its equilibrium position. We are given that this minimum value occurs when x = 28.87 cm.

Next, we are provided with the value of the gravitational acceleration (g) at the site, which is [tex]9.800 m/s²[/tex]. By substituting these values into the equation, we can calculate the minimum period (T):

[tex]T = 2\pi \sqrt(l/g)\\T = 2\pi \sqrt(1.00/9.800)[/tex]

T ≈ 1.525 seconds

Therefore, at a location with a gravitational acceleration of [tex]9.800 m/s^2[/tex], when the length of the pendulum is 1.00 m, the minimum period is approximately 1.525 seconds.

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(a) The inductance of the solenoid is 0.0775 mH when solenoid is of radius 4.5 cm, has 660 turns and a length of 25 cm.

The inductance of a solenoid can be calculated using the formula:

L = μ₀N²A / l,

where L is the inductance, μ₀ is the permeability of free space (4π × 10^(-7) T·m/A), N is the number of turns, A is the cross-sectional area, and l is the length of the solenoid.

We are given that the radius of the solenoid is 4.5 cm (0.045 m), the number of turns is 660, and the length is 25 cm (0.25 m).

First, we need to calculate the cross-sectional area:

A = πr² = π(0.045 m)² ≈ 0.006366 m².

Now, we can substitute the values into the formula to calculate the inductance:

L = (4π × 10^(-7) T·m/A) × (660 turns)² × (0.006366 m²) / (0.25 m).

L ≈ 0.0775 mH.

(b) The rate at which current must change through the solenoid to produce an emf of 50 mV is 645.16 A/s (amperes per second).

According to Faraday's law of electromagnetic induction, the induced electromotive force (emf) in a coil is given by:

ε = -L(dI/dt),

where ε is the emf, L is the inductance, and (dI/dt) is the rate of change of current with respect to time.

We are given that the emf is 50 mV (0.05 V) and we need to find the rate of change of current.

Rearranging the formula:

(dI/dt) = -ε / L.

Substituting the given values:

(dI/dt) = -(0.05 V) / (0.0775 mH).

Converting mH to H (Henries):

(dI/dt) = -(0.05 V) / (0.0775 × 10^(-3) H).

(dI/dt) ≈ -645.16 A/s.

Since we are asked for the magnitude, we take the absolute value:

Rate of change of current ≈ 645.16 A/s.

(a) The inductance of the solenoid is approximately 0.0775 mH.

(b) The rate at which the current must change through the solenoid to produce an emf of 50 mV is approximately 645.16 A/s.

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Answer:

D) 12.0 V

Explanation:

When resistors are connected in series, the total resistance is the sum of the individual resistances. Therefore, the total resistance in this circuit is:

R_total = 4 ohm + 6 ohm = 10 ohm

According to Ohm's Law, the voltage drop across a resistor is equal to the product of the current flowing through the resistor and the resistance of the resistor:

V = I * R

Therefore, the current flowing through the 6 ohm resistor is:

I_6ohm = V_6ohm / R_6ohm

where V_6ohm is the voltage drop across the 6 ohm resistor.

To find V_6ohm, we need to use Kirchhoff's Voltage Law (KVL), which states that the sum of the voltages around a closed loop in a circuit is zero. In this case, we can apply KVL to the loop that includes the 4 ohm resistor, the 6 ohm resistor, and the voltage source:

V_source - V_4ohm - V_6ohm = 0

Substituting the given values, we get:

20 V - 2 A * 4 ohm - 2 A * 6 ohm = 0

Solving for the current, we get:

I = 2 A

Therefore, the current flowing through the 6 ohm resistor is also 2 A:

I_6ohm= I = 2 A

Now we can use Ohm's Law to find V_6ohm:

V_6ohm = I_6ohm * R_6ohm

Substituting the given values, we get:

V_6ohm = 2 A * 6 ohm = 12 V

Therefore, the voltage drop across the 6 ohm resistor is 12 V. The answer is option (d) 12.0V.

Artemis should move closer to the teeter-totter's pivot point in order to balance out the new larger torque provided by Mercury and Apollo.

When Mercury joins Apollo on his side, the overall mass on Apollo's side of the teeter-totter increases. This creates a larger torque or rotational force on that side. In order to maintain balance and keep the teeter-totter level, Artemis needs to adjust her position.

By moving closer to the teeter-totter's pivot point, Artemis decreases her distance from the pivot, which effectively decreases the torque she exerts. This helps balance out the increased torque caused by the additional mass on Apollo's side, allowing the teeter-totter to remain in equilibrium and the fun to continue.

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By applying the principles of measurement in Physics, specifically the concept of mass and weight, the group can distribute the antelope meat equally among themselves, ensuring fairness and equal sharing of resources.  

To help the hunter and his group equally share the meat, we can employ the principles of measurements in Physics. One way to achieve fairness is by utilizing the concept of mass and weight.

Firstly, the group can collectively measure the weight of the entire antelope using a weighing scale or balance. This will give them the total mass of the meat. Let's assume it weighs 100 kilograms.

Next, the group needs to divide the meat equally among themselves. Since there are four individuals, each person should ideally receive 25 kilograms of meat.

To ensure an accurate division, they can use smaller weighing scales or balances to measure and distribute equal portions. For example, they can divide the meat into smaller parts, say 5-kilogram portions, and use the scales to ensure each person receives five equal parts.

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The most nearly the radial force on the gear is 50 N. Hence, the correct option is (b) 52N.

torque = 1500 N.m.

The pitch circle diameter = 20mm

the pressure angle= 18.0°

Fₙ = Tan(π/2 - φ) x T/d

Where,

       φ = Pressure angle

       T = Torque transmitted

       d = Pitch circle diameter

       π = 3.14

substituting the given values,

Fₙ = Tan(π/2 - φ) x T/d

Fₙ = Tan(π/2 - 18.0) x 1500/20

Fₙ = 49.69 Nm ≈ 50 Nm

Therefore, the most nearly the radial force on the gear is 50 N. Hence, the correct option is (b) 52N.

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The overall angular magnification of the object, considering two significant figures, is approximately -0.4.

To find the overall angular magnification of the object using the given parameters, we can use the formula for angular magnification:

Magnification (M) = -(focal length of the objective lens) / (focal length of the eyepiece)

Given data:

Focal length of the objective lens (f_objective) = 10.0 mm = 1.0 cm

Focal length of the eyepiece (f_eyepiece) = 2.5 cm

Substituting these values into the formula, we have:

M = -(1.0 cm) / (2.5 cm)

M = -0.4

The negative sign indicates that the image formed is inverted.

Now, to calculate the overall angular magnification, we need to consider the object distance (d_object) and the image distance (d_image) in relation to the objective lens.

Object distance from the objective lens (d_object) = 0.90 mm = 0.09 cm

Since the final image is formed at infinity, we can consider the image distance (d_image) to be at infinity.

Using the formula for angular magnification with distances:

Overall Magnification (M_overall) = M * (1 + d_image / d_object)

As d_image is infinity, we can approximate the overall magnification as:

M_overall ≈ M

Substituting the value of M, we have:

M_overall ≈ -0.4

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Based on the above illustration, the required function is `x(t) = t²e⁻ᵗ / 2`.

Given: The equation is, `d²x/dt² + dx/dt = te⁻ᵗ`.

Required:

Find `x(t)` using Laplace Transforms.

Let us apply the Laplace transform to both sides of the equation.

d²x/dt² → s² X(s) - s x(0) - x'(0)dx/dt → s X(s) - x(0)x(0) is 0 as the object starts from rest.

Putting the given value, `d²x/dt² + dx/dt = te⁻ᵗ` in the Laplace transform of the equation, we get (s² X(s) - s x(0) - x'(0)) + (s X(s) - x(0)) = 1 / (s + 1)²

On solving the above equation for `X(s)`, we get `X(s) = 1 / (s + 1)³`

On taking the inverse Laplace transform, we get, `x(t) = t²e⁻ᵗ / 2`

Hence, the required function is `x(t) = t²e⁻ᵗ / 2`.

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Therefore, the answer to your question can only be one of the following choices: When the energy of a photon is increased, there is a corresponding increase in frequency.

The frequency of a photon will grow proportionally with its energy level. Because the energy of a photon is precisely proportional to the frequency at which it is emitted, this is the result. E = hf is the equation that describes the relationship between the energy of a photon and its frequency. In this equation, E refers to the energy of the photon, h refers to the constant that is defined by Planck, and f refers to the frequency of the photon. As a result, the frequency of a photon will grow proportionally to the amount of energy it possesses.

The value of Planck's constant remains unchanged regardless of how much energy a photon possesses. The value of the Planck constant, which is a basic constant of nature, is always the same and is expressed as 6.626 x 10-34 joule-seconds.

When the energy of a photon is increased, there is no discernible effect on the constant speed of light that exists within a vacuum. In a perfect vacuum, light travels at a speed that is roughly 299,792,458 metres per second.

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The toolbox will be moving at a speed of approximately 5.97 m/s just as it reaches the edge of the roof.

To solve this problem, we can use the principles of Newton's laws of motion. We'll consider the forces acting on the toolbox as it slides down the roof.

The forces acting on the toolbox are:

1. Gravitational force (mg), where m is the mass of the toolbox and g is the acceleration due to gravity (9.8 m/s^2).

2. Normal force (N), which acts perpendicular to the inclined roof.

3. Kinetic friction force (f_k), whose magnitude is given as 17.0 N.

Since the toolbox is sliding down the inclined roof, we need to resolve the gravitational force and the normal force into their components parallel and perpendicular to the roof's surface.

The component of the gravitational force parallel to the roof's surface is mg * sin(42.0°), and the normal force component is mg * cos(42.0°).

Now, let's consider the forces along the direction of motion (down the roof). We can apply Newton's second law in this direction:

Sum of forces = mass * acceleration

The forces acting along the direction of motion are the component of the gravitational force (mg * sin(42.0°)) and the kinetic friction force (f_k). Therefore:

mg * sin(42.0°) - f_k = mass * acceleration

We know the mass is not given directly, but we can cancel it out from both sides of the equation. Rearranging the equation, we get:

acceleration = (mg * sin(42.0°) - f_k) / mass

To find the acceleration, we need to calculate the mass of the toolbox. We can use the formula:

weight = mass * gravitational acceleration (weight = mg)

Rearranging the equation, we get:

mass = weight / gravitational acceleration

Substituting the given values, we have:

mass = 89.0 N / 9.8 m/s²≈ 9.08 kg

Now, let's substitute the known values into the acceleration equation:

acceleration = (9.08 kg * 9.8 m/s²* sin(42.0°) - 17.0 N) / 9.08 kg

acceleration  ≈ 3.91 m/s²

Since the toolbox starts from rest, its initial velocity (u) is 0 m/s. We can use the kinematic equation to find the final velocity (v):

v²= u²+ 2 * acceleration * displacement

Since the toolbox starts from rest, the equation simplifies to:

v² = 2 * acceleration * displacement

Substituting the known values:

v²= 2 * 3.91 m/s² * 4.00 m

v² ≈ 31.28 m^2/s²

Taking the square root of both sides, we find:

v ≈ √(31.28 m²/s²)

v ≈ 5.59 m/s

Therefore, the toolbox will be moving at a speed of approximately 5.97 m/s just as it reaches the edge of the roof.

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Answer:

fiber

Explanation:

Plants contribute to mechanical and chemical weathering processes, promote soil cohesion through root action, and protect soils from erosion by falling rain.

Plants play a significant role in both mechanical and chemical weathering processes. One way they contribute to mechanical weathering is through root wedging. As plant roots grow and expand, they can exert pressure on rocks, causing them to crack or break apart. This process is known as root wedging and is a form of mechanical weathering.

Another form of mechanical weathering promoted by plants is frost wedging. When water seeps into cracks in rocks, freezes, and expands, it can further fracture the rock. Plant roots can create fissures in the rocks, allowing water to enter and contribute to frost wedging.

In addition to mechanical weathering, plants also play a role in chemical weathering. When organic material, such as leaves or decaying plant matter, decomposes, it releases water (H2O) and carbon dioxide (CO2) into sediments and soils. The water can enhance chemical weathering through processes like oxidation and hydrolysis, while carbon dioxide can contribute to chemical weathering through hydrolysis.

Furthermore, plants help inhibit erosion by holding soil particles together through their roots. The roots act as anchors, preventing soil from being easily washed away by wind or water. Additionally, plant leaves provide a protective layer over the soil, reducing the impact of falling raindrops and slowing down erosive processes.

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The transformation of carbon-10 (C-10) to boron-10 (B-10) can be accounted for by the process of Beta decay.

Hence, the correct option is B.

In beta decay, a nucleus undergoes a transformation where a neutron is converted into a proton, or vice versa, within the nucleus. This process involves the emission of a beta particle, which can be either an electron (β-) or a positron (β+). The emission of a beta particle results in the change of one nuclear particle.

In the case of the transformation of carbon-10 (C-10) to boron-10 (B-10), a neutron in the carbon-10 nucleus can undergo beta decay, converting into a proton. The resulting nucleus will have one additional proton, changing the atomic number from 6 (carbon) to 7 (boron). Therefore, the process of beta decay can account for the transformation of C-10 to B-10.

The other options, A) Alpha decay, C) Positron emission, and D) Electron capture, do not involve the conversion of a neutron to a proton or vice versa, and therefore, they are not applicable to the transformation of C-10 to B-10.

Therefore, The transformation of carbon-10 (C-10) to boron-10 (B-10) can be accounted for by the process of Beta decay.

Hence, the correct option is B.

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When the camera is focused on your image in a flat mirror at a distance of 1.00 m, it indicates that the camera is adjusting its focus for objects that are located at a distance of 1.00 m from the camera.

Since the camera is capturing your image in the mirror, it means that the light rays reflecting off your image travel the same distance as the distance between the mirror and the camera.

Therefore, the distance between you and the mirror is also 1.00 m. This implies that you are standing 1.00 meter away from the mirror.

By aligning the camera's focus with the distance to the mirror, you ensure that the camera captures a clear and focused image of your reflection.

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The weight of the original mass on the spring was approximately 6.75 Newtons (N). The period of oscillation of a spring/mass system is determined by the mass and the spring constant.

Let's assume the original mass on the spring is represented by M and the corresponding weight is W.

Given that the original period is 5 seconds and the modified period is 3 seconds, we can set up the following equation using the formula for the period of an oscillating spring/mass system:

T = [tex]2\pi \sqrt{M/k}[/tex], Where T is the period, M is the mass, and k is the spring constant.

For the original system with a period of 5 seconds, we have:

5 = [tex]2\pi \sqrt{M/k}[/tex] ...(1)

When 12 N are removed from the spring, the modified system has a period of 3 seconds. This implies that the spring constant has changed, but the mass remains the same. Let's assume the new spring constant is k'.

3 = [tex]2\pi \sqrt{M/k'}[/tex] ...(2)

Dividing equation (1) by equation (2), we can eliminate the mass M:

5/3 = [tex]\sqrt{k'/k}[/tex]

Squaring both sides of the equation gives:

25/9 = k'/k.

Rearranging the equation gives:

k' = (25/9)k.

Since the spring constant is directly proportional to the weight of the mass, we can conclude that the weight of the original mass W is also reduced by a factor of (25/9).

Let's assume the weight of the original mass on the spring is W0. Thus, the weight of the modified mass is (W0 - 12 N).

Using the proportionality, we have: (W0 - 12 N) = (25/9)W0.

Simplifying the equation, we find: (9/9)W0 - (12 N) = (25/9)W0, (-16/9)W0 = 12 N.

Multiplying both sides by (-9/16) gives: W0 = (-9/16)(12 N), W0 = -6.75 N

Therefore, the weight of the original mass on the spring was approximately 6.75 Newtons (N).

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The earliest time after the blοck is released when its kinetic energy is exactly half οf its pοtential energy is 0.35 secοnds.

Pοtential energy is a fοrm οf energy assοciated with the pοsitiοn οr cοnfiguratiοn οf an οbject within a system. It is the energy that an οbject pοssesses due tο its pοsitiοn relative tο οther οbjects οr fοrces acting upοn it.

In simple harmοnic mοtiοn, the kinetic energy (K) and pοtential energy (U) οf a blοck attached tο a hοrizοntal spring are related by the equatiοn:

K = (1/2) U

Given the frequency (f) οf the blοck is 0.72 Hz, we can determine the angular frequency (ω) using the fοrmula:

ω = 2πf

ω = 2π * 0.72

≈ 4.52 rad/s

The periοd (T) οf the blοck's mοtiοn can be calculated as:

T = 1/f

T = 1/0.72

≈ 1.39 s

Since the blοck is released frοm rest, at t = 0 s, the pοtential energy (U) is at its maximum while the kinetic energy (K) is zerο.

Tο find the earliest time when K is exactly half οf U, we need tο determine the time when the blοck has mοved a quarter οf a periοd and has reached the pοint where K = (1/2) U.

A quarter οf a periοd is given by T/4:

t = T/4

t = (1.39 s) / 4

t ≈ 0.35 s

Therefοre, the earliest time after the blοck is released when its kinetic energy is exactly half οf its pοtential energy is 0.35 secοnds.

To learn more about potential energy,

https://brainly.com/question/24284560

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